subject
stringclasses 1
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stringlengths 3
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mathematics
|
What is the smallest number which when diminished by 16, is divisible 4, 6, 8 and 10?
|
[
"136",
"192",
"198",
"122",
"142"
] |
Required Number
= (LCM of 4,6,8, and 10) + 16
= 120 + 16 = 136
Option A
The answer is: A
|
A
|
mathematics
|
If 200 lb of a mixture contain 80% husk and 20% sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk?
|
[
"1/4",
"20/3",
"1/2",
"40",
"60"
] |
We need to extract 40 lb of husk.
80 % of 200 = 160
20 % of 200 = 40
Now we have t remove husk to have 75 % of Husk ( key point sand is not supposed to be removed)
Let X be the new quantity after removing husk
So, 40 = 25 % of X
X = 160
Husk will 120 lbs , hence we need to remove 1/4 of the total husk or 40 lbs
ANSWER:D
The answer is: D
|
D
|
mathematics
|
In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1?
|
[
"25",
"45",
"55",
"70",
"30"
] |
Day 1&2 = 80; Only Day 1&2 (80-20) = 60,
Day 2&3 = 70; Only Day 2&3 (70-20) = 50,
Only Day 1 = 175 - (60+50+20) = 45
Answer:B
The answer is: B
|
B
|
mathematics
|
10% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
|
[
"25",
"30",
"50",
"55",
"60"
] |
I came up with (A) 25
Think of 100 people total:
From the first fact, 10 of these are women with fair hair.
From the second fact, these 10 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*10 equals the number of fair haired men, which is 15 men with fair hair.
Add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women.
25%
A
The answer is: A
|
A
|
mathematics
|
What is the probability that a leap year has 53 Sundays and 52 Mondays?
|
[
"0",
"1/7",
"2/7",
"5/7",
"6/7"
] |
A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
ANSWER:B
The answer is: B
|
B
|
mathematics
|
The average weight of A, B and C is 43 kg. If the average weight of A and B be 48 kg and that of B and C be 42 kg, then the weight of B is:
|
[
"55 kg",
"53 kg",
"49 kg",
"52 kg",
"51 kg"
] |
EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (43 x 3) = 129 …. (i)
A + B = (48 x 2) = 96 …. (ii)
B + C = (42 x 2) = 84 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 180 …. (iv)
Subtracting (i) from (iv), we get : B = 51.
B’s weight = 51 kg.
Answer E
The answer is: E
|
E
|
mathematics
|
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
|
[
"1/8",
"1/4",
"2/5",
"2/7",
"1/1"
] |
A
1/8
This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8 and so on.
The answer is: A
|
A
|
mathematics
|
Robert purchased $2000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
|
[
"20",
"27",
"30",
"60",
"70"
] |
I started off with looking at the answer choices... 20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $3000. So with 70 bonds, each $50 = $3500 , we already exceed the $3000 limit. Hence E is the answer.
The answer is: E
|
E
|
mathematics
|
What should be added to 4329 so that it may become a perfect square?
|
[
"24",
"25",
"26",
"27",
"28"
] |
66x66=4356
4356-4329 = 27
If added to 27 get perfect square
answer =D
The answer is: D
|
D
|
mathematics
|
What is the last number in a sequence of 5 consecutive integers, given that their sum is 335?
|
[
"69",
"70",
"68",
"66",
"67"
] |
The median is: 335/5 = 67. Middle position.
Middle position is also: 5/2 = 2.5, rounded up: 3rd position
3rd position is: 5-3 = 2 positions away from the last position
67 + 2 = 69
Answer: A
The answer is: A
|
A
|
mathematics
|
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
|
[
"24",
"25",
"26",
"27",
"28"
] |
Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Three people have $34, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
|
[
"$72",
"$85",
"$98",
"$101",
"$102"
] |
Solution -
Total money distributed is $204. In order to maximize median, one person has to accept $0 and remaining two people share $102 each. Hence median is $102.
