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stringclasses 1
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mathematics
|
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
|
[
"20/68",
"20/63",
"20/69",
"20/64",
"20/62"
] |
Required probability = (β΅Cβ . β΄Cβ)/βΉCβ = (10 * 4)/126 = 20/63.Answer: B
The answer is: B
|
B
|
mathematics
|
A city had 800 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 2 years. If there were 800 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2006 to 2008?
|
[
"2800",
"4400",
"5400",
"6400",
"8800"
] |
The population will increase in the following order:
2000: 800
2002: 1600
2004: 3200
2006: 6400
2008: 12800
Difference between 2006 and 2008 = 6400
Option D
The answer is: D
|
D
|
mathematics
|
If 60% of a number is greater than 30% of 10 by 27, what is the number?
|
[
"50",
"100",
"30",
"75",
"5"
] |
Explanation:
60/100 * x - 30/100 * 10 = 27
60/100 * x - 3 = 27
60/100 * x = 30
x = 30 * 100 / 60
x = 50
Answer: Option A
The answer is: A
|
A
|
mathematics
|
As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y<2x
II. y>x
III. y>3
|
[
"I,II only",
"I only",
"II,III only",
"II only",
"III only"
] |
II. y>x --> since this week, James earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if James sold 3 bicycles this week then this week he earned 30+3*6=$48, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $30. So y must be more than 3;
I. y<2x --> is not always true.
Answer: C
The answer is: C
|
C
|
mathematics
|
Suraj has a certain average of runs for 14 innings. In the 15th innings he scores 140 runs thereby increasing his average by 8 runs. What is his average after the 15th innings?
|
[
"48",
"28",
"36",
"72",
"27"
] |
To improve his average by 8 runs per innings he has to contribute 14 x 8 = 112 runs for the previous 14 innings.
Thus, the average after the 15th innings
= 140 - 112 = 28.
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If 45-[28-{37-(15-*)}]= 56, then * is equal to:
|
[
"-29",
"-19",
"17",
"29",
"39"
] |
45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56
45-[28-37+15-*]=56 => 45[43-37-*]=56
45-[6-*]=56 => 45-6+*=56
39+*=56 => *=56-39
= 17
ANSWER:C
The answer is: C
|
C
|
mathematics
|
You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?
|
[
"3",
"4",
"5",
"6",
"7"
] |
If you grab 3 it might be all different. So take one extra to make sure you have two of the same.
So, take atleast 4
ANSWER:B
The answer is: B
|
B
|
mathematics
|
1!+2!+3!+4!+5!+.......100! is divided by 24. Find the remainder?
|
[
"5",
"7",
"9",
"11",
"14"
] |
By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... = 9
C
The answer is: C
|
C
|
mathematics
|
The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 15 percent, what was the annual interest rate last year?
|
[
"1%",
"1.1%",
"9.1%",
"10%",
"13.63%"
] |
15=1.1*x
X=13.63%
Answer E)
The answer is: E
|
E
|
mathematics
|
A walks at 10 kmph and 10 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
|
[
"100km",
"150km",
"50km",
"120km",
"200km"
] |
Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 10 hours.
x/10 - x/20 = 10
x = 200 km
Answer is E
The answer is: E
|
E
|
mathematics
|
A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :
|
[
"7 only",
"13 only",
"11 only",
"1001 only",
"1003 only"
] |
256256 = 256 x 1001; 678678 = 678 x 1001, etc.
So, any number of this form is divisible by 1001
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
|
[
"23",
"23.5",
"24",
"24.5",
"25"
] |
Let the present ages of sachin and rahul be 7x and 9x
sachin is younger than rahul in 7 years
So 9x-7x=7
2x=7
x=3.5
Sachin;s age= 7x= 7*3.5=24.5
answer :D
The answer is: D
|
D
|
mathematics
|
An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 7 businessmen, how many possible team submissions are possible?
|
[
"76",
"130",
"162",
"198",
"202"
] |
We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 7C2 = 84
2) 2 tech1 businessman: 4C2 x 7C1 =42
3) 3 tech0 businessmen: 4C3 = 4
Total: 84+42+4 = 130
Answer: B
The answer is: B
|
B
|
mathematics
|
In the formula V = 1/(3r)^4, if r is halved, then V is multiplied by
|
[
"64",
"8",
"16",
"1/8",
"1/64"
] |
Say r=2 => V1 = 1/1296
when r=1; V2 = 1/81
V2 = 16*V1.
