mathewhe/aqua_rat huggingface dataset:
Question: What will be the day of the week 15th August, 2010?
(A) Thursday
(B) Sunday
(C) Monday
(D) Saturday
(E) None of these
Rationale: Explanation :
15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday
Answer : Option B
Answer: (B) Sunday
Question: A is twice as good workman as B, and together they complete a work in 10 days. In how many days can the work be complete by B alone?
(A) 35 days
(B) 30 days
(C) 45 days
(D) 75 days
(E) 95 days
Rationale: B=3A
30 days
B
Answer: (B) 30 days
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 20 ps per meter is?
(A) s.122
(B) s.129
(C) s.125
(D) s.95
(E) s.121
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 20) = 190 m
190 * 1/2 = Rs.95
Answer:D
Answer: (D) s.95
Question: What will be the cost of building a fence around a square plot with area equal to 36 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2882
(C) 2999
(D) 2667
(E) 1392
Rationale: Let the side of the square plot be a ft.
a2 = 36=> a = 6
Length of the fence = Perimeter of the plot = 4a = 24ft.
Cost of building the fence = 24 * 58 = Rs. 1392.
Answer: E
Answer: (E) 1392
Question: 36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203. What is the first part?
(A) 15
(B) 19
(C) 23
(D) 24
(E) 25
Rationale: Explanation:
Let the first part be x.
8x + 3 (36 – x) = 203
8x + 108 – 3x = 203
5x + 108 = 203
5x = 95
x = 19
ANSWER: B
Answer: (B) 19
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 16 heads and 41 legs. How many cats does the ship host?
(A) 5
(B) 6
(C) 4
(D) 7
(E) 8
Rationale: sa's +co +ca +cats = 16. sa's + 1 +1 +cats =16 or sa's +cats =14.
sa's(2) +2 +1 +cats*4 =41 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 14-cats +cat*2 =19
then cats =5
A
Answer: (A) 5
Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for?
(A) 12 days
(B) 12 1/4 days
(C) 14 days
(D) 24 1/2 days
(E) None of these
Rationale: Let total money be Rs. x
A's 1 day's wages=Rs.x/21, B's 1 day's wages=Rs.x/28
(A+B)'s 1 day's wages=Rs.(x/21+x/28)=Rs.x/12;
Money is sufficient to pay the wages of both for 12 days.
Correct Option: A
Answer: (A) 12 days
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6360, what is the length of the plot in metres?
(A) 70
(B) 200
(C) 300
(D) 400
(E) 140
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6360
[4L - 40] = 6360 / 26.50 = 240
4L = 280
L = 280/4= 70 meters. Answer: A
Answer: (A) 70
Question: A thief steels a car at 3p.m. and drives it at 20kmph. The theft is discovered at 4p.m. and the owner sets off in another car at 40 kmph. When will he overtake the thief?
(A) 9p.m.
(B) 9.30p.m.
(C) 5p.m.
(D) 6a.m.
(E) 10.15 p.m.
Rationale: Suppose the thief overtakes x hours after 6a.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)
20x = 40(x-1)
20x = 40
x = 2 hrs
Thief is overtaken at 5p.m.
Answer is C
Answer: (C) 5p.m.
Question: In a partnership between A, B and C. A's capital is Rs.6000. If his share of a profit of Rs.700 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) Rs.11000
(B) Rs.11600
(C) Rs.11700
(D) Rs.11100
(E) Rs.11200
Rationale: 200 + 130 = 330
700 - 330 = 370
200 ---- 6000
370 ---- ? => 11100
ANSWER:D
Answer: (D) Rs.11100
Question: The speed at which a boy can row a boat in still water is 36 kmph. If he rows downstream, where the speed of current is 54 kmph, what time will he take to cover 750 metres?
(A) 29
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: Speed of the boat downstream = 36 + 54 = 90 kmph
= 90 * 5/18 = 25 m/s
Hence time taken to cover 750 m = 750/25 = 30 seconds.
Answer: B
Answer: (B) 30
Question: If log√8 x = 3×1/3, find the value of x.