ANS E
The answer is: E
|
E
|
mathematics
|
If |w|=−w, which of the following must be true?
|
[
"x≥0",
"w≤0",
"x2>x",
"x3<0",
"2x<x"
] |
|w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative number. It means w is a non positive number i.e. w<0. Answer is B
The answer is: B
|
B
|
mathematics
|
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(z) is divisible by 4^11, what is the smallest possible value for z?
|
[
"22",
"24",
"28",
"32",
"44"
] |
g(z)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
The answer is: B
|
B
|
mathematics
|
Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
|
[
"7 hrs 30 min",
"8 hrs",
"8 hrs 15 min",
"8 hrs 25 min",
"9 hrs"
] |
Explanation:
Number of pages typed by Ronald in 1 hour = 32/6 = 16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3
Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min
ANSWER IS C
The answer is: C
|
C
|
mathematics
|
Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 8 years more than the present age of Anand. Find the present age of Anand?
|
[
"12",
"14",
"15",
"16",
"18"
] |
Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 8
Substituting b = a + 8 in first equation,
a - 10 = 1/3 (a -2) => 3a - 30 = a - 2
=> 2a = 28 => a = 14.
Answer: B
The answer is: B
|
B
|
mathematics
|
The value of x + x(xx) 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
Answer: (A)
The answer is: A
|
A
|
mathematics
|
A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?
|
[
"78",
"43",
"51",
"66",
"90"
] |
Speed = 250/25 = 10 m/sec.
Required time = (250 + 650)/10 = 90 sec.
Answer: E
The answer is: E
|
E
|
mathematics
|
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 3 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
|
[
"5729",
"5760",
"2889",
"2870",
"4320"
] |
1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 3 = 4320.Answer: E
The answer is: E
|
E
|
mathematics
|
There is a box full of fruits,
all but two are grapes,
all but two are apples,
and all but two are oranges.
How many fruits are in the box ?
|
[
"5 fruits",
"8 fruits",
"4 fruits",
"2 fruits",
"3 fruits"
] |
E
There are 3 fruits (1 grapes, 1 apples, and 1 oranges).
The answer is: E
|
E
|
mathematics
|
Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 20 such machines produce in 4 minutes ?
|
[
"648",
"1800",
"2700",
"10800",
"3600"
] |
Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
∴ 6 × 1 × x = 20 × 4 × 270 ⇔ x = 20x4x270/6= 3600 . Answer E
The answer is: E
|
E
|
mathematics
|
In a class of 37 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
|
[
"6",
"8",
"10",
"12",
"14"
] |
26 + 20 - 17 = 29
37 - 29 = 8 play neither
Answer is B
The answer is: B
|
B
|
mathematics
|
A room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
|
[
"107",
"126",
"117",
"136",
"147"
] |
Let us calculate both the length and width of the room in centimeters.
Length = 6 meters and 72 centimeters = 672 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 672 and 432 = 48
Thus, the number of square tiles required = (672 x 432 ) / (48 x 48) = 14 x 9 = 126
Answer: B
The answer is: B
|
B
|
mathematics
|
Village P’s population is 1200 greater than Village Q's population. If Village Q’s population were reduced by 800 people, then Village P’s population would be 6 times as large as Village Q's population. What is Village Q's current population?
|
[
"1050",
"1100",
"1150",
"1200",
"1250"
] |
P = Q+1200.
P=6(Q-800).
6(Q-800)=Q+1200.
5Q=6000.
Q=1200.
The answer is D.
The answer is: D
|
D
|
mathematics
|
If (18^a) * 9^(3a – 1)= (2^4)(3^b) and a and b are positive integers, what is the value of a?
|
[
"22",
"11",
"9",
"6",
"4"
] |
(18^a) * 9^(3a – 1)= (2^4)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^4)(3^b)
Just compare powers of 2 from both sides
Answer = 4 = E
The answer is: E
|
E
|
mathematics
|
In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a four. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
|
[
"1/48",
"5/16",
"11/16",
"11/12",
"23/48"
] |
First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : C
The answer is: C
|
C
|
mathematics
|
How many multiples of 7 are there between 21 and 343, inclusive ?
|
[
"48",
"47",
"46",
"45",
"44"
] |
7 * 3 = 21
7 * 49 = 343
Total multiples = (49-3) + 1 = 47
Include 21 and 343 = 47
Answer is B
The answer is: B
|
B
|
mathematics
|
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
|
[
"25years",
"45years",
"12years",
"6years",
"16years"
] |
Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Ans: A
The answer is: A
|
A
|
mathematics
|
Four people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
|
[
"1/3",
"2/7",
"3/7",
"4/7",
"None of them"
] |
Original share of 1 person = 1/4
New share of 1 person = 1/3
Increase = (1/3 - 1/4 = 1/12)
Therefore, Required fraction = (1/12)/(1/4) = (1/12)x (4/1) = 1/3
Answer is A.
