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mathematics
|
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 56 with him, what was the average amount with the group before his joining the group?
|
[
"s.13",
"s.12",
"s.15",
"s.22",
"s.14"
] |
Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 56. So, the amount with remaining 6 people = 140 - 56 = Rs. 84
The average amount with them = 84/6 = Rs.14.
Answer:E
The answer is: E
|
E
|
mathematics
|
George baked a total of 150 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
|
[
"5",
"6",
"4",
"3",
"2"
] |
3/5 of the 150 pizzas cooked on Saturday = 90 pizzas
3/5 of the remaining pizzas on Sunday = 36 pizzas
We're left with (150-90-36) =24 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
8 7 6 2 1 =24
W =6
B
The answer is: B
|
B
|
mathematics
|
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 30%?
|
[
"1/2",
"2/6",
"3/6",
"9/6",
"15/2"
] |
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 180% of Re. 1 = Rs. 9/5
For Rs. 9/5 , toffees sold = 6.
For Re. 1, toffees sold = 9 x 5 /6 =15/2.
Answer E
The answer is: E
|
E
|
mathematics
|
A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
|
[
"66 sec",
"46 sec",
"48 sec",
"65 sec",
"64 sec"
] |
D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
The answer is: C
|
C
|
mathematics
|
A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ?
|
[
"7.5km/hr",
"3.5km/hr",
"9km/hr",
"4km/hr",
"5km/hr"
] |
given upstream(u) =5km/hr
down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C)
The answer is: C
|
C
|
mathematics
|
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
|
[
"299",
"277",
"999",
"255",
"245"
] |
a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer: C
The answer is: C
|
C
|
mathematics
|
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/14 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
|
[
"21",
"35",
"39",
"42",
"65"
] |
The total number of the people in the room must be a multiple of both 7 and 14 (in order 3/7 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 14, which is 98.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 98 people in the room.
Therefore there are 3/7*98=42 people in the room under the age of 21.
Answer: D.
The answer is: D
|
D
|
mathematics
|
At a certain conference, 62% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 20% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
|
[
"18.0%",
"62.0%",
"79.2%",
"77.5%",
"82.0%"
] |
Refer to the table in the attachment:
Let y= No. of members who have paid in Full
20 % members paid in full and did not register in advance = 0.2y
62 % registerd in advance and paid in full.
So if total No. of members = 100, then 62 members paid Full and registered in advance.
Hence total members who paid full amount = 0.2y + 62 =y
0.8y =62
Hence y = 77.5
i.e. 77.5 out of 100 or 77.5 %
Ans. D
The answer is: D
|
D
|
mathematics
|
A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:?
|
[
"40",
"60",
"80",
"67",
"30"
] |
Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: C
The answer is: C
|
C
|
mathematics
|
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 28-inch flat-screen television than a square 25 -inch flat-screen television?
|
[
"79.5",
"89.3",
"85.5",
"75.4",
"72.5"
] |
If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 28-inch flat-screen television
The diagonal (hypotenuse) = 28
So, we can apply the Pythagorean Theorem to get x² + x² = 28²
Simplify: 2x² = 28²
Divide both sides by 2 to get: x² = 28²/2
Since the area of the square = x², we can see that the area of this square is 28²/2
square 25-inch flat-screen television
The diagonal (hypotenuse) = 25
So, we can apply the Pythagorean Theorem to get x² + x² = 25²
Simplify: 2x² = 25²
Divide both sides by 2 to get: x² = 25²/2
Since the area of the square = x², we can see that the area of this square is 25²/2
DIFFERENCE IN AREAS =28²/2-25²/2
= (28²- 25²)/2 = (784-625)/2 =159/2=79.5
A
The answer is: A
|
A
|
mathematics
|
The bankers discount of a certain sum of money is Rs. 18 and the true discount on the same sum for the same time is Rs. 15. The sum due is:
|
[
"89",
"90",
"91",
"92",
"93"
] |
Sum = (B.D*T.D)/(B.D-T.D)
(18*15)/18-15;
90
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Find the value of k for which there are infinite solutions for the given set of equations.
5x + 2y = k and 10x + 4y = 3
|
[
"3/0",
"3/2",
"3/1",
"3/8",
"3/4"
] |
For the two sets of equation to have infinite solutions, we have 510=24=k3510=24=k3. Hence, k = 3/2
Answer: B
The answer is: B
|
B
|
mathematics
|
A 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
|
[
"20",
"12",
"13",
"14",
"16"
] |
Amount of salt = 8.0
Assume x gallons of water are added.
