mathewhe/aqua_rat huggingface dataset:
Question: A person travelled from his house to office at 30km/hr and office to house at 15km/hr. Then find the average speed?
(A) 15km/hr
(B) 20km/hr
(C) 32km/hr
(D) 24km/hr
(E) 25km/hr
Rationale: Average speed = (2*30*15)/(30+15)
= 20km/hr
Answer is B
Answer: (B) 20km/hr
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.8
(B) 12.5
(C) 12.9
(D) 12.1
(E) 12.2
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: B
Answer: (B) 12.5
Question: How many multiples of 5 are less than 5000, and also multiples of 50?
(A) 100
(B) 208
(C) 625
(D) 832
(E) 833
Rationale: The LCM of 5 and 50 is 50. Divide 5000/50 = 100.xxx. So A is your answer.
Answer: (A) 100
Question: If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number?
(A) 10
(B) 60
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
6:7
6x + 10 : 7x + 10 = 7 : 8
8[6x + 10] = 7[7x + 10]
48x + 80 = 49x + 70
49x - 48x = 80 - 70
x = 10
Then smallest number is = 6
6x = 60
Answer: Option B
Answer: (B) 60
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 12:8:7, respectively, by weight. If 54 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
(A) 15
(B) 10
(C) 9
(D) 6
(E) 4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 12x : 8x : 7x
We are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
12x + 8x + 7x = 54
27x = 54
x = 2
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (7)(2) = 14
pounds of apples = (12)(2) = 24
Thus we know that there are 24-14 = 10 more pounds of apples than grapes.
Answer is B.
Answer: (B) 10
Question: In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 5 sec
(B) 4 sec
(C) 3 sec
(D) 6 sec
(E) 1 sec
Rationale: T = 30/36 * 18/5 = 3 sec
Answer: C
Answer: (C) 3 sec
Question: Angelina walked 600 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 2
(B) 3
(C) 4
(D) 9
(E) 12
Rationale: let the speed be X...
so time taken from home to grocery= 600/x..
the speed to gym = 2x..
so time taken = 480/2x=240/x..
its given 600/x-240/x=40..
360/x=40..
x=9m/secs..
so grocery to gym=2*9=18m/s...
D
Answer: (D) 9
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?
(A) 10
(B) 15
(C) 22.5
(D) 30
(E) 67.5
Rationale: Plug in the answer choices!
A --- 30/2 + 15 = 30 --- wrong
B --- 45/2 + 15 = not an integer --- wrong
C --- 22.5(3/2) + 15 = not an integer --- wrong
D --- 90/2+15 = 60 --- CORRECT
ANSWER:D
Answer: (D) 30
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (296 + 1)
(B) (216 + 1)
(C) (216 - 1)
(D) (217 - 1)
(E) None
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
Option A
Answer: (A) (296 + 1)
Question: If ‘DELHI’ is coded as ‘FGNJK’, then ‘PUNE’ is coded as
(A) RWPG
(B) TGFR
(C) UHTG
(D) WEDS
(E) OKJY
Rationale: D= 4 = 4+2 = 6 = F
E = 5 = 5+2= 7= G
SIMILARLY,
P = 16 = 16+2 = 18 =R
U = 21 = 21+2 =23 =W
N = 14 = 14+2 =16 = P
E = 5 = 5+2 = 7 = G
SO ANS IS
RWPG
Answer: (A) RWPG
Question: David and Lewis leave Chennai for Hyderabad simultaneously at 8 P.M in the night driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Hyderabad he returns back to Chennai along the same route and meets David on the way back. If the distance between the two cities is 350 miles, how far from Chennai did David and Lewis meet?
(A) 250 miles
(B) 240 miles
(C) 230 miles
(D) 235 miles
(E) 75 miles
Rationale: Time taken by Lewis to reach Hyderabad = 350/70 = 5 hours
In 5 hours, David travels 50*5 = 250 miles
So distance at which they meet should be greater than 250 miles.
Only A satisfies.
Answer is A.
Answer: (A) 250 miles
Question: How many Q ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
(A) 3
(B) 16
(C) 28
(D) 32
(E) 56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen Q= 56 - 24 = 32
Ans: D
Answer: (D) 32
Question: In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
(A) 25
(B) 30
(C) 75
(D) 40
(E) 56
Rationale: 8p2 = 8 x 7 = 56
E)
Answer: (E) 56
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $450 kilograms of pears that day, how many kilograms did he sell in the afternoon?
(A) 120
(B) 180
(C) 300
(D) 280
(E) 320
Rationale: 3x=450
x=150
Therefore, the salesman sold 150kg in the morning and 2⋅150=300 kg in the afternoon. So answer is C.
