mathewhe/aqua_rat huggingface dataset:
Question: How many 1/4s are there in 37 1/2?
(A) 150
(B) 450
(C) 500
(D) 650
(E) 700
Rationale: Required number = (75/2)/(1/4)
= (75/2 x 4/1)
= 150.
ANSWER:A
Answer: (A) 150
Question: When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7?
Putting a value say x = 19 we get remainder as 19 when divided by 52.
When 19 divided by 7 we get 5 as remainder.
D is the answer.
Answer: (D) 5
Question: A cycle is bought for Rs.800 and sold for Rs.1080, find the gain percent?
(A) 22
(B) 20
(C) 35
(D) 88
(E) 11
Rationale: 800 ---- 180
100 ---- ? => 35%
Answer:C
Answer: (C) 35
Question: The cost of producing x tools by a company is given by
C(x) = 2500 x + 5500 (in $)
a) What is the cost of 100 tools?
(A) 222500 $
(B) 125800 $
(C) 225900 $
(D) 255500 $
(E) 122500 $
Rationale: Solution
C(100) = 2500*100 + 5500 = 255500 $
Answer D
Answer: (D) 255500 $
Question: If n is an integer, then the least possible value of |31 - 4n| is?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: |31 - 4n| represents the distance between 31 and 4n on the number line. Now, the distance will be minimized when 4n, which is multiple of 4, is closest to 31. Multiple of 4 which is closest to 31 is 32 (for n = 8),
so the least distance is 1: |31 - 32| = 1.
Answer: B.
Answer: (B) 1
Question: A can do a job in 10days and B in 20days. If they work on it together for 4 days, then the fraction of the work that is left is?
(A) 2/5
(B) 8/15
(C) 3/11
(D) 1/12
(E) 6/13
Rationale: A's 1 day work = 1/10
B's 1day work = 1/20
A+B 1day work = 1/10 + 1/20 = 3/20
A+B 4days work = 3/20*4 = 3/5
Remaining work = 1 - 3/5 = 2/5
Answer is A
Answer: (A) 2/5
Question: Which of the following inequalities is equivalent to −4 < x < 8?
(A) |x - 1| < 7
(B) |x + 2| < 6
(C) |x + 3| < 5
(D) |x - 2| < 6
(E) None of the above
Rationale: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format
-4+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2
Thus, -6< x-2 < 6 => |x-2| < 6.
Hence, answer is D
Answer: (D) |x - 2| < 6
Question: If (x - 1)^2 = 324, which of the following could be the value of x - 3?
(A) 17
(B) 15
(C) 13
(D) -20
(E) -22
Rationale: (x - 1)^2 = 324
(x - 1) = 18 or -18
x = 19 or -17
x - 3 = 16 or -20
The answer is D.
Answer: (D) -20
Question: The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is?
(A) 52
(B) 53
(C) 54
(D) 55
(E) 56
Rationale: Excluded number = (27 * 5) - (20 * 4)
= 135 - 80
= 55.
Answer: D
Answer: (D) 55
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 118, what is the value of K?
(A)  11
(B)  15 3/4
(C)  22
(D)  118
(E)  25 3/10
Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 118
11K = 118 * 4 +1 = 472 +1 = 473
K = 473 / 11 = 43.
Answer D.
Answer: (D)  118
Question: A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?
(A) 10
(B) 12
(C) 08
(D) 14
(E) 16
Rationale: Let the number be x
22x + 308 = 44x
=> 44x - 22x = 308
=> 22x = 308
=> x = 308/22 = 154/11 = 14
Answer is D.
Answer: (D) 14
Question: The average weight of 2 person's increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 74 kg
(B) 76.5 kg
(C) 85 kg
(D) 78
(E) None of these
Rationale: Explanation:
Total weight increased = (2 x 4.5) kg = 9 kg.
Weight of new person = (65 + 9) kg = 74 kg.
Answer: A
Answer: (A) 74 kg
Question: A pair of articles was bought for $720 at a discount of 10%. What must be the marked price of each of the article?