Answer=C=16
The answer is: C
|
C
|
mathematics
|
Equal weights of two alloys containing tin, copper and lead in the ratio 1:2:3 and 4:5:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
|
[
"41:81:37",
"3:9:8",
"1:2:2",
"6:4: 9",
"4:8:9"
] |
Let the weight of the two alloys be w each
Required ratio =
(1w/6 +4w/12): ( 2w/6 +5w/12 ): (3w/6+3w/12)
= 6w/12 : 4w/12 : 9w/12
= 6:4: 9
ANSWER:D
The answer is: D
|
D
|
mathematics
|
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/6, then what is the value of abc/def ?
|
[
"27/4",
"27/8",
"3/4",
"3/8",
"1/4"
] |
Say a = 2. Then:
a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1/6 --> f = 12.
abc/def = (2*6*3)/(6*2*12) = 1/4.
Answer: E.
The answer is: E
|
E
|
mathematics
|
The average age of a husband and his wife was 29 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
|
[
"11",
"23",
"19",
"287",
"27"
] |
Explanation:
Sum of the present ages of husband, wife and child = (29 * 2 + 5 * 2) + 1 = 69 years.
Required average = (69/3) = 23 years.
Answer: B
The answer is: B
|
B
|
mathematics
|
The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
|
[
"16",
"18",
"13",
"20",
"12"
] |
1/2 * d (10 + 6)
= 640
d = 80
Answer: D
The answer is: D
|
D
|
mathematics
|
X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?
|
[
"60",
"77",
"26",
"66",
"281"
] |
We have M1 D1 = M2 D2
120X = (X - 20)180
=> 2X = (X - 20) 3 => 2X = 3X - 60
=> X = 60
Answer:A
The answer is: A
|
A
|
mathematics
|
Rs.8000 become Rs.9724 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
|
[
"6 YEARS",
"7",
"5",
"3",
"4"
] |
Explanation:
9724 = 8000(21/20)N
(21/20)4 = (21/20)N => N = 4
Answer: Option E
The answer is: E
|
E
|
mathematics
|
If a fair die is rolled two times, what is the probability that a 3 occurs on at least one roll?
|
[
"25/36",
"125/216",
"91/216",
"11/36",
"36/216"
] |
Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6) = 1-25/36 = 11/36.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
D is thus the correct answer.
The answer is: D
|
D
|
mathematics
|
pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
|
[
"2",
"9",
"8",
"7",
"1"
] |
x/18 + 12/24 = 1
x = 9.Answer: B
The answer is: B
|
B
|
mathematics
|
If 4a β 2b β 2c = 32 and β3a-β(2b+2c)=4, what is the value of a + b + c?
|
[
"3",
"9",
"10",
"12",
"14"
] |
when we look at the two equations, we can relize some similarity, so lets work on it..
3a β 2b β 2c = 32 can be written as β3a^2-β(2b+2c)^2=32
{β3a-β(2b+2c)}{β3a+β(2b+2c)}=32..
or 4*β3a+β(2b+2c)=32..
or β3a+β(2b+2c)=8..
now lets work on these two equations
1)β3a-β(2b+2c)=4..
2)β3a+β(2b+2c)=8..
A) add the two eq..
β3a+β(2b+2c)+β3a-β(2b+2c)=12..
2β3a=12..
or β3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
β3a+β(2b+2c)-β3a+β(2b+2c)=4..
2β(2b+2c)=4..
β(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
D
The answer is: D
|
D
|
mathematics
|
The unitβs digit in the product (3127)^173 is:
|
[
"1",
"3",
"7",
"9",
"11"
] |
Unit digit in (3127)^173 = Unit digit in 7^173.
Now, 7^4 gives unit digit 1.
Therefore, 7^173= (74)^43 * 7^1. Thus, 7^173 gives unit digit 7.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.4 meters high. What is Mr. Wayne's speed in meters per second?
|
[
"3",
"3.75",
"4",
"4.25",
"5"
] |
IMO: D
15 Floors * 3.4 Meter/Floor = 51 Meters
Time= 12 sec
Rate * 12 = 51
Rate= 51/12
=4.25
Answer D
The answer is: D
|
D
|
mathematics
|
In a public show 60 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
|
[
"100",
"110",
"120",
"140",
"240"
] |
75 % of 600
= 60/100 Γ 600
= 360
Therefore, the number of vacant seats = 600 - 360 = 240.