Answer: (C) 300
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
A. 20/31
(A) 80/63
(B) 20/63
(C) 20/93
(D) 20/03
(E) 20/53
Rationale: Explanation:
Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63
Answer: Option B
Answer: (B) 20/63
Question: In a certain supermarket, a triangular display of cans is arranged in 9 rows, numbered 1 through 9 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 120 cans in the entire display, how many cans are in the seventh row?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Let x be the number of cans in row 1.
The total number of cans is x + (x+3) + ... + (x+24) =
9x + 3(1+2+...+8) =
9x + 3(8)(9)/2 =
9x + 108
Since the total is less than 120, x must equal 1.
The number of cans in the 7th row is 1 + 3(6) = 19
The answer is D.
Answer: (D) 19
Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
(A) 20 kmph
(B) 17 kmph
(C) 15 kmph
(D) 14 kmph
(E) 13 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance
= 40 * 3x = 120x km
He covered 2/3 * 120x
= 80x km in 1/3 * 3x
= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed
= 40x/2x = 20 kmph.
Answer:A
Answer: (A) 20 kmph
Question: If a and b are the two values of t that satisfy
the equation t^2 â€“ 12t + 20 = 0, with a > b, what is the value of a â€“ b?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Factor the left side of the equation:
t^2 â€“ 12t + 20 = 0
(t â€“ 2)(t â€“ 10) = 0
t = 2, t = 10
Thus, a = 10 and b = 2. So a â€“ b = 10 â€“ 2 = 8.
The answer is D.
Answer: (D) 8
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 2877
(C) 2769
(D) 2776
(E) 9871
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer:A
Answer: (A) 1000
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?
(A) 3377
(B) 2688
(C) 2688
(D) 8436
(E) 1268
Rationale: A = 7500(26/25)^3 = 8436
Answer: D
Answer: (D) 8436
Question: Which is the odd number out?
9421, 7532, 9854, 8612, 6531, 8541
(A) 8612
(B) 8626
(C) 2579
(D) 6642
(E) 7493
Rationale: C
8612.
All the other numbers have their digits in descending order.
Answer: (A) 8612
Question: Which of the following can be a perimeter q of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
(A) I only
(B) III only
(C) II and III only
(D) I, II, and III
(E) Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: q>0.
Answer is D.
Answer: (D) I, II, and III
Question: A car is purchased on hire-purchase. The cash price is $23 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment?
(A) $503
(B) $504
(C) $515
(D) $543
(E) $552
Rationale: Explanation:
Cash price = $23 000
Deposit = 10% Ã— $23 000 = $2300
Loan amount = $23000 âˆ’ $2300
Number of payments = 60
= $20700
I=p*r*t/100
I=12420
Total amount = 20700 + 12420 = $33120
Regular payment = total amount /number of payments =552
Answer: E
Answer: (E) $552
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 22
(B) 50
(C) 888
(D) 277
(E) 21
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many year younger than A
(A) A)11
(B) B)12
(C) C)13
(D) D)14
(E) E)15
Rationale: Explanation:
Given that A+B = 13 + B + C
=> A – C = 13 + B – B = 13
=> C is younger than A by 13 years
Answer: Option C
Answer: (C) C)13
Question: Niki covers a distance in 45 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%.
(A) 101.02 kmph
(B) 121.62 kmph
(C) 100.62 kmph
(D) 111.00 kmph
(E) 121.00 kmph
Rationale: Given Speed = 60 Kmph.
It means Niki covered 60 km in 60 min (1 hour). So, in 45 min he will cover 45 km.
50% time reduced = 45 - 50% of 45 = 22.5 min.
Thus, Niki needs to cover 45 km in 22.5 min (0.37hour).
Speed * Time = Distance.
Speed * 0.37 = 45
Speed = 121.62 kmph.
ANSWER : OPTION B
Answer: (B) 121.62 kmph
Question: Anup was asked to find the value of 7/12 of a sum of money T. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
(A)  48
(B)  89
(C)  84
(D)  69
(E)  49
Rationale: T=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: (E)  49
Question: What is the difference between the place values of two fives in the numeral 7589452
(A) 499950
(B) 411150
(C) 500050
(D) 500000
(E) 50
Rationale: Required difference = 500000-50 = 499950
Answer is A
Answer: (A) 499950
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.75, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $250?
(A)  1,108
(B)  2,100
(C)  2,108
(D)  2,628
(E)  2,256
Rationale: To maximize number of hot dogs with 250$
Total number of hot dogs bought in 250-pack = 22.95*10 =229.5$
Amount remaining = 250 - 229.5 = 20.5$
Total number of hot dogs bought in 20-pack = 3.05*6 =18.3$
Amount remaining = 20.5 - 18.3 = 2.2$
Total number of hot dogs bought in 8-pack = 1.55*1 =1.55$
Amount remaining = 2.2 - 1.75 = 0.45$
This amount is too less to buy any 8- pack .
