mathewhe/aqua_rat huggingface dataset:
Question: A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
(A) 3.46%
(B) 4.2%
(C) 4.5%
(D) 5%
(E) None of these
Rationale: Explanation :
Let the sum of Rs.725 is lent out at rate R% for 1 year
Then, at the end of 8 months, ad additional sum of 362.50 more is lent out at rate 2R% for remaining 4 months(1/3 year)
Total Simple Interest = 33.50
=>725×R×1/100+362.50×2R×1/3/100=33.50
=>725×R×1/100+362.50×2R/300=33.50
=>725R/100+725R300=33.50
=>725R(1/100+1/300)=33.50
=>725R(4/300)=33.50
=>725R×4=10050
=>725R=2512.5
=>145R=502.5
=>R=502.5/145
=3.46%
Answer : Option A
Answer: (A) 3.46%
Question: If p^2 – 13p + 40 = d, and p is a positive integer between 1 and 10, inclusive, what is the probability that d < 0?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 3/10
Rationale: p2 – 13p + 40 = d
so (p – 8)(p – 5) = d
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Answer: (B) 1/5
Question: is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, then how old is B?
(A) 16
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
5x = 40 => x = 8
Hence, B's age = 2x = 16 years.
ANSWER:A
Answer: (A) 16
Question: There are 3 men, 8 women, they are standing in a row for a photoshoot, in how many ways they can be arranged if no 2 men can stand together.
(A) 9P3 * 8!
(B) 9P3 * 7!
(C) 9P3 * 6!
(D) 9P3 * 5!
(E) 8P3 * 8!
Rationale: There is restriction on the number of Men, so consideration of problem shall be done by fixing position of Women
_W_W_W_W_W_W_W_W_
In those blank spaces 3 Men can be arranged among 9 positions so that it satisfies the above condition.
No. of ways= 9P3 * 8!
ANSWER:A
Answer: (A) 9P3 * 8!
Question: Find the missing in the series: 70, 58, 47, 37,___
(A) 28
(B) 287
(C) 2679
(D) 2767
(E) 2771
Rationale: Answer:A
Answer: (A) 28
Question: A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?
(A) 12
(B) 13
(C) 15
(D) 18
(E) 19
Rationale: From Team A: 10x+5y = 20
From Team B: 8x+2y=10
Solve using whatever method you choose (i.e. substitution or elimination) --> x = 1/2 & y = 3
Team C: 8(1/2) + 5(3) = 19
Answer is E
Answer: (E) 19
Question: Find the odd man out. 1, 8, 27, 64, 125, 196, 216, 343
(A) 64
(B) 196
(C) 216
(D) 1
(E) 343
Rationale: The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3.
196 is not a perfect cube
Answer is B
Answer: (B) 196
Question: The difference between the compound interest and simple interest at the ratio of 10% per annum at the end of two years is Rs. 496.20. If the compound interest is compounded every six months, what is the sum ?
(A) Rs. 24000
(B) Rs. 30000
(C) Rs. 32000
(D) Rs. 36000
(E) None of these
Rationale: Explanation :
[x (1 + 5/100)4 - x] - (x x 10 x 2)/100 = 496.20
x (0.21550625 - 0.2) = 496.2
∴ x = 496.20/0.01550625 = 32000
Answer : Option C
Answer: (C) Rs. 32000
Question: Joan and Karl each bought a sofa and the sum of their purchases was $600. If twice of what Joan paid was $90 more than what Karl paid, what did Joan pay for her sofa?
(A) $190
(B) $210
(C) $230
(D) $250
(E) $270
Rationale: J+K=600 so K=600-J
2J=K+90
2J=(600-J)+90
3J=690
J=230
The answer is C.
Answer: (C) $230
Question: P can do a certain work in 10 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
(A) 6.25
(B) 6.75
(C) 7.5
(D) 7.75
(E) 8.25
Rationale: Each day, P can do 1/10 of the work.
Each day, Q can do 1.6/10 of the work = 16/100 of the work
The time taken by B alone to complete the total work is 100/16 = 6.25 days.