The answer is: A
|
A
|
mathematics
|
The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 45, find the other?
|
[
"100",
"160",
"120",
"200",
"150"
] |
Other number = 12*600/45= 160
Answer is B
The answer is: B
|
B
|
mathematics
|
If a fair coin is flipped six times in a row, what is the probability that there will be at least one head and one tail?
|
[
"3/4",
"11/12",
"15/16",
"31/32",
"63/64"
] |
The number of possible outcomes is 2^6 = 64
There is one way to get no heads and one way to get no tails.
Thus there are 62 outcomes with at least one head and one tail.
P(at least one head and one tail) = 62/64 = 31/32
The answer is D.
The answer is: D
|
D
|
mathematics
|
f the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?
|
[
"Both a and b can be Prime Numbers.",
"Both a and b can be consecutive integers.",
"All Prime factors of a must be Prime factors of b.",
"a and b do not share any Prime factors.",
"a and b do not have a common factor"
] |
Say a = 2; b = 3; only option C contradicts
All Prime factors of a must be Prime factors of b
Answer = C
The answer is: C
|
C
|
mathematics
|
A dealer offers a cash discount of 16% and still makes a profit of 25% when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
|
[
"50%",
"60%",
"70%",
"75%",
"78+(4/7)%"
] |
Given
Cash Discount - 16%
Profit - 25%
Items Sold - 60
Price Sold at = List Price of 50
Assume List price = $10
Total Invoice = $500
-16% Cash Discount = $420
Let cost price of 60 items be x
So total cost = 60*x
Given the shopkeeper had a profit of 25%
60 * x * 125/100 = 420
or x = $7*4/5=$28/5
Which means his products were listed at $10 which is a 78+(4/7)% markup over $28/5
Answer E
The answer is: E
|
E
|
mathematics
|
A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.
|
[
"48",
"288",
"495",
"990",
"11880"
] |
The number of ways of choosing 4 sites out of 12 are counted by = 12C4 ways = 495
Answer: Option C
The answer is: C
|
C
|
mathematics
|
Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of m crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of m?
|
[
"x/2",
"x",
"3m/2",
"mx",
"mx"
] |
Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Amy carries 3 crumbs per trip. Also let Arthur make 2 trips and so Amy makes 4 trips.
Thus total crumbs carried by Arthur (m) = 2 x 2 = 4, total crumbs carried by Amy = 3 x 4 = 12. 12 is 3 times 4, so E
The answer is: E
|
E
|
mathematics
|
Josh spends a total of $5.00 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?
|
[
"91",
"100",
"101",
"109",
"140"
] |
Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=5.0 ---> x+10y=100 ...(1)
Also, x+y=N ...(2)
Solving 1 and 2 , we get, N = 110-9y ---> only value satisfied is when y = 1---> N = 100-9=91.
A is the correct answer. Other options are not equal to multiples of 9 removed from 100.
The answer is: A
|
A
|
mathematics
|
z is a positive integer and multiple of 2; w = 4^z, what is the remainder when w is divided by 10?
|
[
"10",
"6",
"4",
"0",
"It Cannot Be Determined"
] |
It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since z must be an even integer, the units digit of w=4^z will always be 6. Consequently, the remainder when w=4^z is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
z=2 --> w=4^z=16 --> w/10 = 1 with a remainder of 6
z=4 --> w=4^z=256 -->w/10 = 25 with a remainder of 6
z=6 --> w=4^z=4096 --> w/10 = 409 with a remainder of 6
z=8 --> w=4^z=65536 --> w/10 = 6553 with a remainder of 6
Answer: B.
The answer is: B
|
B
|
mathematics
|
In a office work is distribute between p persons. If 1/7 members are absent then work increased for each person is?
|
[
"13.67%",
"14.67%",
"15.67%",
"16.67%",
"17.67%"
] |
let total % of work is 100%
total person=p
1/7 person are absent of total person . so absent person is 1/7p ie p/7.
left person is, p-p/7=6p/7.
p person do the work 100%
1 person do the work 100*p%
6p/7 person do the work (100*p*7)/6p%=116.67%
work increased for each person is=(116.67-100)%=16.67%
ANSWER:D
The answer is: D
|
D
|
mathematics
|
What least number should be subtracted from 13602 such that the remainder is divisible by 87 ?
|
[
"27",
"29",
"28",
"30",
"31"
] |
13602 ÷ 87 = 156, remainder = 30
Hence 30 is the least number which can be subtracted from 13602 such that the remainder
is divisible by 87
Answer is D
The answer is: D
|
D
|
mathematics
|
How many numbers greater than 1000 can be formed with the digits 3,4,6,8,9 if a digit cannot occur more than once in a number?
|
[
"240",
"120",
"360",
"60",
"600"
] |
This is choosing 4 from 5 (any 4 digit number chosen from 3,4,6,8,9 will be>1000) plus 5 from 5 (any 5 digit number will be >1000), where order is important.