(A) $300
(B) $500
(C) $350
(D) $400
(E) $600
Rationale: S.P. of each of the article = 720/2 = $360
Let M.P = $x
90% of x = 360
x = 360*100/90 =$400
Answer is D
Answer: (D) $400
Question: A pipe can filled a tank in 40 minutes and another pipe can empty it in 1hour. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes?
(A) 25min
(B) 20min
(C) 15min
(D) 10min
(E) 30min
Rationale: T = 1/2 (25*50 / 50-25) = 25 minutes
Tank is filled in 25 minutes
Answer is A
Answer: (A) 25min
Question: Two people P Q start a race in a circular track in opposite way different but constant speed. First they meet 900m cw from the starting pt. Then they meet 800m ccw from the starting pt. What's the circumference of the circle.
(A) 2600
(B) 2700
(C) 2800
(D) 2900
(E) 2500
Rationale: when they first met 900m cw from the starting pt.
second time, they will meet at 1800 m cw from starting point which is 800 m CCW from starting point.
so circumference of circle = 1800+800 = 2600 m
ANSWER:A
Answer: (A) 2600
Question: In a triangle, the ratio of two angles is 7:2, and the third angle is the difference between the first two angles. What is the smallest angle, in degrees?
(A) 90/11
(B) 120/7
(C) 150/11
(D) 180/7
(E) 25
Rationale: the three angles are 7x, 2x, and (7x-2x)=5x for some value x (to create the ratio)
the three angles of a triangle add up to 180, so 7x+2x+5x = 180
14x = 180
x=180/14
x = 90/7
the smallest angle is 2x = 2*(90/7) = 180/7
D
Answer: (D) 180/7
Question: Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be
(A) 1:3
(B) 2:3
(C) 24:25
(D) 20:22
(E) 3:4
Rationale: =(12000*4):(10000*5)
=48000:50000
=24:25
ANSWER:C
Answer: (C) 24:25
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be.
(A) 60 km/h
(B) 55 km/h
(C) 48 km/h
(D) 70 km/h
(E) 65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=50/60hr=5/6hr
New speed = 40* 6/5 kmph= 48kmph
Answer : C
Answer: (C) 48 km/h
Question: 135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is?
(A) 100.6kg
(B) 142kg
(C) 135kg
(D) 110.8kg
(E) 114kg
Rationale: Quantity of tin in 135kg of A = 135*5/8 = 84kg
Quantity of tin in 145kg of B = 145*2/5 = 58kg
Quantity of tin in the new alloy = 84+58 = 142kg
Answer is B
Answer: (B) 142kg
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $9.65 each. One day, she bought 12 t-shirts. How much money did she spend?
(A) $115.8
(B) $248.75
(C) $200
(D) $171.6
(E) $190
Rationale: $9.65*12=$115.8. Answer is A.
Answer: (A) $115.8
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 14 more transactions than Cal. How much transactions did Jade handled?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 14 more transactions than Cal.
Jade = 66 + 14
= 80
Jade handled = 80 transactions.
Answer: A
Answer: (A) 80
Question: 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 70 sq. cm. Find the length of the rectangle.
(A) 12cm
(B) 14cm
(C) 16cm
(D) 18cm
(E) 20cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 70 => 5x - 25 = 70 => x = 18.
Length of the rectangle = 18 cm.
Answer: Option D
Answer: (D) 18cm
Question: A batsman in his 11th inning makes a score of 69 and their by increasing his average by 1. What is his average after the 11th inning?
(A) 58
(B) 59
(C) 68
(D) 69
(E) 78
Rationale: 10x + 69 = 11(x + 1)
x = 58 + 1 = 59
Answer:B
Answer: (B) 59
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 27
(B) 98
(C) 27
(D) 60
(E) 71
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
Answer:D
Answer: (D) 60
Question: In how many different number of ways 7 boys and 4 girls can sit on a shopa which can accommodate 3 persons?