Answer:E
The answer is: E
|
E
|
mathematics
|
Two numbers A and B are such that the sum of 6% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
|
[
"2 : 3",
"1 : 2",
"4 : 3",
"1 : 1",
"3 : 2"
] |
Explanation:
6% of A + 4% of B = 2/3(6% of A + 8% of B)
6A/100 + 4B/100 = 2/3(6A/100+8B/100)
β6A + 4B = 2/3(6A + 8B)
β18A + 12B = 12A + 16B
β 6A = 4B
β AB = 4/6=2/3
β A:B=2:3
Answer: Option A
The answer is: A
|
A
|
mathematics
|
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy?
|
[
"4, 2, 8, 6",
"4 and 2",
"2 and 8 only",
"6 and 4",
"8 and 6"
] |
Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values of X for positive values of a
When,
a=1; X=2
a=2; X=4
a=3; X=8
a=4; X=16
a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4......
Similarly, Finding all values of Y for positive values of b
When,
b=1; Y=3
b=2; Y= 9
b=3; Y= 27
b=4; Y=81
b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=2 and Y=3: Units digit of XY = 6
When X=2 and Y=9: Units digit of XY = 18
When X=2 and Y=7: Units digit of XY = 14
When X=2 and Y=1: Units digit of XY = 2
When X=4 and Y=3: Units digit of XY = 12
When X=4 and Y=9: Units digit of XY = 36
When X=4 and Y=7: Units digit of XY = 28
When X=4 and Y=1: Units digit of XY = 4
When X=8 and Y=3: Units digit of XY = 24
When X=8 and Y=9: Units digit of XY = 72
When X=8 and Y=7: Units digit of XY = 56
When X=8 and Y=1: Units digit of XY = 8
When X=6 and Y=3: Units digit of XY = 18
When X=6 and Y=9: Units digit of XY = 54
When X=6 and Y=7: Units digit of XY = 42
When X=6 and Y=1: Units digit of XY = 6
There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6
Ans: A
The answer is: A
|
A
|
mathematics
|
If a 10 percent deposit that has been paid toward the purchase of a certain product is $110, how much more remains to be paid?
|
[
"$880",
"$990",
"$1,000",
"$1,100",
"$1,210"
] |
10/100P = 110 >> p= 110*100/10 = 1100
1100 - 110 = 990
ANSWER:B
The answer is: B
|
B
|
mathematics
|
A car runs at the speed of 30 km per hour when not serviced and runs at 120 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced?
|
[
"18 hours 12 minutes",
"32 hours",
"28 hours 15 minutes",
"17 hours 12 minutes",
"None"
] |
Explanation :
Time = 120*8 / 30 = 32 hours
Answer Γ’β¬β B
The answer is: B
|
B
|
mathematics
|
A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
|
[
"287",
"699",
"677",
"168",
"200"
] |
Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Answer: E
The answer is: E
|
E
|
mathematics
|
Aman can row 1km upstream in 20 min and back to his starting point in 12 min.How long would he take to row 1km in still water?.
|
[
"12 mins",
"13 mins",
"14 mins",
"15 mins",
"16 mins"
] |
If his speed is x mtr/min in still water and w mtr/minis speed of water, then
x-w= 1000/20=50
x+w= 1000/12= 250/3
adding
2x= 50 + 250/3= 400/3
x=200/3 mtrs/min
time taken to row 1 kms in still water = 1000/(200/3)= 15 mins.
ANSWER:D
The answer is: D
|
D
|
mathematics
|
If A is to be chosen at random from the set {8,1} and B is to be chosen at random from the set {2,7,9,6}, what is the probability that AB will be even?
|
[
"5/9",
"5/4",
"3/8",
"9/7",
"2/5"
] |
Method-1
AB will be even when
1) A is even and B is odd, Probability of A even is (1/2) and Probability of B odd is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
2) A is Odd and B is Even, Probability of A Odd is (1/2) and Probability of B Even is (2/4), so Probability of Case(2) = (1/2)*(2/4) = (2/8)
3) A is even and B is Even, Probability of A even is (1/2) and Probability of B Even is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
Total Favorable Probability = (2/8)+(4/8)+(4/8) = (10/8) = 5/4
Answer: option B
The answer is: B
|
B
|
mathematics
|
Find the number of different meals of 4 items that you can get from the given menu of 6 items and no need to choose different items.
|
[
"120",
"126",
"5040",
"15",
"18"
] |
total item : 6
we can select : 4
thus -> 6C4 which = 6C2
:: 6*5/ 2*1 = 15
ANSWER:D
The answer is: D
|
D
|
mathematics
|
What is the smallest number which, when increased by 9, is divisible by 8, 11, and 24?
|
[
"237",
"246",
"255",
"264",
"273"
] |
LCM(8,11,24)=24x11=264
So the least divisible number is 264, and the number we are looking for is 264-9=255.
The answer is C.
The answer is: C
|
C
|
mathematics
|
The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought?
|
[
"42.",
"38.",
"33.",
"22.",
"20."