8.0 / 80 + x = 8/100
800 = 8x + 640
8x = 160
x = 20
Correct Option: A
The answer is: A
|
A
|
mathematics
|
John and Tony began business with Rs.12000 and Rs.14000 after 8 months, John withdraws Rs.2000 and Tony withdraws Rs.4000. At the end of the year, their profits amounted to Rs.4500 find the share of Tony.
|
[
"2375",
"2325",
"2300",
"3375",
"3300"
] |
(12*8 + 10*4):(14*8 + 10*4)
17:19
19/36 * 4500 = 2375. Answer: A
The answer is: A
|
A
|
mathematics
|
If $800 is deposited into a savings account at an annual interest rate of 3% that compounds monthly, what is the value of the investment after 5 years?
|
[
"$950.00",
"$929.29",
"$973.25",
"$100.25",
"$110.00"
] |
Using CI Formula:
A=P(1+r/n)^n*t
A=800(1+3/5)^3*5
A=929.29
The answer is: A
|
A
|
mathematics
|
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively, who is the most popular student?
|
[
"Johanna",
"Jamal",
"Brianna",
"Dyson",
"They have equal popularity"
] |
Distinct prime factors of 300 (Johanna) : 3, 2 5
Distinct prime factors of 400 (Jamal): 2 and 5.
Distinct prime factors of 150 (Brianna): 2,3, and 5
Distinct prime factors of 420 (Dyson): 2,3,5 and 7.
So most popular student - Dyson
Answer D
The answer is: D
|
D
|
mathematics
|
If x>0, y>0, and |x| > |y|, which of the following must be true?
|
[
"x > y",
"y^2 > x^2",
"x^3 > y^2",
"–x < y",
"x < –y"
] |
Correct Answer: (E)
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true.
The answer is: A
|
A
|
mathematics
|
A and B start a business, with A investing the total capital of Rs.500000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.15000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
|
[
"A)590280",
"B)590100",
"C)591900",
"D)590000",
"E)927000"
] |
Interest received by A from B = 10% of half of Rs.500000 = 10% * 250000 = 25000.
Amount received by A per annum for being a working partner = 15000 * 12 = Rs.180000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (25000 + 180000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(25000 + 180000 + P) = 2(P)
P = 205000
Total profit = 2P + 180000
= 2*205000 + 180000 = 590000
Answer:D
The answer is: D
|
D
|
mathematics
|
Find the missing figures :
?% of 30 = 2.125
|
[
"8.5",
"6.5",
"8.07",
"7.08",
"4.05"
] |
(i) Let x% of 30 = 2.125. Then , (x/100)*30 = 2.125
X = (2.125 * 100/30) = 7.08
Answer is D.
The answer is: D
|
D
|
mathematics
|
A bag holds 4 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
|
[
"1/10",
"1/5",
"3/10",
"2/7",
"1/2"
] |
probability of selecting first red marble = 4/7
probability of selecting second red marble without replacement = 3/6
final probability = 4/7 * 3/6 = 2/7
The correct answer is D.
The answer is: D
|
D
|
mathematics
|
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
|
[
"6 2/5%",
"6 2/7%",
"6 2/3%",
"6 5/3%",
"6 7/3%"
] |
10 CP = 12 SP
12 --- 2 CP loss
100 --- ?
=> 16 2/3%
Answer: C
The answer is: C
|
C
|
mathematics
|
A coin is tossed 3 times. Find out the number of possible outcomes.
|
[
"None of these",
"8",
"2",
"1",
"3"
] |
Explanation :
When a coin is tossed once, there are two possible outcomes - Head(H) and Tale(T)
Hence, when a coin is tossed 3 times, the number of possible outcomes
= 2 x 2 x 2 = 8
(The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT ) Answer : Option B
The answer is: B
|
B
|
mathematics
|
A certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 230 pounds?
|
[
"7",
"8",
"9",
"10",
"12"
] |
Lets assume there are 2X people.
Half of them have average weight of 180 and other half has 230.
Maximum Weight is = 2500
So 180*X + 230*X = 2500
=> 410X = 2500
=> X is approximately equal to 6.
So total people is 2*6 = 12
Answer E.