(A) 800
(B) 900
(C) 200
(D) 990
(E) None
Rationale: Option 'D'
11p3 = 11x10x9 = 990
Answer: (D) 990
Question: Sun Life Insurance company issues standard, preferred and ultra-preferred policies. Among the company's policy holders of a certain age, 50 are standard with the probability of 0.01 dying in the next year, 30 are preferred with a probability of 0.008 of dying in the next year and 20 are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the decreased being a preferred policy holder?
(A) 0.1591
(B) 0.2727
(C) 0.375
(D) 0.2767
(E) None of these
Rationale: Explanation :
The percentage of three different types of policy holders and the corresponding probability of dying in the next 1 year are as follow :
Type, Standard, Preferred, Ultra-Preferred
Percentage	, 50	, 30, 20
Probability, 0.01 , 0.008, 0.007
The expected number of deaths among all the policy holders of the given age [say P] during the next year.
=>T×(50×0.01/100)+(30×0.008/100)+(20×0.007/100).
=>T×(0.88/100).
Where T= Total number of policy holder of age P
If any of these policy holders (who die during the next year) is picked at random, the probability that he is a preferred policy holder is :-
=>((30x0.88xT)/100)/ (Tx(0.88/100)).
=>24/88.
=>3/11.
=>0.2727.
Answer : B
Answer: (B) 0.2727
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 25 kmph
(B) 32 kmph
(C) 40 kmph
(D) 38 kmph
(E) 92 kmph
Rationale: S = (100 + 300)/45 = 400/45 * 18/5 = 32 kmph
answer :B
Answer: (B) 32 kmph
Question: Nine friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
(A) 5%
(B) 10%
(C) 20%
(D) 25%
(E) 33%
Rationale: Let x be the original price of one ticket.
The total original cost is 9x.
The new cost is 10y, where y is the discounted price of one ticket.
9x = 10y
y = 9x/10 = 0.9x which is a discount of 10%.
The answer is B.
Answer: (B) 10%
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
(A) 228
(B) 267
(C) 911
(D) 205
(E) 212
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer: D
Answer: (D) 205
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2.91 m
(B) 3 m
(C) 5.82 m
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Area of the park = (60 x 40) m2 = 2400 m2
Area of the lawn = 2109 m2
Area of the crossroads = (2400 - 2109) = 291
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
=> x2 - 100x + 291 = 0
=> (x - 97)(x - 3) = 0
=> x = 3
Answer: B
Answer: (B) 3 m
Question: 15.06 * 0.000001 = ?
(A) 15060000
(B) 0.001506
(C) 0.01506
(D) 1.506e-05
(E) None of these
Rationale: Explanation:
Clearly after decimal 8 digits should be there.
Option D
Answer: (D) 1.506e-05
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
(A) 720
(B) 420
(C) 450
(D) 350
(E) 5040
Rationale: Explanation:
The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters =10X9X8
=720
ANSWER IS A
Answer: (A) 720
Question: A fish tank is half full of water. If 10 gallons of water were added, the tank would be 7/8 full. What is the capacity of the tank (in gallons)?
(A) 11 3/7
(B) 22 3/7
(C) 26 2/3
(D) 30 3/8
(E) 32 1/8
Rationale: Solution -
Let capacity of tank be X gallons.
Water level increased to 7/8 from 1/2 when 10 gallons of water added ---> (7/8 - 1/2)*X = 10
X = 80/3 = 26 2/3.
ANS C.
Answer: (C) 26 2/3
Question: For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution?
(A) 15
(B) 16
(C) 18
(D) 19
(E) 17
Rationale: Solve the first equation 2x + 4 = 4(x - 2) to obtain .
x = 6
Substitute x by 6 (same solution) in the second equation and solve for k.
- 6 + k = 2(6) - 1
solve for k.
k = 17
correct answer E
Answer: (E) 17
Question: The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
(A) 400
(B) 360
(C) 480
(D) 320
(E) 380
Rationale: T.D.	=	B.D. x 100 / 100 + (R x T)
= Rs.(420 x 100	/ 100 + (15 x 1/3))
= Rs. (420 x 100 / 105)
= Rs. 400.
Correct Answer is A.
Answer: (A) 400
Question: A worker is paid a regular rate of Rs.20 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 10% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?