] |
Let X pizzas of 2 slices and Y pizzas of 4 slices.
2X + 4Y.
Lets check options wise.
A. 42 => 2(15) + 4(3)
B. 38 => 2(15) + 4(2)
C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out.
D. 22 => 2(10) + 4(3)
E. 20 => 2(6) + 4(2)
Answer: correct option is C
The answer is: C
|
C
|
mathematics
|
If the sides of a triangle are 26 cm, 18 cm and 10 cm, what is its area?
|
[
"90",
"110",
"130",
"140",
"150"
] |
The triangle with sides 26 cm, 18 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 18 * 10 = 90 cm2
Answer: Option A
The answer is: A
|
A
|
mathematics
|
An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
|
[
"6",
"9",
"12",
"24",
"48"
] |
In 24 ounces, gold is 24 * (70/100) = 16.8 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 16.8 + x = (24 + x)* 90/100 => x =48.
Answer is E.
The answer is: E
|
E
|
mathematics
|
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
|
[
"11:9",
"11:20",
"9:20",
"11:8",
"None of these"
] |
Explanation :
In the same time, they cover 110 km and 90 km respectively.
=> Ratio of their speeds = 110 : 90 = 11 : 9
Answer : A
The answer is: A
|
A
|
mathematics
|
Meera purchased two three items from a shop. Total price for three items is Rs.3200/- She have given Rs. 6000/- What is the balance amount meera got?
|
[
"650",
"1400",
"1350",
"8200",
"2800"
] |
Total cost of Items : 3200/-
amount Paid : 6000/-
Balance receivable : 6000 - 3200 = 2800/-
Answer is E
The answer is: E
|
E
|
mathematics
|
The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
|
[
"78",
"65",
"58",
"62",
"48"
] |
6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*58+6*65-11*60 = 78
Answer is A
The answer is: A
|
A
|
mathematics
|
If w = 9/25, m = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
|
[
"c, m, w",
"c, w, m",
"m, w, c",
"w, c, m",
"w, m, c"
] |
Answer B - c, w, m
w ~ 1/3
m ~ 1/2
and m+w+c = 1 hence c ~ 1/6
Hence increasing order would be c -> w -> m
Answer B
The answer is: B
|
B
|
mathematics
|
Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 90 players took part in that tournament.
How many matches were played?
|
[
"99 matches.",
"89 matches.",
"77 matches.",
"66 matches.",
"55 matches."
] |
Solution:
89 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 89 matches were played.
Answer B
The answer is: B
|
B
|
mathematics
|
if x:y = 1:3, then find the value of
(7x+3y):(2x+y)
|
[
"14:5",
"15:5",
"16:5",
"17:5",
"18:5"
] |
Explanation:
let x = 1k and y = 3k,
so
=7(k)+3(3k)/2(k)+1(3k)
=16k/5k
=16:5
ANSWER IS C
The answer is: C
|
C
|
mathematics
|
Veena ranks 65rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
|
[
"96",
"108",
"110",
"90",
"93"
] |
total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-65+1=96
ANSWER:A
The answer is: A
|
A
|
mathematics
|
One used-car salesperson receives a commission of $ 200 plus 3 percent of $ 1,000 less than the carβs final sale price. Another car salesperson earns a straight commission of 6 percent of the carβs final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
|
[
"$ 5,000",
"$ 6,000",
"$ 8,000",
"$ 10,000",
"$ 12,000"
] |
This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the carβs final sale price.
2) A straight commission of 6 percent of the carβs final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
D
The answer is: D
|
D
|
mathematics
|
Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
|
[
"three times as much",
"twice as much",
"the same",
"half as much",
"a third as much"
] |
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
correct answer B
The answer is: B
|
B
|
mathematics
|
What is the greatest prime factor of (12!11!) + (12!13!)?
|
[
"41",
"71",
"107",
"157",
"211"
] |
12!11! + 12!13!
= 12!11! (1+12*13)
= 12!11!(157)
The answer is D.
The answer is: D
|
D
|
mathematics
|
If there are 4 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
|
[
"32",
"24",
"56",
"44",
"40"
] |
The first member can be anybody, so 8 possibilities.
The second member cannot be the sibling of the previous member, therefore 6 possibilities (anybody from the remaining 3 pairs).
Finally, the third member, can be chosen from the remaining 2 pairs, so 4 possibilities.
This would give us 8*6*4 possibilities, but in this case we don't care about the order in which we choose them, we have to divide the product we obtained by 6(=3!), which is the number of possibilities we can chose the same three distinct members, say ABC (it can be BAC, CAB,...). You can count those possibilities for such a small number as 3, but why avoid permutations? Is it better to start listing the possibilities instead of just accepting the already proven result?