So the number of ways we can arrange the given digits so that our resulting number is greater than 1000 such that no digit occurs more than once, is:
5P4 + 5P5 = 240
A
The answer is: A
|
A
|
mathematics
|
Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 70 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
|
[
"45",
"50",
"63",
"75",
"80"
] |
AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 70
y - 70 + (y/4) = 70
5y/4 = 140
y = 112
2x/3 = 112 - 70 = 42
x = 126/2 = 63
Answer: C
The answer is: C
|
C
|
mathematics
|
[(7/2 ÷ 1/2 × 7/2)]/[(7/2 × 1/2 ÷ 7/2)] = ?
|
[
"45",
"49",
"44",
"43",
"42"
] |
Explanation:
[(7/2 ÷ 1/2 × 7/2)]/[(7/2 × 1/2 ÷ 7/2)]
= [7/2 × 2/1 × 7/2]/[7/2 × 1/2 × 2/7]
= 49/2 / 1/2 = 49/2 x 2/1 = 49
Answer: Option B
The answer is: B
|
B
|
mathematics
|
A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 12 minutes earlier. How far is the office from his house?
|
[
"4 1/5 Km",
"4 1/7 Km",
"3 1/5 Km",
"3 1/7 Km",
"4 Km"
] |
Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 20/6
= 24/2 * 20/60
= 10 * 2/5
= 20/5 = 4 Km
E)
The answer is: E
|
E
|
mathematics
|
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
|
[
"32 sec",
"17 sec",
"12 sec",
"46 sec",
"15 sec"
] |
D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer:C
The answer is: C
|
C
|
mathematics
|
The price of a car is marked at $12,000. If the car has successive discounts of 20%, 10% and 5%, then at what price does a customer buy the car?
|
[
"$8208",
"$8312",
"$8424",
"$8536",
"$8610"
] |
0.95*0.9*0.8*12000 = $8208
The answer is A.
The answer is: A
|
A
|
mathematics
|
How many multiples of 2 are there between 10 and 100(both are inclusive)?
|
[
"2",
"7",
"6",
"46",
"3"
] |
the answer is (100-10)/2+1=46
Answer is D
The answer is: D
|
D
|
mathematics
|
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 200 m. Then, A wins by:
|
[
"60 m",
"100 m",
"43m",
"20m",
"23m"
] |
To reach the winning post A will have to cover a distance of (500 - 200)m, i.e., 300 m.
While A covers 3 m, B covers 4 m.
While A covers 300 m, B covers 4 x 300/3 m = 400 m.
Thus, when A reaches the winning post, B covers 400 m and therefore remains 100 m behind.
A wins by 100 m.
Answer: B
The answer is: B
|
B
|
mathematics
|
The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-fourth of the males and one-half of the females in the class?
|
[
"128",
"136",
"144",
"152",
"160"
] |
1/4*2/5 + 1/2*3/5 = 2/20 + 6/20 = 2/5
The number of degrees is 2/5 * 360 = 144 degrees
The answer is C.
The answer is: C
|
C
|
mathematics
|
During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 300 percent. Which of the following is the percent change in the stock's value during those two years?
|
[
"60 percent decrease",
"20 percent decrease",
"20 percent increase",
"60 percent increase",
"140 percent increase"
] |
Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-80/100)=100*0.2=20 and in 2002 its value would be 20*(1+300/100)=80. Hence during those two years the value of the stock decreased from 100 to 80, so by 20%.
Answer: B.
The answer is: B
|
B
|
mathematics
|
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
|
[
"25",
"34",
"50",
"67",
"50"
] |
Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 6 oz can = 300 oz/6 oz = 50
Answer E, 50 cans
The answer is: E
|
E
|
mathematics
|
A 6 by 8 rectangle is inscribed in circle. What is the circumference of the circle?
|
[
"5π",
"10π",
"15π",
"20π",
"25π"
] |
The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: B
The answer is: B
|
B
|
mathematics
|
How many of the positive divisors of 120 are also multiples of 4 not including 120?
|
[
"3.",
"4.",
"5.",
"7.",
"8."
