mathewhe/aqua_rat huggingface dataset:
Question: If 5 spiders make 2 webs in 8 days, then how many days are needed for 1 spider to make 1 web?
(A) 10
(B) 15
(C) 30
(D) 20
(E) 16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)5:1
(webs) 1:8}::x:2
â‡’5Ã—1Ã—8=1Ã—2 Ã— x
â‡’x=20
Answer: Option D
Answer: (D) 20
Question: We made a down payment of $25 and borrowed the balance on a new sofa which cost $250. The balance with interest was paid in 23 monthly payments of $11 each and a final payment of $17. The amount of interest paid was what percent of the amount borrowed?
(A) 20%
(B) 22%
(C) 25%
(D) 27%
(E) 30%
Rationale: We borrowed $225.
To pay back this loan, we paid 23*$11 + $17=$270.
The interest was $270-$225=$45.
The percentage was $45/$225=0.2=20%.
The answer is A.
Answer: (A) 20%
Question: Rs.500 amounts to Rs.670 in 5 years at simple interest. If the interest is increased by 2%, it would amount to how much?
(A) 150
(B) 550
(C) 760
(D) 450
(E) 260
Rationale: (500*5*2)/100 = 50
500+ 50 = 550
Answer: B
Answer: (B) 550
Question: A Man travelled a distance of 51 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
(A) 16 km
(B) 24 km
(C) 12 km
(D) 10 km
(E) None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 51 km
So,
4x + 9(9-x) = 51
=> 5x = 30
=> x = 6
So distance traveled on foot = 4(6) = 24 km
Answer: Option B
Answer: (B) 24 km
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) 17
(B) 25
(C) 88
(D) 26
(E) 27
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:B
Answer: (B) 25
Question: If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
(A) 50%
(B) 75%
(C) 120%
(D) 133 1/3%
(E) 150%
Rationale: The price on June 1st = 12 (assume);
The price on May 1st = 2/3*12 = 8;
The price on July 1st = 8*1.50 = 12.
The average price of the bond on May 1st and July 1st = (8+12)/2 = 10.
The price of the bond on June 1st (12) is 6/5 times (120%) the average price of the bond on May 1st and July 1st.
Answer: C.
Answer: (C) 120%
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?
(A) 6620
(B) 2888
(C) 2776
(D) 9930
(E) 2718
Rationale: A = 30000(11/10)^3
= 39930
= 30000
----------
9930.Answer: D
Answer: (D) 9930
Question: At what rate percent per annum will a sum of money double in 8 years.
(A) 12.5%
(B) 12.9%
(C) 18.5%
(D) 11.5%
(E) 12.3%
Rationale: Explanation:
Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum.
Answer: A) 12.5%
Answer: (A) 12.5%
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
(A) 240
(B) 180
(C) 160
(D) 140
(E) 120
Rationale: 3x + 4x = 420
x = 60 => 3x = 180
ANSWER:B
Answer: (B) 180
Question: A train covers a distance of 12 km in 10 minutes. If it takes 8 seconds to pass a telegraph post, then the length of the train is
(A) 100m
(B) 120m
(C) 140m
(D) 160m
(E) 170cm
Rationale: Explanation:
Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.
Length of the train = (Speed x Time) = (20 x 8) m = 160 m
Answer: Option D
Answer: (D) 160m
Question: 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. -3
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: 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.
Answer: (C) I and II only
Question: A father was as old as his son's present at the time of your birth. If the father's age is 44 years now, the son's age 5years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 17 years
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22.
Son's age 5 years back (22 - 5) = 17 years.
E
Answer: (E) 17 years
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 5, how many people got on at the first stop?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 5
=> 2^(5-1) = 2^4 = 16
=> answer is D
Answer: (D) 16
Question: If a is an odd integer and b is an odd integer and a > b which of the following must be an odd integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) option A B and C
Rationale: a= odd = e.g 9
b= odd = e.g 3
A. odd/odd for example 9/3 = 3 odd
B. odd * odd = 3 * 9 = 27 odd
C. 2*odd + odd = even + odd odd
D. 2(odd + odd) = 2(even) even
Hence E it is.
Answer: (E) option A B and C
Question: The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Also note here the relevance of 'K must be less than 400'.
21K is 180n (a multiple of 180).
180n = 2^2 * 3^2 * 5 * n = 3*7*K
n must have a 7 at least.
K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60.
So K has the following prime factors: 2, 3 and 5. Can it have any other prime factors? The next smallest prime factor is 7. But 60*7 = 420 - a number greater than 400. This means that if K is greater than 60, the only other prime factors that K can have must be out of 2, 3 and 5 only. That is, K may be 60*2 or 60*3*2 or 60*5 etc. This tells us that K has exactly 3 prime factors. If we did not have this condition of K less than 400, we would not know exactly how many factors K has.