The answer is: E
|
E
|
mathematics
|
A bus takes 4 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?
|
[
"50 Kmph",
"90 Kmph",
"95.9 Kmph",
"95.4 Kmph",
"90.5 Kmph"
] |
Time = 4
Distance = 480
4/3 of 4 hours = 4 * 4/3 = 5.3 Hours
Required speed = 480/5.3 = 90.5 Kmph
E
The answer is: E
|
E
|
mathematics
|
Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 13 from the product of their ages a year from today. What is their age today?
|
[
"2.",
"6.",
"5.",
"7.",
"9."
] |
ad = (a+1) (d+1) -13
0= a+d-12
a+d = 12
a=d (as they are twin brothers)
a=d=6
B is the answer
The answer is: B
|
B
|
mathematics
|
A cubical block of metal weighs 4 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
|
[
"48",
"32",
"24",
"18",
"12"
] |
For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 4 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 4 pounds = 32 pounds
So answer is B
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
4 * 8 = 32
So answer is B
The answer is: B
|
B
|
mathematics
|
If x and d are integers and 2x–d= 11, then 4x+ d CANNOT be
|
[
"–5",
"1",
"13",
"17",
"551"
] |
2x-d=11....d=2x-11
4x+d=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D
The answer is: D
|
D
|
mathematics
|
x<3y<0 which of the following is the greatest?
|
[
"x+2y",
"-2x+y",
"3x-y",
"-(2x+2y)",
"x-y"
] |
Plugging in -1 for both x and y we get
A. x+2y =-3
B. -2x+y =1
C. 3x-y =-2
D. -(2x+2y) =4
E. x-y =0
Answer: D
The answer is: D
|
D
|
mathematics
|
What is the units digit of (493) (915) (381) (756) (22)
|
[
"0",
"1",
"4",
"5",
"6"
] |
Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.
I also tried it using the calculator and the answer is 1.
IMO B.
The answer is: B
|
B
|
mathematics
|
Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
|
[
"157",
"213",
"221",
"223",
"226"
] |
For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A
The answer is: A
|
A
|
mathematics
|
How many words can be formed by using all letters of the word “PACKHORSE”
|
[
"40320",
"44000",
"42340",
"56000",
"14000"
] |
The word PACKHORSE contains 8 different letters.
Required number of words = 8p8 = 8! = (8x7x6x5x4x3x2x1) = 40320.
Answer A.
The answer is: A
|
A
|
mathematics
|
A car covers a certain distance at aspeed of 60 kmph in 4 hours. To cover the same distance in 2hr, it must travel at a speed of?
|
[
"567 km/hr",
"678 km/hr",
"782 km/hr",
"120 km/hr",
"720 km/hr"
] |
Distance = (60 x 4) = 240 km.
Speed = Distance/Time
Speed = 240/2 = 120 kmph
Answer : D
The answer is: D
|
D
|
mathematics
|
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
|
[
"200 meters",
"225 meters",
"245 meters",
"250 meters",
"300 meters"
] |
Given, Length of the train = 130 meters
Speed of the train = 45 km/hr = 45 * 518 m/sec = 252 m/sec
Time = 30 secs
Let the length of the bridge be x meters .
The distance travelled by the train while crossing the bridge will be sum of the length of train and Length of the bridge = (x+130) meters
so , 252 = x+13030
= 30*25 = 2x + 260
= 750 - 260 = 2x
= 490 = 2x
=x = 245 meters. ANSWER C
The answer is: C
|
C
|
mathematics
|
The value of land increases by x% during June and decreases by y% during July. If the value of the land is the same at the end of July as at the beginning of June, what is y in terms of x?
|
[
"200x/(100+2x)",
"100x/(100+x)",
"x(2+x)/(1+x)2",
"x(200+x)/10000",
"2x/x+2x"
] |
The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
B
The answer is: B
|
B
|
mathematics
|
A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match
|
[
"36",
"37",
"38",
"39",
"40"
] |
Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Answer: Option D
The answer is: D
|
D
|
mathematics
|
If the price of a TV is first decreased by 20% and then increased by 40%, then the net change in the price will be :
|
[
"4% increase",
"12% increase",
"10% decrease",
"6% increase",
"None of these"
] |
Explanation :
Solution: let the original price be Rs. 100.
New final price = 140% of(80% of 100) =Rs. 140/100 * 80/100 * 100 = Rs. 112.