] |
Given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120.
Consider factors of 120
4 * 30
6 * 20
15 * 8
24 * 5
60 * 2
Total we get 5 different ways and all are part of 4.
Answer:C is correct option.
The answer is: C
|
C
|
mathematics
|
By the how much is two-fifth of 200 greater than three -fifths of 125?
|
[
"15",
"3",
"5",
"30",
"None of these"
] |
Reqd no. = 2⁄5 × 200 - 3⁄5 × 125
= 80 - 75 = 5
Answer C
The answer is: C
|
C
|
mathematics
|
A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint?
|
[
"9",
"16",
"15",
"25 1/3",
"28 1/2"
] |
3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
30 pints will require 9/17 * 30= 15 pints..
C
The answer is: C
|
C
|
mathematics
|
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
|
[
"1/20",
"1/6",
"1/5",
"4/21",
"5/21"
] |
Series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 4*x
Hence, a1+a2+..+a20+n = 24x
So, the fraction asked = 4x/24x = 1/6;
Answer: B.
The answer is: B
|
B
|
mathematics
|
A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 18 miles per hour." What was their average speed in the whole journey?
|
[
"10 miles/hour",
"12 miles/hour",
"11 miles/hour",
"13 miles/hour",
"12.9 miles/hour"
] |
2xy/x+y=12.9 miles/hour
ANSWER:E
The answer is: E
|
E
|
mathematics
|
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
|
[
"5760",
"14400",
"480",
"56",
"40320"
] |
Consider the following arrangement:
*B*B*B*B*B*
Now, if girls occupy the places of 6 stars no girls will be together.
# of ways 3 girls can occupy the places of these 6 stars is C36=20;
# of ways 3 girls can be arranged on these places is 3!=6
# of ways 5 boys can be arranged is 5!=120
So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20∗6∗120=14,400
ANS:B
The answer is: B
|
B
|
mathematics
|
if the ratio of two number is 6:7 and LCM of the number is 450 then what is the number.
|
[
"11",
"20",
"25",
"30",
"35"
] |
product of two no = lcm *hcf
6x*7x=450*x
x=11
ANSWER:A
The answer is: A
|
A
|
mathematics
|
At a particular pizza shop, a pizza can be created from any combination of 6 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
|
[
"6",
"35",
"120",
"450",
"900"
] |
Number of possible ways to select 1 type of spice = 6c1 = 6
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 6*6 * 25
=900
Answer E
The answer is: E
|
E
|
mathematics
|
The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
|
[
"120",
"278",
"378",
"368",
"367"
] |
4*5*6
= 120
Answer: A
The answer is: A
|
A
|
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 20 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?
.
|
[
"20",
"30",
"50",
"80",
"100"
] |
150 employees
80 are full-time
100 have worked at company X for at least a year
20 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?
150-80=70 employees not full time
70-20= 50 employees not full time who worked over a year
100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year
ANSWER:C
The answer is: C
|
C
|
mathematics
|
If $ 5,000 is invested in an account that earns 4% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
|
[
"$ 4",
"$ 8",
"$ 12",
"$ 16",
"$ 432"
] |
Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.04/2)^2= 5404
Amount (SI) = P+PTR/100 = 5000+(5000*1*4/100)=5400
Difference = 5404-5400=4 $
A
The answer is: A
|
A
|
mathematics
|
The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a jack?
|
[
"1/52",
"1/13",
"5/13",
"1/4",
"1/26"
] |
The question should ask about the probability not the odds.
There are 13 spades, the probability that the spade we already have is a jack is therefore 1/13.
Answer: B.
The answer is: B
|
B
|
mathematics
|
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
|
[
"(1.5)^4",
"4(1.5)",
"(1.05)^4",
"1 + (0.05)^4",
"1 + 4(0.05)"
] |
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
1(1.05)^4
1.05^4
C. (1.05)^4
ANSWER:C
The answer is: C
|
C
|
mathematics
|
To a sugar solution of 3 litres containing 40% sugar, one litre of water is added. The percentage of sugar in the new solution is
|
[
"22",
"30",
"99",
"88",
"27"
] |
Explanation:
Quantity of sugar = kg = 1.2 kg.
New percentage = = 30%.