The answer is A.
Answer: (A) 6.25
Question: Find the simple interest on Rs 18 000 at 18% per annum for the period from 12th November 2016 to 16th December 2016.
(A) Rs. 201.8
(B) Rs. 1301.8
(C) Rs. 341.8
(D) Rs. 531.8
(E) Rs. 401.8
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which
money is withdrawn is counted.
So lets calculate the number of days now,
Time = (18+16) days = 34/365 years
P = 18 000
R = 18%
S.I. = =18 000Ã—18Ã—34/(365*100)=301.8
Answer: C
Answer: (C) Rs. 341.8
Question: Each week, Harry is paid x dollars per hour for the first 18 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
(A) 34
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 42x=18x+1.5x(H-18)
==> 42=18+1.5(H-18)
==> H-18 = 24/1.5=16 ==> H = 34
Answer is A
Answer: (A) 34
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 488
(B) 200
(C) 289
(D) 150
(E) 822
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer:D
Answer: (D) 150
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4991
(B) 5000
(C) 4800
(D) 5500
(E) 6000
Rationale: Let the sale in the sixth month = x
=>6435+6927+6855+7230+6562+x/6 = 6500
6435+6927+6855+7230+6562+x=6*6500
x=39000
x=39000-34009 = 4991
ANSWER A
Answer: (A) 4991
Question: In an election between two candidates first candidate got 80% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
(A) 12000 votes
(B) 13000 votes
(C) 14000 votes
(D) 10980 votes
(E) 19900 votes
Rationale: Total = 100 %,
First person got 80%
second person got remaining 20 % of votes.
than 20 % = 2800
20% = 20Ã—140 = 2800
100% =100Ã—140 =1400 votes
C
Answer: (C) 14000 votes
Question: Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
(A) 50 sec
(B) 58 sec
(C) 24 sec
(D) 22 sec
(E) 21 sec
Rationale: Explanation:
Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s
We are calculating the time taken by the slower train to pass the driver of the faster one
.Hence the distance = length of the smaller train = 500 m
Time = distance/speed = 500/(125/6) = 24 sec
Answer: Option C
Answer: (C) 24 sec
Question: The average of 10 numbers is calculated as 46. It is discovered later on that while calculating the average, the number 75 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
(A) 48
(B) 51
(C) 60
(D) 71
(E) 96
Rationale: The total sum of the numbers should be increased by 50.
Then the average will increase by 50/10 = 5.
The correct average is 51.
The answer is B.
Answer: (B) 51
Question: A man is 32 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 16
(B) 19
(C) 15
(D) 22
(E) 30
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 32) + 2 = 2(x + 2)
x + 34 = 2x + 4
=> x =30 .
Answer: E
Answer: (E) 30
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 245
(C) 400
(D) 35
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 56, so 0.14*{total} = 56 --> {total} = 400.
Answer: C.
Answer: (C) 400
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 8m.
(B) 6m.
(C) 4m.
(D) 2m.
(E) 5m.
Rationale: Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Answer: (D) 2m.
Question: If x^2=x+4, then x^3=?
(A) 3x+2
(B) 3x-2
(C) 2x+1
(D) 2x-3
(E) 5x+4
Rationale: Given X^2 = X+4
X^3 = X*X^2 = x*(X+4)-- Substituted from above.
= X^2 + 4X = X+4+4X = 5X+4.
Hence E.
Answer: (E) 5x+4
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:122
(B) 81:121
(C) 81:122
(D) 81:197
(E) 81:112
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92:112
= 81:121
Answer: B
Answer: (B) 81:121
Question: If x^2 - 1 = 0 and x > 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= 1 in the equation x^2 +2x-3 = 1+2-3 = 0
D is also the answer
Answer: (D)  x^2 + 2x - 3
Question: If 235477 × 455233 × K^2 is divisible by 3, which of the following could be the value of K?
(A) 6000209
(B) 6111209
(C) 3456576
(D) 6111309
(E) 6111109
Rationale: The first two terms are not divisible by 3, so we need the third term to be divisible by 3. The only way that (k^2) is going to be a multiple of 3 is if k is a multiple of 3. Therefore, we need the single answer that is a multiple of 3.