Answer (C)
Answer: (C) 3
Question: If f(x)=x^2 and x is a natural number, what CANNOT be the solution to f(f(f(x)))?
(A) 16384
(B) 65536
(C) 6561
(D) 256
(E) 1
Rationale: Answer A is equal to 4^7 and cannot be a solution because f(f(f(x)) is equivalent to x^8 and 4^7 cannot equal to anything to the power of 8.
Answer: (A) 16384
Question: The speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:
(A) 9.4 km
(B) 10.2 km
(C) 10.4 km
(D) 9.2 km
(E) None of these
Rationale: Explanation :
Speed downstream = (22 + 4) = 26 kmph
Time = 24 minutes = 24/60 hour = 2/5 hour
distance travelled = Time × speed = (2/5)×26 = 10.4 km. Answer : Option C
Answer: (C) 10.4 km
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 1/2 hours; pumps A and C, operating simultaneously, can fill the tank in 1/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1
(E) 5/6
Rationale: A+B =1/2 ; A+C =1/2 ,B+C =2 ; ADD THEN 2*(A+B+C) = 3
A+B+C = 3/2 HRS
E
Answer: (E) 5/6
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 4 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
(A) 1.6
(B) 1
(C) 0.4
(D) 0.16
(E) 0.016
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*16*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 160/10,000 = 16/1000 = 0.016 ft
The answer is E.
Answer: (E) 0.016
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 1868
(C) 6286
(D) 2678
(E) 1524
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer: A
Answer: (A) 1261
Question: The diagonals of a rhombus are 16 cm and 20 cm. Find its area?
(A) 160
(B) 288
(C) 150
(D) 238
(E) 31
Rationale: 1/2 * 16 * 20 = 160
Answer: A
Answer: (A) 160
Question: A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?
(A) 17/42
(B) 18/27
(C) 5/42
(D) 3/15
(E) 15/47
Rationale: 3 letters can be choosen out of 9 letters in 9C3 ways
(2 vowels + 1 constant or 3 vowels) -> 4C2*85C1) + 4C3 ways
=> req probability = (4C2 * 5C1)+4C3/9C3 = 17/42
ANSWER A
Answer: (A) 17/42
Question: A shopkeeper sells 600 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) 12
(B) 27
(C) 29
(D) 35
(E) 21
Rationale: SP per metre = 18000/600 = Rs. 40 Loss per metre = Rs. 5 CP per metre = 40 + 5 = Rs. 45.Answer: D
Answer: (D) 35
Question: each interior angle of a regular polygon is 120 degrees greator than each exterior angle.how many sides are there in the polygon
(A) 6
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Interior angle = 180 - (360/n)
Exterior angle = (360/n)
Given: IA = 120 + EA
=> 180 - (360/n) = 120 + (360/n)
=> n = 12
ANSWER:C
Answer: (C) 12
Question: A person borrows Rs. 8000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
(A) 100 rs
(B) 150 rs
(C) 160 rs
(D) 180 rs
(E) 200 rs
Rationale: Gain in 2 years =
[(8000*6*2)/100]-[(8000*4*2)/100]
960-640=320
Gain in 1 year =(320/2)=160 rs
ANSWER:C
Answer: (C) 160 rs
Question: Insert the missing number
3, 4, 7, 16, 43, 124, ...
(A) 367
(B) 356
(C) 125
(D) 1222
(E) 1322
Rationale: Series is having difference between susequest next number and the nuber with multiplication by 3
3, 4, 7, 16, 43, 124, ...
Differnce between 4 and 3 is 1, multiply with three and add 4 to it. 7 will come
Differnce between 7 and 4 is 3, multiply with three and add 7 to it. 16 will come
differnce between 16 and 7 is 9, multiply with three and add 16 to it. 43 will come
differnce between 43 and 16 is 27, multiply with three and add 43 to it. 124 will come
differnce between 124 and 43 is 81, multiply with three and add 124 to it. 367 will come
ANSWER:A
Answer: (A) 367
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
A. 32 km B. 25 km
(A) 65 km
(B) 88 km
(C) 44 km
(D) 02 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: E
Answer: (E) 20 km
Question: If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A^B is also a prime number.
(A) 1 only.
(B) 2 only.
(C) 3 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Answer : 2 and 3 only
ANSWER:D
Answer: (D) 2 and 3 only.
Question: A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
(A) 4/19
(B) 7/19
(C) 12/19
(D) 21/99
(E) 26/77
Rationale: Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E
Answer: (E) 26/77
Question: How many arrangements can be made if there are 5 balls from which 3 are red, 1 is green, 1 is yellow. find the probability of getting all 3?