Answer: B) 30
The answer is: B
|
B
|
mathematics
|
A trumpet section includes four musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
|
[
"240",
"125",
"120",
"100",
"24"
] |
We have a word problem using permutations. We must identify the number of total items in the group. There are four possible musicians who could be placed in the first chair, three possible musicians for the second, two for the third, one for the fourth. To determine the number of possible orderings, we multiply these numbers, which we can express as 4!. Now 4! = (4)(3)(2)(1) = 24=E
The answer is: E
|
E
|
mathematics
|
A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -5
|
[
"I only",
"II only",
"I and II only",
"II and III only",
"I, II, and III"
] |
The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
The answer is: C
|
C
|
mathematics
|
Shop Offered 20% offer for every Shirt, Smith bought a shirt at Rs. 780. and What was the shop's original selling Price?
|
[
"500",
"550",
"600",
"700",
"975"
] |
SP* (80/100) = 780
SP= 9.75 * 100 => CP = 975
Answer:E
The answer is: E
|
E
|
mathematics
|
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%?
|
[
"228",
"299",
"266",
"600",
"188"
] |
(x*5*1)/100 + [(1500 - x)*6*1]/100 = 84
5x/100 + 90 – 6x/100 = 84
x/100 = 6
=> x = 600
Answer:D
The answer is: D
|
D
|
mathematics
|
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
|
[
"276",
"299",
"322",
"345",
"395"
] |
Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A
The answer is: A
|
A
|
mathematics
|
It costs $4 for the first 1/4 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 3 hours and 25 minutes, how much will it cost him?
|
[
"$25",
"$32",
"$36",
"$40.",
"$42."
] |
3 hrs 25 min = 205 min
First 15 min ------> $4
Time left is 190 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
190 min costs $ 12/60*190 => $ 38
So, Total cost will be $38 + $4 => $ 42
Hene answer will be (E) $ 42
The answer is: E
|
E
|
mathematics
|
A clerk multiplied a number by ten when ten should have divided it. The answer he got was 100.what should the ans have been?
|
[
"3",
"1",
"2",
"4",
"5"
] |
let the number be x
actually form = x/10
but x*10=100
=>x=10
means the number the should be divided is 10
=>the answer would have been (10/10)=1
ANSWER:B
The answer is: B
|
B
|
mathematics
|
The average of first five multiples of 2 is :
|
[
"3",
"9",
"12",
"15",
"E"
] |
Solution
Average = 2(1+2+3+4+5)/5 =30/5 =6 Answer E
The answer is: E
|
E
|
mathematics
|
The product of x and y is a constant. If the value of x is increased by 30%, by what percentage must the value of y be decreased?
|
[
"16%",
"23.07%",
"25%",
"30%",
"35%"
] |
x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.3x (130)
i.e. 130*New 'y' = 10000
i.e. New 'y' = 10000/130 = 76.92
i.e. y decreases from 100 to 76.92 i.e. Decrease of 23.07%
B
The answer is: B
|
B
|
mathematics
|
From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
|
[
"20",
"10",
"30",
"50",
"40"
] |
Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+45) and number of girls were 5x
Hence, 2(5x) = x + 45
=> 10x = x + 45
=> x = 5
Number of girls in the beginning = (5x + 15) = (5×5 + 15) = 40
Answer is E.
The answer is: E
|
E
|
mathematics
|
A group of boy scouts and girls scouts is going on a rafting trip. 70% of the scouts arrived with signed permission slips. If 60% of the scouts were boy scouts and 75% of the boy scouts arrived with signed permission slips, then what percentage of the girl scouts arrived with signed permission slips? Round to the nearest percent.
|
[
"50%",
"60%",
"63%",
"66%",
"70%"
] |
60% were boy scouts so 40% (100-60=40) were girl scouts.
# of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed
(75% of 60% of the total going) + (?% of 40% of the total going) = 70% of the total going
We can let the "total going" = 1,000 arbitrarily since we only care about the percent (of girl scouts w/ permission signed)
.75*.60*1,000 + x*.40*1,000 = .70*1,000
450 + x*400 = 700
400x=250
x=250/400
x=.625
Converting this to a percent, we have 62.5%. Rounding, we have 63%.
C
The answer is: C
|
C
|
mathematics
|
If Ram and gohul can do a job in 10 days and 15 days independently, How many days would they take to complete the same job working simultaneously?
|
[
"10",
"5",
"8",
"6",
"13"
] |
If total work is X.