.'. Increase = 12%
Answer : B
The answer is: B
|
B
|
mathematics
|
If 4x + y = 12 and −x + y = 44, then what is the value of 3x + 2y?
|
[
"1/7",
"3",
"15",
"52/7",
"56"
] |
4x + y = 12
−x + y = 44
Adding both the equations --> 3x + 2y = 56
Answer: E
The answer is: E
|
E
|
mathematics
|
A shopkeeper sells 300 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
|
[
"12",
"27",
"29",
"50",
"65"
] |
SP per metre = 18000/300 = Rs. 60 Loss per metre = Rs. 5 CP per metre = 60 + 5 = Rs. 65.Answer: E
The answer is: E
|
E
|
mathematics
|
Exactly 3/5 of the people in the room are under the age of 21, and exactly 5/13 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
|
[
"21",
"35",
"39",
"60",
"42"
] |
The total number of the people in the room must be a multiple of both 5 and 14 (in order 3/5 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 5 and 14, which is 70.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.
Therefore there are 3/5*70=42 people in the room under the age of 21.
Answer: E.
The answer is: E
|
E
|
mathematics
|
The measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
|
[
"50,000",
"40,000",
"45,000",
"50,000",
"60,000"
] |
The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 100*100*1 = 10,000 cubic centimeters.
So, approximate maximum possible difference is 15,000 + 15,000 + 10,000 = 40,000 cubic centimeters.
Answer: B.
The answer is: B
|
B
|
mathematics
|
By investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is:
|
[
"Rs. 5640",
"Rs. 5760",
"Rs. 7500",
"Rs. 8600",
"Rs. 9600"
] |
To earn Rs. 50/3 , investment = Rs. 64.
To earn Rs. 1500, investment = Rs.64 x 3/50x 1500 = Rs. 5760.
ANSWER :B
The answer is: B
|
B
|
mathematics
|
When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born?
|
[
"10 years",
"11 years",
"12 years",
"13 years",
"14 years"
] |
his brother is x years old
thn his father is 6+32=38 when rajeev was born
and his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born
and his sister is 25 year younger thn his mother
so rajeev's sister was 10 years old when rajeev was born.
ANSWER:A
The answer is: A
|
A
|
mathematics
|
The sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?
|
[
"145 cm",
"135 cm",
"121 cm",
"141 cm",
"151 cm"
] |
Perimeter of the sector = length of the arc + 2(radius)
= (270/360 * 2 * 22/7 * 21) + 2(21)
= 99 + 42 = 141 cm
Answer: D
The answer is: D
|
D
|
mathematics
|
Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
|
[
"10",
"30",
"50",
"80",
"100"
] |
Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 10
Answer: Option A
The answer is: A
|
A
|
mathematics
|
If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $19,000 is invested at the same interest rate, what is the interest from the investment?
|
[
"$700",
"$750",
"$800",
"$950",
"$900"
] |
-> 250/5,000=5% and 19,000*5%=950.
Thus, D is the answer.
The answer is: D
|
D
|
mathematics
|
A certain sum amounts to Rs.640 in 4 years and Rs.760 in 6 years. Find the rate % per annum?
|
[
"9%",
"5%",
"3%",
"1%",
"8%"
] |
4 --- 640
6 --- 760
--------------
2 --- 120
N = 1 I = 60 R = ?
P = 640 - 240 = 400
60 = (400*1*R)/100
R = 15%
Answer: E
The answer is: E
|
E
|
mathematics
|
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
|
[
"256",
"375",
"287",
"255",
"123"
] |
CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
The answer is: B
|
B
|
mathematics
|
Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x +3 = 0?
|
[
"28.3",
"1.45",
"2.78",
"6.84",
"7.23"
] |
a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -9/1 = -9
ab = 3/1 = 3
Hence a/b + b/a = [(-9)2 - 2(3)]/3 = 56/4 = 28.3.
A)
The answer is: A
|
A
|
mathematics
|
The average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
|
[
"76",
"79",
"85",
"87",
"89"
] |
Explanation:
Average = total runs / no.of innings = 35
So, total = Average x no.of innings = 35 x 10 = 350.
Now increase in avg = 4runs. So, new avg = 35+4 = 39runs
Total runs = new avg x new no. of innings = 39 x 11 = 429
Runs made in the 11th inning = 429 - 350 = 79 Answer: B
The answer is: B
|
B
|
mathematics
|
A certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale?
|
[
"20",
"36",
"48",
"60",
"84"
] |
First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that P increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, P will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
The answer is: C
|
C
|
mathematics
|
A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
|
[
"35 Days",
"36.5 Days",
"37 Days",
"37.5 Days",
"38 Days"
] |
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Answer is D.