So, the correct answer is 8*4=32.
Answer A.
The answer is: A
|
A
|
mathematics
|
We made a down payment of $25 and borrowed the balance on a new sofa which cost $250. The balance with interest was paid in 23 monthly payments of $11 each and a final payment of $17. The amount of interest paid was what percent of the amount borrowed?
|
[
"20%",
"22%",
"25%",
"27%",
"30%"
] |
We borrowed $225.
To pay back this loan, we paid 23*$11 + $17=$270.
The interest was $270-$225=$45.
The percentage was $45/$225=0.2=20%.
The answer is A.
The answer is: A
|
A
|
mathematics
|
The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?
|
[
"93",
"39",
"75",
"48",
"Either (a) or (b)"
] |
Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.
E
The answer is: E
|
E
|
mathematics
|
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
|
[
"144ΒΊ",
"150ΒΊ",
"168ΒΊ",
"180ΒΊ",
"190ΒΊ"
] |
Angle traced by the hour hand in 6 hours =360/12x 6ΒΊ= 180ΒΊ.
Answer: Option D
The answer is: D
|
D
|
mathematics
|
Sanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
|
[
"1/24",
"1/8",
"1/4",
"1/3",
"3/8"
] |
Total Sanya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
The answer is: D
|
D
|
mathematics
|
A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
|
[
".4 km",
"1.4 km",
"2.4 km",
"3.4 km",
"None of these"
] |
Explanation:
Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
=> 2x + 3x = 12
=> x = 12/5 = 2.4 km
Option C
The answer is: C
|
C
|
mathematics
|
Find the odd man out. 15, 25, 30, 51, 85, 90, 115
|
[
"15",
"25",
"51",
"90",
"91"
] |
Explanation :
All except 51 are multiples of 5. Answer : Option C
The answer is: C
|
C
|
mathematics
|
P is a set containing 8 different positive odd numbers. Q is a set containing 7 different numbers, all of which are members of P. Which of the following statements CANNOT be true?
|
[
"The range of Q is even.",
"The mean of P is even.",
"The mean of Q is even.",
"The range of P is equal to the range of Q.",
"The median of Q is equal to the mean of Q."
] |
Given: P is a set containing 8 different positive odd numbers
Easily inferred: Q is a set containing 7 differentoddnumbers
(A) The range of Q is even. - Always even, since it is a difference of two odd numbers
(B) The mean of P is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of Q is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of P is equal to the range of Q.
(E) The median of Q is equal to the mean of Q
Option C.
The answer is: C
|
C
|
mathematics
|
A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
|
[
"3388",
"3120",
"2177",
"1987",
"1268"
] |
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
The answer is: B
|
B
|
mathematics
|
If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is
|
[
"1/25",
"1/29",
"1/26",
"1/24",
"1/21"
] |
We have 1, 8, 27 and 64 as perfect cubes from 1 to 100.
Thus, the probability of picking a perfect cube is
4/100 = 1/25.
Answer:A
The answer is: A
|
A
|
mathematics
|
Dimitri weighs x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of 2y-y pounds. Which of the following represents Allenβs weight?
|
[
"y - x/2",
"2x - y/2",
"(y - x)/2",
"y - 2x",
"2x - y"
] |
These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs X pounds more than Allen weighs and that they weight a combined TOTAL of 2Y-Y or Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
The answer is: C
|
C
|
mathematics
|
workers in a factory store products inside two different sized boxes. The bigger of the boxes can store 50 products while the smaller box can store 40 products. If a fresh batch of products numbering 212 in total were to be stored, what is the least number of products that will not be boxed?
|
[
"23",
"11",
"2",
"10",
"12"
] |
Total products to be stored 212
The big box can store 50
small box can store 40
storing 212 products in big box 212/50 =4 r 12
least number of toys that will be left unboxed=12
Answer: E
The answer is: E
|
E
|
mathematics
|
When 24 is divided by the positive integer b, the remainder is 4. Which of the following statements about b must be true?