Ram working rate=X/10 per day.
Working rate of gohul=X/15 per day.
Rate of work=(X/10)+(X+15)=30X/5X=6 days
The answer is option D
The answer is: D
|
D
|
mathematics
|
The ratio T , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
|
[
"79 litres",
"78 litres",
"77 litres",
"152 liters",
"304 litres"
] |
I guess it should be
the ratio T, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
The answer is: C
|
C
|
mathematics
|
Mr. JACK invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $100,000. In one year, Fund X paid 33% and Fund Y paid 15%. The interest earned in Fund Y was exactly $500 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?
|
[
"31,041.66",
"45,041.66",
"37,041.78",
"78,041.90",
"99,041.78"
] |
X+Y=100,000
0.15Y=0.33A+500
Take away decimals first: 15Y+33X+50,000
Isolate first equation to solve for X (your goal): Y=100,000-Y
Plug in for B:
15(100,000-X)=33X+30,000
1,500,000-15X=33X+10,000
1,490,000=48X
1,490,000/48=X
X=31,041.66=Answer Choice A
The answer is: A
|
A
|
mathematics
|
A boat can travel with a speed of 40km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 45km downstream.
|
[
"1 hr",
"2 hrs",
"3 hrs",
"4 hrs",
"5 hrs"
] |
Speed downstream = (40 + 5) km/hr = 45 km/hr.
Time taken to travel 45 km downstream = 45/45 hrs = 1 hrs.
Answer : A
The answer is: A
|
A
|
mathematics
|
A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price B per t-shirt that the vendor paid for these purchases?
|
[
"$12.20",
"$12.50",
"$12.55",
"$12.70",
"$13.00"
] |
Correct Answer: A
Explanation: The relevant formula for this problem is Average B= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
The answer is: A
|
A
|
mathematics
|
The average of seven numbers is 15. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
|
[
"6",
"29",
"31",
"34",
"35"
] |
The total of seven numbers = 7X15 = 105
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (105 - 99 ) = 6
A
The answer is: A
|
A
|
mathematics
|
A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?
|
[
"1/8",
"1/4",
"1/3",
"1/2",
"2/3"
] |
First child ---- Second child:
B ---------------------------- B;
B ---------------------------- G;
G ---------------------------- B;
G ---------------------------- G.
We know that one if the kids is a girl. So, we have one of the three cases in red. Each case there is equally likely (each has the probability of 1/2*1/2=1/4). So, the probability of GG is 1/3.
Answer: C.
The answer is: C
|
C
|
mathematics
|
A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33kms in 45minutes. The ratio of their speeds is?
|
[
"1:2",
"3:4",
"2:5",
"3:7",
"1:3"
] |
Ratio of speeds = (550/60) 18/5 : 60*33/45 = 33:44 = 3:4
Answer is B
The answer is: B
|
B
|
mathematics
|
If n = 8^8 – 5, what is the units digit of n?
|
[
"0",
"1",
"2",
"3",
"5"
] |
8 ^ 8 - 8 = 8 (8 ^ 7 - 1)
==> 8 (2 ^ 21 - 1)
Last digit of 2 ^ 21 is 2 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit. Now on multiply this with 5, we get unit digit as 5
Answer : E
The answer is: E
|
E
|
mathematics
|
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -7?
|
[
"-1",
"7",
"10",
"11",
"20"
] |
We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
t10 = -4
t11 = -7
So, ourANS is D.
The answer is: D
|
D
|
mathematics
|
A Women can cover a distance in 1 hr 24 min by covering 2/3 of the distance at 4 km/h and the rest at 5 km/h. The total distance is
|
[
"4 km",
"8 km",
"2 km",
"6 km",
"9 km"
] |
D
6 km
Distance = 2/3S
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S * 3
S= 6km
The answer is: D
|
D
|
mathematics
|
How many positive integers less than 5,000 are evenly divisible by neither 13 nor 21?
|
[
"4,514",
"4,475",
"4,521",
"4,428",
"4,349"
] |
integers less than 5000 divisible by 13 5000/13 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 13 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 13 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4349 answer E.