Greatest number of hot dogs one can buy with 250 $ = 250*10+20*6+8*1 = 2628
Answer D
Answer: (D)  2,628
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
(A) 144
(B) 150
(C) 168
(D) 180
(E) None
Rationale: Explanation :
Angle traced by hour hand in
5 hrs 10 min. = (360/12 x 6)
= 180.
Answer : D
Answer: (D) 180
Question: For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all n > 1, an = an−1an−1 + 4 if n is odd and an = an−1 if n is even. What is the value of a1a1 if a34 = 68?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 21
Rationale: a34= 68 = a33 - 1 = a32 - 1 +4 ... and so on
So observing the trend,
a34 = a1 +(32/2) * 4 - (34/2) * (-1)
[32/2 to get all the even n (from 32 to 2) and 34/2 to get all the odd n (from 33 to 1) including 33 and 1]
a1 = 68-64+17 = 21
Hence, answer will be E.
Answer: (E) 21
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 6 days
(B) 7 days
(C) 4 days
(D) 9 days
(E) 2 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: (D) 9 days
Question: Patanjali walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 24
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: Patanjali walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles
Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Total Distance travelled on three days = 18+20+24 = 62
Answer: Option E
Answer: (E) 62
Question: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: let's take answer choice D -10 h
if it took 10 h for 40 pages, then it took 5 hours for 20 pages
since it takes Jack 2 more hours than Tom to type 20 pages, Tom's time is 5-2=3 h
their combo time 5*3 /(5+3)=15/8
if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages
as u see 15/8 <12/5 . so D is out, and we should check E, whose number is more than D's
answer choice E = 12 for 40 pages or 6 for 20 pages
then Tom's time =6-2=4 h
combo time =6*4/(6+4)=12/5
if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages
12/5=12/5
answer choice E
Answer: (E) 12
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 36
(C) 34 2/7
(D) 21 3/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 8 tons of cement, then we'll get 5/7*30 =21 3/7 tons of mixture.
Answer: D.
Answer: (D) 21 3/7
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 45
(B) 65
(C) 75
(D) 78
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 6 = 74
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 74 + 4 = 78
D
Answer: (D) 78
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) None of them
Rationale: Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = (3 -(3x/8)+ x)litres
Quantity of syrup in new mixture = (5 - 5x/8) litres
Therefore, (3 - (3x/8)	+ x)	= 5 -	5x/8)
= 5x + 24 = 40 - 5x
= 10x = 16
= x = 8/5
So, part of the mixture replaced = (8/5 x 1/8)= 1/5
Answer is A.
Answer: (A) 1/5
Question: The average of thirteen numbers is 9. The average of first six numbers is 5 and the average of last six numbers is 7. What is the middle number?
(A) 47
(B) 45
(C) 25
(D) 37
(E) 44
Rationale: The total of thirteen numbers = 13X9 = 117
The total of first 6 and last 6 numbers is = 6 X 5+6 X 7 = 72
So, the middle number is (117 - 72 ) = 45
B
Answer: (B) 45
Question: [(5/2 ÷ 1/2 × 5/2)]/[(5/2 × 1/2 ÷ 5/2)] = ?
(A) 25
(B) 20
(C) 18
(D) 16
(E) 14
Rationale: Explanation:
[(5/2 ÷ 1/2 × 5/2)]/[(5/2 × 1/2 ÷ 5/2)]
= [5/2 × 2/1 × 5/2]/[5/2 × 1/2 × 2/5]
= 25/2 / 1/2 = 25/2 x 2/1 = 25
Answer: Option A
Answer: (A) 25
Question: A man spent 1/5 of his loan amount on house construction and 1/4 of the remaining on his office renovation. How much fraction of the loan amount is he left with after spending on house and office renovation?
(A) 3/5
(B) 2/6
(C) 5/4
(D) 1/5
(E) 4/3
Rationale: The man spent 1/5 his loan amount on house construction, remaining amount is 4/5
He spent 1/4 of the remaining amount for office renovation, 1/4*4/5=4/20
Total loan amount spent on house and office renovation =1/5+4/20
To get a common denominator we use 20, so 1/5 is 4/20
4/20+4/20=8/20 is the total amount spent on house construction and office renovation.
remaining 12/20 is left with the man, 3/5
Answer is A
Answer: (A) 3/5
Question: If a and b are different values and a – b = 6(√a - √b), then in terms of b, a equals:
(A) √b
(B) b
(C) b - 12√b + 36
(D) b + 2√b + 1
(E) b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 6(√a - √b) -----> ( √a + √b) ( √a - √b) = 6(√a - √b) -------> √a + √b = 6, so
√a = 6 - √b, square both sides and solve. Answer is C.