Answer =(E)
Answer: (E) 6111109
Question: Twin primes are defined as prime numbers that can be expressed as p and (p + 2), and any number p that is a member of such a pair is considered to have a twin. For example, 3 and 5 are twin primes, and 3 has a twin. Each of the following prime numbers has a twin EXCEPT
(A) 7
(B) 13
(C) 17
(D) 23
(E) 29
Rationale: A. 7 --> 5 is a twin prime of 7;
B. 13 --> 11 is a twin prime of 13;
C. 17 --> 19 is a twin prime of 17;
D. 23 --> neither 23-2=21 nor 23+2=25 is a prime, hence 23 has no twin prime;
E. 29 --> 31 is a twin prime of 29.
Answer: D.
Answer: (D) 23
Question: Tough and Tricky questions: Number Properties.
If (z + 3)/6 is an integer, what is remainder when z is divided by 6?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 6/6=1
Ans B
Answer: (B) 3
Question: If the number 892,132,27x is divisible by 11, what must be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,132,27x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 7 = 19 (ii)
(i) - (ii) = 15 + x - 19 = x - 4
Hence x should be = 4 to make this a multiple of 11 (0) Option D
Answer: (D) 4
Question: Express 35 mps in kmph?
(A) 122
(B) 188
(C) 126
(D) 140
(E) 124
Rationale: 35 * 18/5 = 126 kmph
Answer: C
Answer: (C) 126
Question: Abhijit started a business investing 4000. Anuja joined him after six months with an amount of 8000 and Sunil joined them with 12,000 after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, two years after Abhijit started the business?
(A) 2 : 4 : 3
(B) 2 : 4 : 4
(C) 2 : 5 : 5
(D) 2 : 3 : 3
(E) 2 : 5: 3
Rationale: Ratio of their investments
= 4× 24 : 8 × 18 : 12 × 12 = 2 : 3 : 3
Answer D
Answer: (D) 2 : 3 : 3
Question: What are the chances you would pull an Ace or Heart from a well-shuffled deck of cards?
(A) 1 of 4
(B) 4 of 12
(C) 1 of 13
(D) 4 of 13
(E) 1 of 52
Rationale: You must add the number of cards in each suit in the deck (13/52) to the number of aces of in the deck (4/52) and subtract the number of aces of hearts in the deck (1/52). This will give you the number of 16/52 which when the fraction is reduced will give you the answer of 4/13. Answer is D.
Answer: (D) 4 of 13
Question: A moving truck uses 28 gallons of diesel fuel in traveling 504 miles. In order for the truck to travel the same distance using 21 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
(A) 6
(B) 10
(C) 8
(D) 12
(E) 21
Rationale: There are two sets 28G1 gallons and 21G2 gallons details given.
28 gallons covering 504 miles
Then 1 G1 is used to cover 18 miles.
Now for 21 G2 covering 504 miles.
then 1 G2 is used to cover 24 miles.
There must 24 - 18 = 6 miles per gallon increment is needed for 21 gallons to improve the mileage to cover 504 miles.
IMO A is correct answer.
Answer: (A) 6
Question: 25 bikes are running between two places A & B. In how many ways can a person go from A to B and return by a different bikes?
(A) 200
(B) 250
(C) 400
(D) 600
(E) 650
Rationale: He can go in any car out of the 25 cars.
Hence He can go in 25 ways.
Since he can not come back in the same car that he used for travelling,
He can return in 24 ways.
Total number of ways = 25 x 24 = 600
D
Answer: (D) 600
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $35 more. What was his original selling price?
(A) $180
(B) $280
(C) $420
(D) $550
(E) $700
Rationale: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 35
0.07 = 35
P = 500
The original selling price was 500*1.1 = 550.
The correct answer is D.
Answer: (D) $550
Question: If 5 |x| /=1, which of the following must be true?