The answer is: D
|
D
|
mathematics
|
Two trains are running in opposite directions with the same speed. If the length of each train is 130 m and they cross each other in 12 sec, then the speed of each train is?
|
[
"30",
"35",
"36",
"37",
"39"
] |
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (130 + 130)/12 => x = 10.83
Speed of each train = 10 m/sec.
= 10.83 * 18/5 =- 39 km/hr.
Answer: Option E
The answer is: E
|
E
|
mathematics
|
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 25 miles per gallon, and from Town B to Town C, the car averaged 30 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
|
[
"24",
"25",
"23",
"22",
"26.5"
] |
step 1) took LCM of 25 and 30.. came as 150.
step 2) 150 distance between B to C... do 150/30 hence 5 gallons used
step 3) twice distance.. hence 150*2= 300... do as above.. 300/25= 12 gallons used
step 4) total gallons.. 5+12= 17 gallons
step ) total miles= 150+300= 450 miles
hence.. average of whole journey = 450/17 which comes to 26.5
Answer : E
The answer is: E
|
E
|
mathematics
|
A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
|
[
"8",
"7",
"5",
"2",
"1"
] |
70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
Answer: D
The answer is: D
|
D
|
mathematics
|
Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
|
[
"12,7",
"12,9",
"10,5",
"11,6",
"15,4"
] |
x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER A
The answer is: A
|
A
|
mathematics
|
Pointing to a girl in the photograph, Amar said, "Her mother's brother is the only son of my mother's father." How is the girl's mother related to Amar ?
|
[
"Mother",
"Sister",
"Aunt",
"Grandmother",
"Brother"
] |
Explanation:
Only son of Amar's mother's father — Amar's maternal uncle.
So, the girl's maternal uncle is Arnar's maternal uncle. Thus, the girl's mother is Amar's aunt.
Answer: C
The answer is: C
|
C
|
mathematics
|
5358 x 51 = ?
|
[
"273762",
"283758",
"273298",
"273258",
"277382"
] |
D
273258
5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
The answer is: D
|
D
|
mathematics
|
John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
|
[
"50",
"58",
"60",
"65",
"70"
] |
(x+x1+...x14)/15 = 40
50
Option A
The answer is: A
|
A
|
mathematics
|
Ajay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?
|
[
"A, B",
"A, C",
"B, C",
"A, D",
"None of these"
] |
Time taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.
Therefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively.
In 30 minutes, how many times do they toll together?
|
[
"12",
"14",
"15",
"16",
"17"
] |
Explanation :
Here's the simple solution :
Take lcm of 2,4,6,8,10,12 seconds
The outcome is 120seconds.
Convert it into minutes = 120 / 60
= 2 minutes
In 30mins it will rings 15times together
But ,In 0th second all bells rings together
Hence Total number of bell rings is = 15 + 1
= 16
Hence (D) is the correct answer.
Answer : D
The answer is: D
|
D
|
mathematics
|
L = {3, 4, 5, 5, 6, 7}
M = {2, 2, 2, 8, 8, 8}
N = {15, 15, 15, 15, 15, 15}
Rank those three sets from least standard D eviation to greatest standard deviation.
|
[
"L, M, N",
"M, L, N",
"M, N, L",
"RANKING=N, L, M",
"N, M,"
] |
Square of Standard deviation is sum of squares of deviation from the mean divided by the number of terms.
If deviation from the mean is higher for the same number of elements, standard deviation will be higher.
L = {3, 4, 5, 5, 6, 7}
Mean is 5 and deviation of 2 elements from mean is 0, of 2 elements is 1 and of 2 elements is 2.
M = {2, 2, 2, 8, 8, 8}
Mean is 5 and deviation of all elements from the mean is 3. So SD here will be higher than SD of L.
N = {15, 15, 15, 15, 15, 15}
Mean is 15 here and all elements have 0 deviation from mean so SD = 0 here. This is the minimum possible SD.