(A) 25
(B) 32
(C) 37
(D) None of these
(E) Cannot be determined
Rationale: Solution
log√8 x	= 10/3.
x	=( √8)10/3
=2( 3/2×10/3)
=2 5
= 32.
Answer B
Answer: (B) 32
Question: If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of
Rs. 1000
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
Clue: Answer will be 5% of 1000 - 4% of 1000
Answer: Option A
Answer: (A) 10
Question: The measurements obtained for the interior dimensions of a rectangular box are 50 cm by 50 cm by 75cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
(A) 12,000
(B) 13,000
(C) 14,000
(D) 10,000
(E) 15,000
Rationale: The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*50*75 = 3750 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 50*1*75 = 3750 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 50*50*1 = 2500 cubic centimeters.
So, approximate maximum possible difference is 3750 + 3750 + 2500 = 10,000 cubic centimeters.
Answer: D.
Answer: (D) 10,000
Question: What is the remainder when 7^74 - 5^74 is divided by 8?
(A) 0
(B) 2
(C) 0
(D) 3
(E) None of these
Rationale: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (48+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans : C
Answer: (C) 0
Question: 7 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2 candidates. In how many ways can one cast his vote?
(A) 41
(B) 42
(C) 45
(D) 46
(E) 47
Rationale: There are 10 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 10C2 = 45.
C
Answer: (C) 45
Question: The ratio of number of boys and girls in a school is 2:7. If there are 360 students in the school, find the number of girls in the school?
(A) 150
(B) 250
(C) 300
(D) 370
(E) 280
Rationale: Let the number of boys and girls be 2x and 7x
Total students = 360
Number of girls in the school = 7*360/9 = 280
Answer is E
Answer: (E) 280
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 2 cups of tea. Last week Mo drank a total of 16 cups of tea and hot chocolate together. If during that week Mo drank 4 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 6
(B) 3
(C) 4
(D) 5
(E) 2
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 16 T-C=4 -> T= 10. C=6.
Mo drinks 5 cups of tea a day then number of days that are not rainy = 10/2 = 5
So number of rainy days = 7-5 = 2
E is the answer.
Answer: (E) 2
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?
(A) 2
(B) 8
(C) 7
(D) 3
(E) 10
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 72,000 m : C is the circumference
C = 3 meters
Answer: (D) 3
Question: If the length of the sides of two cubes are in the ratio 7:1, what is the ratio of their total surface area?
(A) 7:1
(B) 14:1
(C) 21:1
(D) 42:1
(E) 49:1
Rationale: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(7x)^2=294x^2.
The ratio of surface areas is 49:1.
The answer is E.
Answer: (E) 49:1
Question: The food in a camp lasts for 40 men for 45 days. If ten more men join, how many days will the food last?
(A) 32days
(B) 34days
(C) 36days
(D) 38days
(E) 40days
Rationale: one man can consume the same food in 40*45 = 1800 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1800/50 = 36 days.
Answer: C
Answer: (C) 36days
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 3940 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
(A) 2160
(B) 2350
(C) 2000
(D) 2300
(E) None of these
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+3940 = 19440
Exp in % = 100-10 = 90%, 19440 = 90%
Saving = 10 % = 19440 X 10/90 = Rs. 2160
Answer : A
Answer: (A) 2160
Question: A train passes a station platform in 33 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 228
(B) 240
(C) 887
(D) 195
(E) 1811
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/33 = 15 => x = 195 m.
Answer: D
Answer: (D) 195
Question: A tourist purchased a total of $1,600 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,370
(C) $1,290
(D) $1,270
(E) $1,150
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1600 - 230 = 1370 hence answer is B
Answer: (B) $1,370
Question: A data set with a mean of 60 has a standard deviation of 1.5. Which of the following is the smallest number that falls within one standard deviation of the mean?
(A) 53
(B) 56
(C) 58
(D) 63.5
(E) 65
Rationale: One standard deviation of the mean is from{mean}-{deviation}=60-1.5=58.5 to{mean}+{deviation}=60+1.5=61.5. The smallest number within this range from the options is 58.