(A) 3/10
(B) 4/10
(C) 6/10
(D) 7/10
(E) 9/10
Rationale: arrangement = 5!/3!=20
Probability of getting all 3 balls=
3 from 5=5c3
1 from 3 red ball,1 green,1 yellow
(3c1*1c1*1c1)/5c3 =3/10
ANSWER:A
Answer: (A) 3/10
Question: Fresh grapes contain 60% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30kg of fresh grapes?
(A) 10 kg
(B) 15 kg
(C) 20 kg
(D) 25 kg
(E) 40 kg
Rationale: From the question we know: 30kg * 60% = 18 kg of water in the fresh grapes
30kg - 18kg of water = 12kg of non-water mass
We are looking for the weight of the dry grapes (X).
Since the question tells us that 20% of the weight of the dry graps is water and we know that 12kg is non-water mass we can set up the following equation:
X = 1/5(X) + 12kg
4/5(X) = 12kg
X = 15 kg
Answer- B
Answer: (B) 15 kg
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 15
(B) 10
(C) 20
(D) 18
(E) 12
Rationale: 1/6 â€“ 1/15 = 1/10 => 10
ANSWER B
Answer: (B) 10
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 28,000. What was Simran's share in the profit?
(A) Rs. 9423
(B) Rs. 10,250
(C) Rs. 12,000
(D) Rs. 14,000
(E) None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 28000 * 3/7 = Rs. 12000
ANSWER:C
Answer: (C) Rs. 12,000
Question: A library has 360 math books; 60 Calculus books, 120 Geometry books, and 180 Algebra books. What percentage of books are Geometry books ?
(A) 33.3 %
(B) 16.7 %
(C) 66.7 %
(D) 77 %
(E) None of these
Rationale: Explanation :
Geometry Book percentage = (120/360 x 100)%
= 33.3 %
Answer : A
Answer: (A) 33.3 %
Question: Rick deposited $650 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
(A) 5.
(B) 25.
(C) 50.
(D) 35.
(E) 65.
Rationale: 5x+15y=650 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=650
5x+5y=300
10y= 350
y=35 and x = 25
therefore $15 bills = 35
Answer D
Answer: (D) 35.
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, 3158, 9476, 28430,x
(A) 2643
(B) 5464
(C) 3456
(D) 7554
(E) 85292
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
1052 Ã— 3 + 2 = 3158
3158 Ã— 3 + 2 = 9476
9476 Ã— 3 + 2 = 28430
28430 Ã— 3 + 2 = 85292
E
Answer: (E) 85292
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 900 then loss of Pyarelal?
(A) 610
(B) 710
(C) 810
(D) 900
(E) 1000
Rationale: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 900, loss of Pyarelal= 900*9x/10x=810
ANSWER:C
Answer: (C) 810
Question: How many multiples of 2 are there between 1 and 60, exclusive?
(A) 21
(B) 22
(C) 29
(D) 26
(E) 28
Rationale: 29
multiples of 2 between 1 and 60 exclusive.
from 2 * 1 upto 2*29, (1,2,3,4,...,29). Hence, 29 multiples !
correct option is C
Answer: (C) 29
Question: In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 6 to 8 at bats in a recent game and had anywhere from 3 to 4 hits in the same game, the player’s actual batting average for that game could fall anywhere between
(A) 0.25 and 0.30
(B) 0.25 and 0.75
(C) 0.37 and 0.75
(D) 0.33 and 0.50
(E) 0.50 and 0.66
Rationale: Average Range = Hits to Bats i.e 3/8 to 4/6 = 0.37 to 0.66
Answer: C
Answer: (C) 0.37 and 0.75
Question: A bag marked at $200 is sold for $120. The rate of discount is?
(A) 10%
(B) 25%
(C) 20%
(D) 50%
(E) 40%
Rationale: Rate of discount = 80/200 * 100 = 40%
Answer is E
Answer: (E) 40%
Question: It costs $4 for the first 1/4 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $10 per hour. If a certain customer uses the laundry machine for 2 hours, how much will it cost him?
(A) $20.
(B) $22.
(C) $24.
(D) $26.
(E) $28.
Rationale: 2 hrs = 120 min
First 15 min ------> $4
Time left is 120 min...
Now, 60 min costs $ 10
1 min costs $ 10/60
120 min costs $ 10/60*120 => $ 20.00
So, Total cost will be $20 + $4 => $ 24
Hence answer will be C
Answer: (C) $24.
Question: $406 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?
(A) $208
(B) $216
(C) $224
(D) $232
(E) $240
Rationale: Let the shares for A, B, and C be x, 2x, and 4x respectively.