Answer N, L, M
Answer (D)
The answer is: D
|
D
|
mathematics
|
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?
|
[
"50",
"100",
"200",
"1,000",
"2,000"
] |
y = 50% of 50% 0f x
= x/4
and
y/100 of x = 100
y /100 *4y =100
y = 50
and x= 200
Answer - C
The answer is: C
|
C
|
mathematics
|
A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,
also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs
|
[
"6root(3)",
"12root(3)",
"9root(3)",
"18root(3)",
"12root(3)"
] |
Lets take, QR=PS= a m and RS=b m, So, PQ=3b m
now if are of a square is 36 sqm, then perimeter is 24
now perimeter of the inscribed quadrilateral is 4b+2a= 24
so, 2b+a=12
from this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)
Now, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}
Here s= 12
now by trial and error method we can get the solution
appprox area is 18root(3)
ANSWER:D
The answer is: D
|
D
|
mathematics
|
The sum of three consecutive even numbers is 63. Find the middle number of the three?
|
[
"14",
"23",
"25",
"29",
"21"
] |
Middle no=63/3
=21
Ans E
The answer is: E
|
E
|
mathematics
|
A man can row downstream at the rate of 32 Kmph and upstream at 8 Kmph. Find the man’s rate in still water and rate of current?
|
[
"20 Kmph, 10 Kmph",
"12 Kmph, 22 Kmph",
"22 Kmph, 12 Kmph",
"20 Kmph, 12 Kmph",
"None of these"
] |
Explanation:
Rate of still water = 1/2 (down stream + upstream)
= 1/2 (32 + 8) = 20 Kmph
Rate of current = 1/2 (down stream - upstream)
= 1/2 (32 - 8)
= 1/2 (24)
= 12 kmph
Answer: Option D
The answer is: D
|
D
|
mathematics
|
There are, in a certain league, 8 teams, and each team face another team for a total of 12 times. How many games are played in the season?
|
[
"150",
"121",
"144",
"180",
"1200"
] |
By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 144
Option C.
The answer is: C
|
C
|
mathematics
|
Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 1 muffins remained. How many guests did Monica plan on?
|
[
"3.",
"4.",
"5.",
"6.",
"7."
] |
Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 1 = 5x + 2
6x - 5 = 5x + 2
x = 7
Answer: E
The answer is: E
|
E
|
mathematics
|
In how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together?
|
[
"A)10000",
"B)12100",
"C)14400",
"D)1097",
"E)2781"
] |
Treat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 5! * 5! = 120 * 120
= 14400.
Answer:C
The answer is: C
|
C
|
mathematics
|
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
|
[
"11",
"23",
"25",
"77",
"81"
] |
Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
The answer is: C
|
C
|
mathematics
|
PZQW : NXOU :: FISK :?
|
[
"EFPJ",
"FERI",
"DGQI",
"HKUM",
"HKUN"
] |
Difference of one alphabet on each side of proportion term. Answer is thus DGQI
ANSWER:C
The answer is: C
|
C
|
mathematics
|
A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?
|
[
"100",
"150",
"200",
"250",
"350"
] |
A+B+C = 900
A+C = 400
B+C = 750
--------------
A+B+2C = 1150
A+B+C = 900
----------------
C = 250
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Two sides of a triangle have length 5 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
|
[
"I, II, and III",
"I and II only",
"II and III only",
"I and III only",
"I only"
] |
Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
The answer is: A
|
A
|
mathematics
|
A car going at 40 miles per hour set out on an 90-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?
|
[
"45",
"50",
"53",
"55",
"90"
] |
Let Car A = car that starts at 9 AM
Car B = car that starts at 9:10 AM
Time for which car A travels at speed of 40 m per hour = 1.5 hours
Distance travelled by Car A = 40 *1.5 = 60 miles
Since Car B catches up Car A at 10:30 , time = 90 mins = 3/2 hour
Speed of Car B = 60/(3/2) = 90 miles per hour
Answer E
The answer is: E
|
E
|
mathematics
|
Of the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
|
[
"24",
"36",
"72",
"1",
"216"
] |
Assume: a,b,c is the digit and a,b,c not= 0
Thus a,b,c could be 1, 2, 3, 4, 5, 6, 7, 8, and 9
Count the possible way to get three digit number abc.
a = b, and c must be different from a, b
Thus, there are 3 possible ways of digit arrangement: aac, aca, caa
Case I: aac
=> (digit 1st) x (digit 2nd) x (digit 3rd)
=> 9 x 1 x 8 {pick any number from group = 9 possible ways} x {pick number the same as the first pick = 1 way} x {pick any number from the rest = 8 possible ways}
= 9 x 1 x 8 = 72 possible ways
Case II: aca
=> same as case I you have 72 possible ways
Case III: caa
=> same as case I you have 72 possible ways
total of this set of number = 72 + 72 + 72 = 216
E) is the answer
The answer is: E
|
E
|
mathematics
|
Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 95% water by weight. What is the new weight of the cucumbers, in pounds?
|
[
"2",
"20",
"92",
"96",
"98"
] |
Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 95% water and 5% of non-water, so now 1 pound of non-water composes 5% of cucucmbers, which means that the new weight of cucumbers is 1/0.05=20 pounds.