Answer: C.
Hope this helps.
Answer: (C) 58
Question: 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 W odds that it is an ace?
(A) 1/52
(B) 1/26
(C) 1/13
(D) 1/4
(E) 5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability W that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: (C) 1/13
Question: 2 numbers are there in the ratio 1:3. If 4 is to be added to both of the numbers the ratio will become 4:9 then find initial numbers?
(A) 6,7
(B) 6.7,20.1
(C) 5.6,13.7
(D) 12.6,15.3
(E) 4.6,18.6
Rationale: Let 2 numbers are x,3x
after adding 3 on both numbers x+4, 3x+4
x+4:3x+4 = 4:9
9(x+4) = 4(3x+4)
x = 6.7
Intial numbers = 3x,4x = 6.7,20.1
Answer is B
Answer: (B) 6.7,20.1
Question: Monisha are used to buy a video game for $40. Lately, these games were subject to 20% price increase. What is the new price of the video game?
(A) $46
(B) $47
(C) $48
(D) $49
(E) $45
Rationale: Solution:
The price increase is 40 x 20/100 = $8
The new price is 40 + 8 = $48
Answer C
Answer: (C) $48
Question: If x = (y)(y + 1) and y is a prime number less than 8, which of the following could not be the product of 2 consecutive integers?
(A) a) 5x
(B) b) 11x
(C) c) 13x
(D) d) 57x
(E) e) 21x
Rationale: Given y is a prime number less than 11
possible values of y are 2 3 5 7
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
if y = 7 x=7*8=56
so possible values of x are 6,12,30,56
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 57x can be (56*57)
E. 21x cannot be
So answer option E
Answer: (E) e) 21x
Question: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 4 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
(A) 2
(B) 9
(C) 15
(D) 18
(E) 30
Rationale: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.
Then under plan A the cost would be $0.6+0.06(t-4) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-4)=0.08t --> 60+6(t-4)=8t --> t=18.
Answer: D.
Answer: (D) 18
Question: There are two sections P and Q of a class, consisting of 144 and 176 students respectively. If the average weight of sections A is 160 kg and that of sections Q is 140 kg. Find the average weight of the whole class
(A) 147.5
(B) 148.0
(C) 148.5
(D) 149.0
(E) None
Rationale: Solution
Total weight of(144+176)Students	= (144x160+176x140)Kg
= 47680 kg.
Average weight of the whole class	= (47680 / 320)
= 149.00.
Answer D
Answer: (D) 149.0
Question: A trader bought a car at 20% discount on its original price. He sold it at a 45% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 72%
(C) 12%
(D) 82%
(E) 16%
Rationale: Original price = 100
CP = 80
S = 80*(145/100) = 116
100 - 116 = 16%
Answer:E
Answer: (E) 16%
Question: Pipe P can drain the liquid from a tank in 2/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
(A) 3/13
(B) 8/23
(C) 3/8
(D) 17/29
(E) 3/4
Rationale: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(2/4)rQ] = 4/2
Also, rP = rR/(2/3) => 2 = rR/(2/3) => rR = 4/3
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 2 + 4/3 = 13/3 = 1/(3/13)
Thus running simultaneously, Pipe Q will drain 3/13 of the liquid.
Thus answer = A.
Answer: (A) 3/13
Question: On a certain island, 5% of the 10000 inhabitants are one-legged and half of the others go barefooted. What is the least number of Shoes needed in the island?
(A) 10200
(B) 10000
(C) 9500
(D) 9000
(E) None
Rationale: Explanation :
=> One-legged =5% of 10000=500
=> Remaining=10000-500=9500
=> Barefooted=9500/2=4750
=> Remaining people= 9500-4750=4750
=> Hence required number of shoes= 4750*2+500*1=10000
Hence (B) is the correct answer.