I. b is even
II. b is a multiple of 5
III. b is a factor of 20
|
[
"III only",
"I and II only",
"I and III only",
"II and III only",
"I, II, and III"
] |
24= m*b + 4
m*b=20
put values of m
m=1 b=20
m=2 b=10
m=4 b=5
I. not true
II. true
III. true
D. correct
The answer is: D
|
D
|
mathematics
|
The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 20 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?
|
[
"13",
"14",
"15",
"20",
"22"
] |
a must be an integer as it is the number shoots at a rate of 20sec/shoot
3*60 + 20a = 10*60
20a = 420
a = 21
The total number of shoots -->1 +21 = 22 and
23th shoot will be taken at 620 seconds which is above 10 minutes
ANSWER: E
The answer is: E
|
E
|
mathematics
|
Josh spends a total of $5.5 buying Q items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then Q may be which of the following?
|
[
"99",
"100",
"101",
"112",
"113"
] |
Q items in the convenience store $5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
The answer is: C
|
C
|
mathematics
|
75% of a number when added to 75 is equal to the number. The number is ?
|
[
"150",
"200",
"225",
"300",
"None"
] |
Answer
75 + 75% of N = N
β N -3N/4 = 75
β N/4 = 75
β΄ N = (75 x 4) = 300
Correct Option: D
The answer is: D
|
D
|
mathematics
|
The diameter of a garden roller is 1.2 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use Γβ¬ = 22Γ’Ββ7)
|
[
"40 m2",
"44 m2",
"48 m2",
"37.7 m2",
"None of these"
] |
Required area covered in 5 revolutions
= 5 Γβ 2Γβ¬rh = 5 Γβ 2 Γβ 22Γ’Ββ7 Γβ 0.6 Γβ 2 = 37.7 m2
Answer D
The answer is: D
|
D
|
mathematics
|
(A% of 6B + B% of A) is equal to ?
|
[
"A% of B",
"B% of A",
"7% of AB",
"AB% of 3",
"None"
] |
Answer
A% of 6B + B% of A =6AB/100 + AB/100
= 7AB/100 = 7% of AB
Correct Option: C
The answer is: C
|
C
|
mathematics
|
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 185 cms. What was the ratio of men to women?
|
[
"5:2",
"5:1",
"4:3",
"2:1",
"3:1"
] |
We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 185cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 185M)/(W+M) = 180
170W + 185M = 180W + 180M
5M = 10W
M = 2W
M/W = 2/1
The ratio of men to women is 2 to 1.
D
The answer is: D
|
D
|
mathematics
|
A trader has 50 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
|
[
"5 and 45 kg",
"10 and 40 kg",
"15 and 35 kg",
"20 and 30 kg",
"40 and 30 kg"
] |
Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 50/1+9 *1 = 5 kg
Quantity sold at 6% loss = 50/1+9 *9 = 45kg
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
|
[
"10",
"12",
"14",
"16",
"18"
] |
Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
|
[
"255",
"267",
"255",
"277",
"211"
] |
Speed = [45 X 5/18] m/sec = [25/2] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (120 + x)/30 = 25/2
=> x = 255 m. Answer:C
The answer is: C
|
C
|
mathematics
|
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 300 votes. Find the number of votes casted to the winning candidate?
|
[
"456",
"744",
"912",
"1200",
"775"
] |
W = 62% L = 38%
62% - 38% = 24%
24% -------- 300
62% -------- ? => 775
ANSWER:E
The answer is: E
|
E
|
mathematics
|
In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
|
[
"N/9",
"8N/9",
"11N/18",
"17N/18",
"31N/36"
] |
The number of people who answered yes to both questions is (1/3)(1/6)N = N/18
The number of people who did not answer yes to both is 1 - N/18 = 17N/18
The answer is D.
The answer is: D
|
D
|
mathematics
|
A woman gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
|
[
"60%",
"34%",
"140%",
"100%",
"55%"
] |
C
C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
The answer is: C
|
C
|
mathematics
|
189. The inside dimensions of a rectangular wooden box
are 12 inches by 14 inches by 16 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
|
[
"3",
"4",
"5",
"6",
"7"
] |
Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 16x14width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 14, so the radius will be 7.
E
The answer is: E
|
E
|
mathematics
|
If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?
|
[
"1/4",
"1/3",
"1/2",
"2/3",
"None"
] |
Solution: Let the initial price of the commodity be 100.
After 50% increase in price, It will become,
100 ------50% increase----> 150.
Now, we have to reduce the consumption to keep expenditure 100.
Increase in price= 150 - 100 = 50
We have to reduce the consumption,
= (50/150)*100 = 1/3 or 33.33%
Other Method:
Here, we use, Final product constant graphic.
100 ==50% up== 150===33.33% down===>100.
Consumption Reduce = 33.33% = 1/3.