(A) 570
(B) 670
(C) 1070
(D) 470
(E) 2070
Rationale: amount earned by using her cell phone = 35 * 22 = 770
amount earned as usual = 15 * 20 = 300
Total = 770+300 = 1070
Answer : C
Answer: (C) 1070
Question: Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements Q are possible?
(A)  30
(B)  60
(C)  90
(D)  180
(E)  540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements Q including the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X--	Y--	Z
12--	34--	56
12--	56--	34
34--	12--	56
34--	56--	12
56--	12--	34
56--	34--	12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..=C
Answer: (C)  90
Question: A batsman in his 19th inning makes a score of 100 and their by increasing his average by 2. What is his average after the 19th inning?
(A) 58
(B) 60
(C) 62
(D) 64
(E) 66
Rationale: 18x + 100 = 19(x + 2)
x = 62 + 2 = 64
Answer:D
Answer: (D) 64
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 13 brown mice in the experiment, how many mice in total are in the experiment?
(A) 39
(B) 33
(C) 26
(D) 21
(E) 10
Rationale: Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 13
=> M = 39
Answer A
Answer: (A) 39
Question: If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = 6
10 * 11 = ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: B
2
Logic :
40*14=560=5+6+0=11
30*13=390=3+9+0=12
20*12=240=2+4+0=6
So 10*11=110=1+1+0=2
Answer: (B) 2
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 288
(B) 665
(C) 168
(D) 127
(E) 664
Rationale: Explanation:
8 * 84 = 672 â€“ 7 = 665
Answer:B
Answer: (B) 665
Question: How many integers are there between 55 and 108, inclusive?
(A) 51
(B) 54
(C) 56
(D) 57
(E) 58
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (108 - 55) + 1 =54. Option B
Answer: (B) 54
Question: 3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions?
(A) (A + B)2 - 4AB
(B) (A – B)2 + 4AB
(C) A2 + B2 - 4AB + 2AB
(D) A2 – B2 + 2B(B – A)
(E) None of these
Rationale: 1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB
2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB
3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB
4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB
Therefore, (1) = (3) = (4) ≠ (2)
Therefore, expression (2) is wrong
ANSWER IS B
Answer: (B) (A – B)2 + 4AB
Question: P is three times as fast as Q and working together, they can complete a work in 36 days. In how many days can Q alone complete the work?
(A) 16
(B) 48
(C) 88
(D) 55
(E) 778
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 36 days, which means Q can do the work in 144 days.
Hence, P can do the work in 48 days.
Answer:B
Answer: (B) 48
Question: Difference between two numbers is 5, six times of the smaller lacks by 8 from the four times of the greater. Find the numbers?
(A) 5,1
(B) 7,3
(C) 9,8
(D) 11,6
(E) 13,7
Rationale: Explanation:
x – y = 5
4x – 6y = 8
x = 11 y = 6
D)
Answer: (D) 11,6
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 12
(B) 13
(C) 15
(D) 16
(E) 18
Rationale: 2 day work = 1/20*2=1/10
A+B+C 1 day work = 1/10
work done in 3 days = 1/5
1/5 work is done in 3 days
whole work will done in (3*5)=15 days
Answer: (C) 15
Question: Some of 10%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 15%. What fraction of the original paint was replaced?
(A) 2/5
(B) 2/3
(C) 1/2
(D) 1/3
(E) 1/5
Rationale: Let total paint = 1
Let amount replaced = x
10 (1-x) + 20x = 15
x = 1/2
ANSWER:C
Answer: (C) 1/2
Question: Solve x2 â€“ 7x = 0
(A) 0,7
(B) 1.7
(C) 2.7
(D) 3,7
(E) 4,7
Rationale: This quadratic factors easily: Copyright Â© Elizabeth Stapel 2002-2011 All Rights Reserved
x2 â€“ 7x = 0
x(x â€“ 7) = 0
x = 0 or x â€“ 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
ANSWER A
Answer: (A) 0,7
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
(A) 30, 40
(B) 30, 46
(C) 30, 29
(D) 31, 40
(E) 30, 90
Rationale: Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Answer: A
Answer: (A) 30, 40
Question: Can you analyze what is the probability of meeting someone in your lifetime who is having an above average no of arms?