Answer : B
Answer: (B) 10000
Question: A can do a piece of work in 13 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 15 10/11 days
(B) 10 10/11 days
(C) 12 10/11 days
(D) 19 10/11 days
(E) 13 10/11 days
Rationale: B
(x â€“ 5)/13 + x/20 = 1
x = 10 10/11 days
Answer: (B) 10 10/11 days
Question: If the price of petrol increases by 25% and Kevin intends to spend only 15% more on petrol. By how much percent should he reduces the quantity of petrol that he buys?
(A) 8
(B) 9
(C) 7
(D) 2
(E) 6
Rationale: Explanation:
Let Petrol Price 100 per Liter and Quantity he purchases equals to 100 Liters
Then total expenditure = 100 × 100 = 10000
Petrol Price is increased by 25%. So new price = 125 per litre
And he increases the expenditure by 15%. So expenditure limit = 11500
Now his quantity = 11500/125 = 92 liters
So the quantity is reduced by 8%
Answer: A
Answer: (A) 8
Question: A train 360 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 30 sec
(C) 26 sec
(D) 27 sec
(E) 34 sec
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/50
= 30 sec
Answer: B
Answer: (B) 30 sec
Question: what is average of 2000 terms of the given series
1,-3,2,-4,3,-5,4,....
(A) 1
(B) 0.5
(C) -0.5
(D) -1
(E) -2
Rationale: 1-3=-2
2-4=-2
3-5=-2...
we get 1000 -2s for 2000 numbers.
for 2000 terms the average= -2(1000)/2000
= -1
ANSWER:D
Answer: (D) -1
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/5 % his yearly income diminishes by Rs.61.50. his capital is
(A) 153.75
(B) 37.78
(C) 246.0
(D) 27.88
(E) 127.71
Rationale: Explanation:
Capital = Rs.x , then
2/5x = 153.75
Answer: A) Rs.153.75
Answer: (A) 153.75
Question: A clock shows the time as 9 a.m. If the minute hand gains 7 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 30 min
(B) 35 min
(C) 63 min
(D) 50 min
(E) 55 min
Rationale: there are 9 hours in between 9 a.m. to 6 p.m.
9*7=63 minutes.
ANSWER:C
Answer: (C) 63 min
Question: Which of the following is the smallest multiple of 3!-4?
(A) 4!-22
(B) 4!-10
(C) 3!+1
(D) 4!+20
(E) 3!+4
Rationale: The expression 3!-4 can be expanded out to (3*2)-4
Therefore (3*2)-4=6-4=2
Looking at the options the one that gives the lowest multiple of 2 is option A)
Answer: (A) 4!-22
Question: The average age of 16 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 12th student is
(A) 11
(B) 66
(C) 18
(D) 16
(E) 42
Rationale: Explanation:
Age of the 16th student = [16 * 16 - (14 * 5 + 16 * 9)] = (256-214) = 42 years.
Answer: E
Answer: (E) 42
Question: What quantity of water should taken out to concentrate 15 liters of 40% acidic liquid to 60% acidic liquid?
(A) 5liters
(B) 10liters
(C) 15liters
(D) 8liters
(E) 6liters
Rationale: Required answer is = 15(60-40)/60 = 5 liters
Answer is A
Answer: (A) 5liters
Question: ((-1.9)(0.6) – (2.6)(1.2))/4.0 = ?
(A) -0.71
(B) 1.0
(C) 1.07
(D) 1.71
(E) -1.065
Rationale: Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/4.0 = -1.065
Answer E
Answer: (E) -1.065
Question: the ratio of water and milk is 2:3.after adding 4litre milk ratio become 1:2? calculate amount of water?
(A) 6
(B) 8
(C) 5
(D) 10
(E) 12
Rationale: water is 2x and milk is 3x.
2x/3x+4=1/2,4x=3x+4,x=4
amount of water=2x=8 litre
answer B
Answer: (B) 8
Question: What day of the week will 22 Apr 2222 be?