Answer: B.
The answer is: B
|
B
|
mathematics
|
In an examination it is required to get 30% of minimum marks to pass. A student got 170 marks and was declared failed by 10 marks difference. Then what is total marks:?
|
[
"550",
"500",
"600",
"700",
"None of these"
] |
Explanation:
30 % -------> 180 ( 30 * 6 = 180)
100% -------> 600 (100 * 6 = 600)
Answer: Option C
The answer is: C
|
C
|
mathematics
|
Find the length of the altitude of an equilateral triangle of side 3√3 cm.
|
[
"4.5cm",
"7.2cm",
"4.3cm",
"5.6cm",
"5.7cm"
] |
Area of the triangle = (√3/4) x (3√3)2 = 27√3. Let the height be h.
Then, (1/2) x 3√3 x h = (27√3/4) X(2/√3) = 4.5 cm.
Ans: A
The answer is: A
|
A
|
mathematics
|
Average expenditure of a person for the first 3 days of a week is Rs. 330 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
|
[
"350",
"370",
"390",
"430",
"None"
] |
Explanation:
Assumed mean = Rs. 330
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 330 + Rs. 40 = Rs. 370
Correct Option: B
The answer is: B
|
B
|
mathematics
|
Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740?
|
[
"Rs.1000",
"Rs.1550",
"Rs.1510",
"Rs.1500",
"None of these"
] |
Explanation:
1740 = P [1 + (5*16/5)/100]
P= 1500
Answer: Option D
The answer is: D
|
D
|
mathematics
|
In how many different number of ways 1 boys and 3 girls can sit on a bench?
|
[
"720",
"730",
"740",
"24",
"800"
] |
npn = n!
4p4 = 4 × 3 × 2 × 1 = 24
D
The answer is: D
|
D
|
mathematics
|
Four friends decided to go on a vacation to a hill station. During their vacation, they experienced 13 days of heavy snowfall. When it used to snow in the morning, the afternoon was clear and when it used to snow in the afternoon, the day was followed by a clear morning.
In total, they had eleven clear mornings and twelve clear afternoons. Is there a way you can calculate the number of days they spent in their vacation?
|
[
"16",
"21",
"18",
"19",
"25"
] |
C
18
Number of days with snow in morning and clear afternoon = A
Number of days with clear morning and snow in afternoon = B
Number of days with no snowfall in morning or afternoon = C
Now, number of days with snowfall = A + B = 13
Number of days with clear mornings = B + C = 11
Number of days with clear afternoons = A + C = 12
Adding these three equations, we get
2 * (A + B + C) = 36
Or, A + B + C = 18
Therefore, they spent eighteen days in total at their vacation.
The answer is: C
|
C
|
mathematics
|
A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back, how far is the place?
|
[
"24km",
"30km",
"48km",
"120km",
"15km"
] |
Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 25
2x+3x = 600
x = 120 km
Answer is D
The answer is: D
|
D
|
mathematics
|
Which of the following equations describes a line that is perpendicular to y = x/2 + 5?
|
[
"y = x − 5",
"y = −3 − 2x",
"y = 5x",
"y = 5x - 1",
"y = 1/x + 5"
] |
Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y = x/2 + 5 is 1/2 so the slope of a perpendicular line will be -2.
The answer is B.
The answer is: B
|
B
|
mathematics
|
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.180 only. Men’s wages are?
|
[
"6Rs",
"2Rs",
"4Rs",
"9Rs",
"12Rs"
] |
5M = xW = 8B
5M + xW + 8B ----- 180 Rs.
5M + 5M + 5M ----- 180 Rs.
15M ------ 180 Rs. => 1M = 12Rs.