7x = 406
x = 58
4x = 232
The answer is D.
Answer: (D) $232
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/6 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 9 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 16
(D) 21
(E) 27
Rationale: Machine K works at a rate of 1/18 of the units per hour.
The rate of K + M together is 5/6 * 1/9 = 5/54 of the units per hour.
The rate of machine M is 5/54 - 3/54 = 1/27.
It would have taken machine M a total time of 27 hours.
The answer is E.
Answer: (E) 27
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
(A) 16.35
(B) 16.31
(C) 16.32
(D) 16.3
(E) 16.31
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.
S.P. per kg = 819/50 = Rs. 16.38 = 16.30.
Answer:D
Answer: (D) 16.3
Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: Let the required no of working hours per day be x.
More pumps , Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
pumps 4:3 and Days 1:2::8:x
Therefore, 4x1x(x)=3x2x8
X=(3x2x8)/4
X = 12.
Answer is C.
Answer: (C) 12
Question: The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 240
(C) 245
(D) 250
(E) 265
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (110 + x)/30 = 25/2 => 2(110 + x) = 750 => x = 265 m.
Answer: Option E
Answer: (E) 265
Question: The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 18, and k < m < r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers?
(A) 16
(B) 23
(C) 19
(D) 20
(E) 22
Rationale: We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r.
The average of the positive integers is 18 which means that in effect, all numbers are equal to 18. If the largest number is 40, it is 22 more than 18. We need r to be maximum so k and m should be as small as possible to get the average of 16. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 17 less than 18 and 2 is 16 less than 18 which means k and m combined are 33 less than the average. 40 is already 22 more than 18 and hence we only have 33 - 22 = 11 extra to distribute between r and s. Since s must be greater than r, r can be 18+5 = 23 and s can be 18+6 = 24.
So r is 23
Answer (B)
Answer: (B) 23
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.900, what is the reduced price for kg?
(A) 45
(B) 60
(C) 70
(D) 80
(E) 20
Rationale: A
900*(25/100) = 225 ---- 5
? ---- 1 => Rs.45
Answer: (A) 45
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one yellow marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
(A) 160
(B) 220
(C) 180
(D) 200
(E) 240
Rationale: # ways to distribute Blue marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute yellow marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
C
Answer: (C) 180
Question: Which of the following is not divisible by 6?
(A) 10032
(B) 21192
(C) 47816
(D) 91232
(E) 72031
Rationale: Divisibility rule of 6: Number must be divisible by both 2 and 3
Option A: 10032, Divisible by 2. Hence divisible by 6
Option B: 21192, Divisible by 2 & 3. Hence divisible by 6
Option C: 47816, Divisible by 2. Hence divisible by 6
Option D: 91232, Divisible by 2. Hence divisible by 6
Option E: 72031, Not divisible by 2 or 3. Hence 72031 is not divisible by 6
Answer: (E) 72031
Question: A tour group of 25 people paid a total of $840 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $32
(D) $25.20
(E) $30
Rationale: Soln:-
840/25=x+0.05x
840/25=1.05x
x=32
ANSWER:C
Answer: (C) $32
Question: The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the numbers is?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 5
Rationale: Let the numbers be 3x,4x,5x
then, 9x^2+16x^2+25x^2 = 1250
50x^2 = 1250
x^2 = 25
x=5
Answer is E
Answer: (E) 5
Question: A box measuring 30 inches long by 48 inches wide by 12 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
(A) 78
(B) 80
(C) 85
(D) 88
(E) 90
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
6 is the biggest number that could divide all three, 30, 48 and 12.
Thus side of cube must be 6, and total number of cubes = 30/6 * 48/6*12/6 = 80
Ans B.
Answer: (B) 80
Question: The length of a bridge in meters, which a train 100-meters long and traveling at 45 km/hr can cross in 30 seconds is?
(A) 225
(B) 245
(C) 275
(D) 325
(E) 375
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+100 = 375 meters
x = 275 meters
The answer is C.
Answer: (C) 275
Question: When N is divided by T, the quotient is S and the remainder is M. Which of the following expressions is equal to N?
(A) ST
(B) S + V
(C) ST + M
(D) T(S+V)
(E) T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + M C is correct
Answer: (C) ST + M
Question: Three members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 3 club members, how many members does the club have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 11
Rationale: Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(3!)(n-3)!] = 36
i.e. n*(n-1)*n-3!/ [(3!)n-3!] = 36
i.e. n*(n-1) = 108
(for Positive Values of n)
therefore, n*(n-1) = 108
i.e. n=11
Answer: Option E
Answer: (E) 11