(A) Monday
(B) Tuesday
(C) Sunday
(D) Thursday
(E) None of these
Rationale: Explanation :
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday. Answer : Option A
Answer: (A) Monday
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 9%. If Ron imported a $18,000 imported car and ended up paying $1950 in taxes, what is the first tier's price level?
(A) $11500
(B) $11000
(C) $12000
(D) $12100
(E) $12500
Rationale: Let T be the tier price, P be total price = 18000
Per the given conditions:
0.12T + 0.09(P-T) = 1950
0.12T+0.09*18000-0.09T =1950
0.03T +1620 = 1950
0.03T = 1950-1620 = 330
T = 330/0.03 =11000
Answer B
Answer: (B) $11000
Question: The value of (9x10^7)(3x10^8) is closest to which of the following?
(A) 10^11
(B) 10^12
(C) 10^13
(D) 10^17
(E) 10^18
Rationale: multiplying these we get,
27 x 10^7 x 10^8
= 2.7 x 10^16
which is closer to 10^17
Answer: D
Answer: (D) 10^17
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.6
(B) 1.2
(C) 1.9
(D) 1.3
(E) 1.5
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: E
Answer: (E) 1.5
Question: A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 6 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.
If 6 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.
8k-5k = 6
k = 2
8k + 10k = 16 + 20 = 36
The answer is D.
Answer: (D) 36
Question: What will be the cost of building a fence around a square plot with area equal to 81 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2287
(C) 2977
(D) 2088
(E) 1298
Rationale: Let the side of the square plot be a ft.
a2 = 81=> a = 9
Length of the fence = Perimeter of the plot = 4a = 36ft.
Cost of building the fence = 36 * 58 = Rs. 2088.
Answer:D
Answer: (D) 2088
Question: The average age of 29 students in a group is 15 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
(A) 31
(B) 36
(C) 29
(D) 53
(E) 57
Rationale: age of the teacher=(29*16-29*15)
=29 years.
ANSWER:C
Answer: (C) 29
Question: If 0.60 : x : : 6 : 2, then x is equal to
(A) 0.2
(B) 0.5
(C) 2.5
(D) 1.8
(E) None
Rationale: Sol.
(x×6) = (0.60×2) ⇒ x = 0.60/6 = 0.2.
Answer A
Answer: (A) 0.2
Question: Of the mutual funds on a “select list,” 1/2 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?
(A) 500
(B) 750
(C) 1,000
(D) 1,200
(E) 1,500
Rationale: C
Fraction of 5- and 4-star funds: 1/2 + (2/5)*(1/2) = 1/2 + 1/5 = 7/10
Fraction of 3-star funds = 1 - 7/10 = 3/10
(3/10)*Total = 300
Total = 1000
Answer: (C) 1,000
Question: What will come in place of the x in the following number series? 12, 26, 54, 110, 222, x
(A) 444
(B) 446
(C) 448
(D) 452
(E) 454
Rationale: 1212 × 2 + 2 = 2626 × 2 + 2 = 5454 × 2 + 2 = 110110 × 2 + 2 = 222222 × 2 + 2 = 446 B
Answer: (B) 446
Question: What approximate value should come in place of the question mark (?) in the following equation?
248.251 ÷ 12.62 × 20.52 = ?
(A) 400
(B) 450
(C) 600
(D) 350
(E) 375
Rationale: 248.251 ÷ 12.62 × 20.52 = ?
or,? ≈ 240 ÷ 12 × 20 = 20 × 20 = 400
Answer A
Answer: (A) 400
Question: A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 feet per second and through steel at 16,500 feet per second. How far away is that spike?
(A) 7070.25
(B) 7080.25
(C) 6070.25
(D) 8070.25
(E) 7170.25
Rationale: d = 1100(t + 6 ), d = 16500t, so 1100(t + 6) = 16500t
1100t + 6600 = 16500t, 1100t - 1100t + 6600 = 16500t-1100t, 6600 = 15400t
6600/15400 = 15400t/15400, 0.4285 = t, 1100(.4285 + 6) = 7071.35, 16500(.4285) = 7070.25
ANSWER:A
Answer: (A) 7070.25