Answer: Option B
The answer is: B
|
B
|
mathematics
|
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?
|
[
"1/5",
"1/4",
"1/3",
"2/3",
"4/5"
] |
the successful events are when Sarah pulls 2 matching pair of socks out of 3 matching pairs of socks, which can be done in 3C2 ways as the order is not important
So,3C2 = 3 ways are:
RRBB
RRGG
BBGG
Now,the ways in which 4 socks can be pulled out of 6 socks (3 pairs) = 6C4 = 15
So, probability = 3/15 = 1/5
Ans: A
The answer is: A
|
A
|
mathematics
|
David obtained 86, 85, 82, 87 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
|
[
"75",
"276",
"87",
"85",
"11"
] |
Explanation:
Average = (86+ 85+ 82+ 87+ 85 )/ 5 = 425/5 = 85.
Answer:D
The answer is: D
|
D
|
mathematics
|
In how many ways can the letters L, I, M, I, T, S be arranged so that the two I's are not next to each other?
|
[
"36",
"48",
"240",
"296",
"428"
] |
1 L
2 I
1 M
1 T
1 S
Number of ways these letters can be arranged = 6!/2! (2! to account 2 same Is) = 360
Consider 2 Is as 1 entity and thus the number of arrangements for (II)LMTS = 5! = 120
Total allowed cases = 360-120 =240
C is the correct answer.
The answer is: C
|
C
|
mathematics
|
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?
|
[
"98",
"115",
"122",
"126",
"165"
] |
We need to break the grouping down to 2 scenarios : with the married couple or without the married couple in the group of 4 people for the trip
1) With the married couple in the group, we have to find the number of possibilities for the other 2 spots in the group from the left 8 people = 8!/(2!*6!) = 28
2) Without the married couple in the group, we have to find the number of possibilities for picking 4 people from the 8 unmarried people from the group = 8!/(4! * 4! ) = 70
Total number of possibilities = 28 + 70 = 98 (A)
The answer is: A
|
A
|
mathematics
|
What is the greatest integer m for which the number 50!/10^m is an integer?
|
[
"5",
"8",
"10",
"11",
"12"
] |
As for 50!/10^m, the greatest value of m will be obtained by finding the maximum number of 5s in 50!
The quick process for that (discussed in the link above) is
50/5 = 10
10/5 = 2
Total number of 5s is 12. So maximum value of m will also be 12.
Answer (E)
The answer is: E
|
E
|
mathematics
|
If 90% of A = 30% of B and B = C% of A,then the value of C is ?
|
[
"900",
"800",
"600",
"300",
"None"
] |
Answer
β΅ 90A/100 = 30B/100 = (30/100) x AC/100
β΄ C = 100 x (100/30) x (90/100) = 300
Correct Option: D
The answer is: D
|
D
|
mathematics
|
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 60 percent on clothing, 20 percent on food, and 20 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
|
[
"10",
"20",
"30",
"25",
"15"
] |
Assume she has $200 to spend.
TAX
Clothing = 60% = $120= $12.00
Food = 20% = $ 40 = $0.00
Items = 20% = $ 40 = $ 8.00
Total tax = $20.00
% of total amount = 20/200 * 100 = 10%
Answer A
The answer is: A
|
A
|
mathematics
|
In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 300 more than the correct answer. Find the number.
|
[
"125",
"280",
"384",
"400",
"576"
] |
Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 300
25*x/48 = 300
x = 576
ANSWER E
The answer is: E
|
E
|
mathematics
|
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
|
[
"200",
"278",
"100",
"202",
"270"
] |
Profit on first article = 10% of 1000 = 100.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: C
The answer is: C
|
C
|
mathematics
|
Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 72. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
|
[
"(a) 80",
"(b) 81",
"(c) 60",
"(d) 83",
"(e) 84"
] |
T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (72-6)/6+1=12 such multiples.
So, final number of sets is 12*5=60
Answer : C
The answer is: C
|
C
|
mathematics
|
What is the average (arithmetic mean) of the numbers 2, 4, 6, 8, 10, 12, 14 and 16?
|
[
"9",
"10",
"15",
"12",
"14"
] |
avg = sum of observations/number of observations
avg =(2+4+6+8+10+12+14+16)/8 = 9
Answer is A
The answer is: A
|
A
|
mathematics
|
A shop keeper marked 30% above the cost price and offered 20% discount then find it's net profit?
|
[
"2%",
"2.5%",
"3.7%",
"4.6%",
"5%"
] |
Net profit = 30-20 + (30*(-25)/100) = 2.5%
Answer is B
The answer is: B
|
B
|
mathematics
|
The ratio of the ages of Mona and Sona is 4:5. Twelve years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years?
|
[
"8",
"10",
"12",
"14",
"66"
] |
Let their present ages be 4x & 6x
Then (4x + 12)/(5x + 12) = 5/6 ; x=12
Sona's age after 6 years = (5x +6) = 66 years
ANSWER:E
The answer is: E
|
E
|
mathematics
|
In X game of billiards, X can give Y 20 points in 60 and he can give Z 50 points in 60. How many points can Y give Z in X game of 100?
|
[
"30",
"20",
"25",
"40",
"75"
] |
X scores 60 while Y score 40 and Z scores 10.