Answer: (C) b - 12√b + 36
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 6 hours?
(A) 60X/Y.
(B) 360X/Y.
(C) 60Y/X.
(D) 120Y/X.
(E) (X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 6 hrs(360mins)he can pack 360X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 360X/Y
(ANSWER B)
Answer: (B) 360X/Y.
Question: The positive numbers w, x, y, and z are such that x is 30 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?
(A) 15.2%
(B) 16.0%
(C) 20.0%
(D) 23.2%
(E) 24.8%
Rationale: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:
z=100
y=120 (20% greater than z)
z=144(20% greater than y)
Now calculate w 20% less than z = 144*80/100= 115.2
Now by just looking, relation between w and z:
w-z/z*100 = 20 - Answer
C
Answer: (C) 20.0%
Question: After three successive equal percentage rise in the salary the sum of 100 rupees turned into 140 rupees and 49 paise. Find the percentage rise in the salary.
(A) 12%
(B) 22%
(C) 66%
(D) 82%
(E) 77%
Rationale: Solution:
We solve it through options. Choosing options for trial depends on mental thought.
100 ==12% up ==>112 ==12% up ==>125.44 ==12% Up ==> 140.49
So, answer is 12%.
Answer: Option A
Answer: (A) 12%
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:45
(C) 39:40
(D) 39:41
(E) 39:42
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: If x > 5 and y < -5, then which of the following must be true ?
(A) x/y > 1
(B) x/y < -1
(C) x/y < 0
(D) x + y > 0
(E) xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
A should be the answer.
Answer: (A) x/y > 1
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.70 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
(A) $255
(B) $357
(C) $510
(D) $1,250
(E) $2,550
Rationale: Total no. Of boxes = 3060000/(20×20×15) = 510
Total cost = 510×$0.7=$357
Answer B
Answer: (B) $357
Question: In a family 13 people eat only vegetarian, 7 people eat only non veg., 8 people eat both veg and non veg.. How many people eat veg in the family?
(A) 20
(B) 11
(C) 9
(D) 31
(E) 21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 13+8= 21
Answer = E
Answer: (E) 21
Question: Average weight of 10 people increased by 2.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Explanation:
Total weight increased is 2.5 * 10 = 25.
So weight of new person is 45+25 = 70
Answer: Option E
Answer: (E) 70
Question: If 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
(A) 127
(B) 237
(C) 360
(D) 450
(E) 281
Rationale: Explanation:
Let the required no of hectares be x. Then
Men --- Hectares---Days
10---------80---------24
36---------x---------30
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
x=36/10*30/24*80
x= 360
Answer: C
Answer: (C) 360
Question: 8, 27, 64, 100, 125, 216, 343
(A) 40
(B) 100
(C) 290
(D) 102
(E) 293
Rationale: The pattern is 23, 33, 43, 53, 63, 73. But, 100 is not a perfect cube.
Answer: (B) 100
Question: The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 24 per kg. The inflation rate for the years 1994 and 1995 are expected to be 20% each. The expected price of sugar on January 1, 1996 would be
(A) 23.6
(B) 36.45
(C) 35.72
(D) 24.6
(E) None of these
Rationale: Explanation :
Increase in the price of sugar = (20+2)= 22%
Hence, price of the sugar on Jan 1, 1996
=> (24 * 122 * 122)/( 100 * 100 ) = Rs 35.72.
Answer : C
Answer: (C) 35.72
Question: A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Answer: Option D
Answer: (D) 39
Question: f(1)=1,where f(x+y)=f(x)+f(y)+8xy-2.then f(7)=?
(A) 162
(B) 163
(C) 164
(D) 165
(E) 166
Rationale: f(1)=1
f(2)= f(1+1)= 1+1+8-2= 8
f(3) = f(2+1)= 8+1+ (8*2*1)-2 = 23
f(6)= f(3+3)= 23+23+ (8*3*3)-2= 116
f(7) = f(6+1)= 116+1+(8*6*1)-2= 163
thus ans is 163
ANSWER:B
Answer: (B) 163
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 35% lemonade syrup?
(A) 1.5
(B) 1.75
(C) 2.14
(D) 2.34
(E) 2.64
Rationale: Let the total solution is 150 L with 80 L water70 L syrup.
To make 35% syrup solution, the result solution must have 97.5 L syrup and 52.5 L syrup.
Therefore we are taking 17.5 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
17.5 L syrup in 37.5 L solution
We started by multiplying 10
Now to get to the result we need to divide by 17.5 => amount of solution to be replaced with water (37.5/17.5)=2.14.
Correct option : C
Answer: (C) 2.14