(A) impossible
(B) unlikely
(C) fifty fifty
(D) fairly likely
(E) Certain
Rationale: Correct Answer : E
The average number of arms is less than 2
Answer: (E) Certain
Question: Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business?
(A) $11,000
(B) $50,000
(C) $16,500
(D) $ 6,600
(E) $ 3,600
Rationale: Total Investment between 5: (x/5)
Total investment including 2200 less between 3 people(x-(2200*3))/3
Set both eq. equal to each other.
16,500
Answer C)
Answer: (C) $16,500
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 15
(B) 77
(C) 25
(D) 18
(E) 12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer:C
Answer: (C) 25
Question: A car dealer has only blue and white cars in his show room. He has 24 blue cars and 30 white cars. He wants to have 60% more blue cars then white. How many whites cars does he have to sell to achieve his sales goal?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: We can use simple arithmetic to solve this problem by testing our answers.
Lets test B:
If he sold 13 white cars:
24 blue cars and 17 white cars for a total of 41 cars
24/41=58.5% not quite our answer
Lets test C
If he sold 14 white cars
24 blue cars and 16 white cars for a total of 40 cars
24/40=60%
Our answer is C
Answer: (C) 14
Question: if x:y = 1:5, then find the value of
(7x+3y):(2x+y)
(A) 14:5
(B) 15:5
(C) 16:5
(D) 22:7
(E) None of these
Rationale: Explanation:
let x = 1k and y = 5k, so
=7(k)+3(5k)/ 2(k)+1(5k)
=22k/7k
=22:7
Option D
Answer: (D) 22:7
Question: If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
(A) 43
(B) 40
(C) 87
(D) 77
(E) 22
Rationale: A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75 = 40.
Answer:B
Answer: (B) 40
Question: The denominator of a fraction is 6 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 4â„5. What is the value of the original fraction?
(A) 17/23
(B) 23/29
(C) 29/35
(D) 31/37
(E) 33/39
Rationale: Let the numerator be x.
Then the denominator is x+6.
x+1 / x+7 = 4/5.
5x+5=4x+28.
x=23.
The original fraction is 23/29.
The answer is B.
Answer: (B) 23/29
Question: An article is bought for Rs.600 and sold for Rs.1000, find the gain percent?
(A) 73 1/3%
(B) 63 1/3%
(C) 33 1/3%
(D) 66.66%
(E) 33 1/3%
Rationale: Explanation:
600 ---- 400
100 ---- ? => 66.66%
Answer:D
Answer: (D) 66.66%
Question: The function f is defined by subtracting 25 from the square of a number and the function c is defined as the square root of one-half of a number. If c(f(x))=10, then which of the following is a possible value of x?
(A) -15
(B) -5
(C) 0
(D) 5
(E) 25
Rationale: f(x) = x^2-25
c(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
c(f(x)) = 10
c(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: (A) -15
Question: Seven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
(A) 7 years
(B) 5 years
(C) 3 years
(D) 8 years
(E) 10 years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 25
= (25+ 7) * 2 = 64 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 64 = 5 years
Answer: Option B
Answer: (B) 5 years
Question: A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles
(A) 60bm/c
(B) bm/60c
(C) bc/60m
(D) 60b/cm
(E) None of these
Rationale: Explanation:
Substitute sensible numbers and work out the problem. Then change the numbers back to letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put 6 /2 caps on per minute, or (6 /2) x 60 caps per hour. Putting letters back this is 60c/m.If you divide the required number of caps (b) by the caps per hour you will get time taken in hours. This gives bm/60c
Answer: B
Answer: (B) bm/60c
Question: How many positive integers less than 100 are there such that they are multiples of 13 or multiples of 12 but not both?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: for 13: 13...91=13*7 = 7
for 12: 12...96=12*8 =8
but there is no integer 13*12. so
N=(7)+(8)=15
A
Answer: (A) 15