The number of points that Z scores when Y scores 100 = (100 * 50)/40 = 25.
In X game of 100 points, Y gives (100 - 25) = 75 points to C.
E
The answer is: E
|
E
|
mathematics
|
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee?
|
[
"38",
"40",
"42",
"46",
"49"
] |
1W 2M 2W 1M 3W
= 3C1 Γ 5C2 + 3C2 Γ 5C1 + 3C3s
= 3 Γ (5 Γ 4)/2 + 3 Γ 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
Atleast one women = total - with out women
Atleast one women = 56 - 10 = 46
D)
The answer is: D
|
D
|
mathematics
|
I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 3 senior and 3 junior staff officers, how many possible committees are there?
|
[
"12",
"44",
"56",
"80",
"200"
] |
6C3*4C3
=80=D
The answer is: D
|
D
|
mathematics
|
If 2x^2 + y^2 = 2xy, then (x - y)^2 =
|
[
"-x^2",
"3x^2",
"4xy",
"2y^2",
"β y^2"
] |
(x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2-2x^2-y^2 = -x^2
Correct option : A
The answer is: A
|
A
|
mathematics
|
Which of the following ratios is greatest ?
|
[
"7 :15",
"15 :23",
"17 :25",
"21 :29",
"1 : 2"
] |
7/15 = 0.466,
15/23 = 0.652,
17/25 = 0.68
21/29 = 0.724
Clearly, 0.724 is greatest
therefore, 21 : 29 is greatest
ANSWER:D
The answer is: D
|
D
|
mathematics
|
A farm has chickens, horses and sheep. There are six times the number of chickens and cows than sheep. If there are more horses than chickens or sheep, and together, horsess and chickens have a total of 100 feet and heads, how many sheep live at the farm?
|
[
"5",
"4",
"10",
"14",
"17"
] |
Chicken - ch
horses - H
Sheep -S
ch+H=6S
H> ch and H>s
Each Horse has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5h+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
h=11 and ch=9 or
h=14 and ch=10
Since from first equation where ch+h=6s
The sum of ch and c should be divisbile by 6. 20 is not so the only possible solution is h=14 and ch=10. So s=4
Answer : B
The answer is: B
|
B
|
mathematics
|
A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
|
[
"253 mph.",
"378 mph.",
"565 mph.",
"431 mph.",
"642 mph."
] |
The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x β 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x β 23)
420(x β 23) = 350(x + 23)
420x β 9660 = 350x + 805
420x β 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer A
The answer is: A
|
A
|
mathematics
|
If each of 4 digit code is formed of integers from 1 to 50, inclusively, and each of the digits are different, how many possible codes are there?
|
[
"5527200",
"5586300",
"5598600",
"5547800",
"2569800"
] |
Code consists of 4 digits and no digit is repeated.
First digit of the code can have 50 possibilities
Second digit can have 49 possibilities
Third digit can have 48 possibilities
fourth digit can have 47 possibilities
Total number of possible codes = 50*49*48*47 = 5527200
Answer: A
The answer is: A
|
A
|
mathematics
|
After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
|
[
"20 days",
"24 days",
"27 days",
"21 days",
"26 days"
] |
A
20 days
1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30
2/3 ----? => 20 days
The answer is: A
|
A
|
mathematics
|
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
|
[
"2 years",
"4 years",
"6 years",
"7 years",
"8 years"
] |
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 6) years = 44 years.
Required difference = (44 - 36) years = 8 years.
Answer: Option E
The answer is: E
|
E
|
mathematics
|
A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup?
|
[
"1.5",
"1.75",
"2.14",
"2.34",
"2.64"
] |
Let the total solution is 150 L with 80 L water70 L syrup.
To make 30% syrup solution, the result solution must have 105 L syrup and 45 L syrup.
Therefore we are taking 25 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
25 L syrup in 53.6 L solution
We started by multiplying 10
Now to get to the result we need to divide by 25 => amount of solution to be replaced with water = (53.6/25) = 2.14.
Correct option : C
The answer is: C
|
C
|
mathematics
|
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
|
[
"76 kg",
"76.5 kg",
"85 kg",
"90 kg",
"NOne"
] |
Sol.
Total weight increased
= (8 Γ 2.5) kg
= 20 kg.
Weight of new person
= (65 + 20) kg
= 85 kg.
Answer C
The answer is: C
|
C
|
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