The answer is: E
|
E
|
mathematics
|
A bag contains 50black pens and 60 white pens. One ball is drawn at random. What is the probability that the ball drawn is black?
|
[
"2/3",
"3/14",
"1/7",
"5/11",
"6/13"
] |
total number of pens = 110
number of black pens = 50
drawing a black pens= 50/110 = 5/11
Answer is D
The answer is: D
|
D
|
mathematics
|
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
|
[
"11",
"61",
"88",
"66",
"35"
] |
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E
The answer is: E
|
E
|
mathematics
|
?⁄50 = 60.5⁄?
|
[
"55",
"1512.5",
"52.5",
"57.5",
"None of these"
] |
?⁄50 = 60.5⁄?
or,?2 = 50 × 60.5 or, ?2 = 3025
or, ? = √3025 = 55
Answer A
The answer is: A
|
A
|
mathematics
|
In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are strategy majors?
|
[
"3",
"5",
"8",
"11",
"13"
] |
pqrs = 1365 = 3 * 5 * 7 * 13
Since 1< p < q < r < s, the number of students who are strategy majors is s = 13.
The answer is E.
The answer is: E
|
E
|
mathematics
|
The cost of 6 bags and 8 purses is Rs.1300, what is the cost of 10 bags and 30 purses?
|
[
"Rs.3600",
"Rs.3500",
"Rs.3800",
"Rs.3250",
"None of these"
] |
Explanation:
Cost of 6 bags + 8 purses = Rs.1300
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.3250.
Answer: Option D
The answer is: D
|
D
|
mathematics
|
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
|
[
"20cm",
"40cm",
"30cm",
"60cm",
"50cm"
] |
Let breadth =x cm
Then, length =2x cm
Area =x×2x=2x2 sq.cm.
New length =(2x−5) cm
New breadth =(x+5) cm
New area =(2x−5)(x+5) sq.cm.
Given that, new area = initial area +75 sq.cm.
⇒(2x−5)(x+5)=2x2+75⇒2x2+10x−5x−25=2x2+75⇒5x−25=75⇒5x=75+25=100⇒x=1005=20 cm
Length =2x=2×20=40cm
Answer is B.
The answer is: B
|
B
|
mathematics
|
You keep tossing a fair coin for twenty times. Each time, the coin lands up with tails up.
What is the probability that if you toss it now, the coin will land with heads up this time?
|
[
"30%",
"50%",
"78%",
"72%",
"91%"
] |
B
50%
The probability will be 50% only as it always was. The next flip of coin is not dependent on what the results were in the previous flips.
The answer is: B
|
B
|
mathematics
|
A garage has a bin that is used by an "add stuff" worker and a "throw away" worker. Working alone, the "add stuff" worker can fill the bin in 5 hours. Working alone, the "throw away" worker can empty the bin in 15 hours. If it is desired that the bin should be filled, from empty, exactly 6 hours after the "add stuff" worker begins his shift at 9:30am, then at what time should the "throw away" worker begin his own shift?
|
[
"10:00am",
"10:45am",
"12:00pm",
"12:30pm",
"1:30pm"
] |
In 6 hours the "add stuff" worker can fill the bin equal to 6*1/5 = 6/5 of the bin. So, 1/5 more than necessary, which should be compensated by the "Throw away" worker. To get rid of 1/5 of the inventory the "throw away"worker needs 15/5 = 3 hours.
Therefore, the "throw away" worker should begin his shift at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
The answer is: D
|
D
|
mathematics
|
Find the average of the series : 220, 180, 328, 147 and 160?
|
[
"230",
"200",
"250",
"201",
"207"
] |
Average = (220 + 180 + 328 + 147 + 160)/5
= 1035/5
= 207
Answer: E
The answer is: E
|
E
|
mathematics
|
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
|
[
"20 ft",
"25 ft",
"750 ft",
"900 ft",
"2400 ft"
] |
Point to note: Both the wheels would have traveled the same distance.
Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).
Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 32. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)
Solving this eqn. gives x=75.
Sub x=75 either in (x+5)*30 or in x * 32 to get the distance, which is 2400. So the correct choice is E.
The answer is: E
|
E
|
mathematics
|
Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream.
|
[
"3 kmph",
"9 kmph",
"4 kmph",
"8 kmph",
"6 kmph"
] |
Speed in still water = (13 + 5)1/2 kmph = 9 kmph.
answer :B
The answer is: B
|
B
|
mathematics
|
If 1400*x=1050. The, x=?
|
[
"1.4",
"3/5",
"2/3",
"3/4",
"None of these"
] |
1400*x=1050; x=1050/1400; x =3/4
Correct Option: D
The answer is: D
|
D
|
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