Answer: E
The answer is: E
|
E
|
mathematics
|
Find the least number of five digits which is exactly divisible by 12, 15 and 18?
|
[
"10080",
"1080",
"10025",
"10050",
"10024"
] |
LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER A
The answer is: A
|
A
|
mathematics
|
Find the circumference of radius 7 cm.
|
[
"44",
"55",
"66",
"77",
"88"
] |
Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44 cm
ANSWER : A
The answer is: A
|
A
|
mathematics
|
What is the number of integers from 1 to 900 (inclusive) that are divisible by neither 11 nor by 35?
|
[
"884",
"890",
"892",
"910",
"945"
] |
Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)
In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2
Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 892
Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
C
The answer is: C
|
C
|
mathematics
|
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10 a.m.?
|
[
"5",
"6",
"7",
"8",
"10"
] |
Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour
Time duration from 8 am to 10 am = 2 hour
Hence they cross each other 10 times before 10 am
Answer is E
The answer is: E
|
E
|
mathematics
|
A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.
|
[
"360000;180000;270000",
"270000;180000;360000",
"180000;360000;270000",
"270000;360000;270000",
"None of them"
] |
Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,
(3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5
1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5
108x /(72x+6480000)=3/4 432x = 216x + 19440000
=216x = 19440000
=x=90000
Hence, A’s initial investment = 3x = Rs. 2,70,000;
B's initial investment = 2x = Rs. 1,80,000;
C's initial investment = 4x = Rs. 3,60,000.
Answer is B.
The answer is: B
|
B
|
mathematics
|
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
|
[
"11",
"444",
"420",
"287",
"221"
] |
1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420
Answer:C
The answer is: C
|
C
|
mathematics
|
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 48 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
|
[
"3%",
"5%",
"8%x",
"10%",
"12%"
] |
Bob's time = 600 secs.
His sis' time = 528 secs.
Percent increase needed = (600-528/600) * 100 = 72/600 * 100 = 12%. Ans (E).
The answer is: E
|
E
|
mathematics
|
A woman bought a pack of 36 eggs, but the seller told her that there were 3 rotten eggs in the pack. She forgot it and begun to prepare a recipe that needs 2 eggs. What is the probability that both choosen eggs will be rotten?
|
[
"1/210",
"2/210",
"3/210",
"1/119",
"2/119"
] |
There are 3 rotten eggs in a pack of 36. Thus the probability of picking 2 rotten eggs is: (3/36)(2/35) = 1/210. The correct answer is A.
The answer is: A
|
A
|
mathematics
|
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
|
[
"77.14 cm",
"47.14 cm",
"84.92 cm",
"94.94 cm",
"23.57 cm"
] |
Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
ANSWER:E
The answer is: E
|
E
|
mathematics
|
The president of a country and 6 other dignitaries are scheduled to sit in a row on the 7 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
|
[
"720",
"5",
"20",
"24",
"120"
] |
IMO A
Given that one chair is taken, i think the remaining 6 dignitaries can be arranged 6!. That is 6*5*4*3*2*1=720.
The answer is: A
|
A
|
mathematics
|
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 30 are on geology, and 100 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
|
[
"81",
"159",
"166",
"285",
"304"
] |
I solve it using the tough luck technique:
According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.
80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=100>80
Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books
What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.
We picked:
50 Botany Books
65 Zoology Books
30 Geology Books
Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!
Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick
79*2+1 books
Because, we could have picked the books in following order;
1st book picked: Physics
2nd book picked: Chemistry
3rd book picked: Physics
Thus, Total= 50+65+30+79*2+1=145+1+158=304
Ans:E
The answer is: E
|
E
|
mathematics
|
X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13970 ?
|
[
"3200",
"4064",
"3250",
"3825",
"3985"
] |
Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 13970 × 16/55 = Rs.4064.
Share of Z in the profit is Rs.4064.
Option B
The answer is: B
|
B
|
mathematics
|
What is the remainder when 1201 × 1202 ×1203 × 1207 is divided by 6?
|
[
"0",
"1",
"2",
"3",
"4"
] |
The remainders when dividing each number by six are: 1, 2, 3, and 1.
The product is 1*2*3*1 = 6
The remainder when dividing 6 by 6 is 0.
The answer is A.
The answer is: A
|
A
|
mathematics
|
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
|
[
"2",
"2/5525",
"2/5527",
"3",
"None"
] |
Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
Answer: Option 'B'
The answer is: B
|
B
|
mathematics
|
If x/5 - 6/x = 1/5, what are the values of 3x - 7?
|
[
"-22 and 11",
"8 and 24",
"17 and 21",
"12 and 29",
"17 and 29"
] |
I got the same thing A is the answer -22 or 11
The answer is: A
|
A
|
mathematics
|
The value of x + x(x*x*(in x)) when x = 2 is:
|
[
"10",
"16",
"18",
"36",
"64"
] |
x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Correct Answer:A)10
The answer is: A
|
A
|
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