(A) x>1/5
(B) x<1/5
(C) x=1/5
(D) x=1
(E) x=10
Rationale: if 5 |x| /=1
then |x|=1/5
ANSWER C x=1/5
Answer: (C) x=1/5
Question: A pool which was 2/3 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
(A) 8 hrs 45 mins.
(B) 9 hrs.
(C) 9 hrs 30 mins.
(D) 11 hrs 40 mins.
(E) 15 hrs 30 mins
Rationale: The pool was 2/3 full initially.
In 5/3 hrs, it was filled to 6/7 of its capacity.
Therefore, in 5/3 hrs, 6/7 - 2/3 was the amount of volume filled.
So, 5/3 hrs = 6/7 - 2/3 = 4/21
Therefore, for filling the vessel from empty to full, you would require 5/3 * 21/4 = 35/4 = 8 Hrs 45 Mins.
Hence A
Answer: (A) 8 hrs 45 mins.
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W?
(A)  60
(B)  61
(C)  62
(D)  63
(E)  64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=W
answer is A.
Answer: (A)  60
Question: A is twice as good a workman as B and together they finish a piece
in 18 days. In how many days will A alone finish the work?
(A) 27 days
(B) 32 days
(C) 54 days
(D) 16 days
(E) 29 days
Rationale: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1.
:. A’s 1 day's work =(1/18*2/3)=1/27
Hence, A alone can finish the work in 27 days.
Option: A
Answer: (A) 27 days
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 30% ?
(A)  0
(B)  1
(C)  2.50
(D)  1.73
(E)  4
Rationale: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/30 (this probability is less than 30%)
Solving for x we get, x(x-1)< 3. This implies that the maximum value of x can be 1.73.
Answer D!
Answer: (D)  1.73
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 14 km/hr respectively. They will meet for the first time in?
(A) 50min
(B) 40min
(C) 34min
(D) 25min
(E) 20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+14 = 34 km apart, they take 1 hour
To be 1000 m apart, they take 34 * 1000/1000 = 34 min.
Answer is C
Answer: (C) 34min
Question: An article is bought for Rs.1000 and sold for Rs.700, find the loss percent?
(A) 18 2/3%
(B) 16 7/3%
(C) 16 2/8%
(D) 16 2/3%
(E) 30%
Rationale: 1000 ---- 300
100 ---- ? => 30%
Answer:E
Answer: (E) 30%
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 100%
(D) 250%
(E) 200%
Rationale: Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage =(295/420 x 100)%=(1475/21)%=70%(approximately).
ANSWER IS B
Answer: (B) 70%
Question: Write 890,000,000,000 in scientific notation.
(A) 8.9 * 10 11
(B) 800.900 * 10 11
(C) 8.900 * 10 11
(D) 80.9000* 10 11
(E) 08.900 * 10 11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
890,000,000,000 = 8.9* 100,000,000,000 = 8.9 * 10 11**
correct answer A
Answer: (A) 8.9 * 10 11
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 18 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
(A)  3
(B)  6
(C)  7.2
(D)  7.8
(E)  9
Rationale: Answer is E.
x/x+36=1/5
x=9
18-9=9
Answer: (E)  9
Question: In how many ways to select 3 girls and 2 boys from a class? A class contains 5 boys and 5 girls.
(A) 10
(B) 30
(C) 22
(D) 20
(E) 25
Rationale: The way is 5C3+5C2
5C3=5!/2!*3!=5*4*3!/3!*2*1=10
5C2=5!/2!*3!=5*4*3!/3!*2*1=10
=10+10=20 ways to select 3 girls and 2 boys from a class
Answer is option D
Answer: (D) 20
Question: If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
(A) 3⁄7
(B) 4⁄7
(C) 3⁄4
(D) 4⁄3
(E) 7⁄4
Rationale: Should be a sub-600 level Q..
volume= {3/7}/{4/7}=3/4
ANSWER:C
Answer: (C) 3⁄4
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :
(A) 500
(B) 387
(C) 298
(D) 267
(E) 191
Rationale: Explanation:
Given that the student got 125 marks and still he failed by 40 marks
=> The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
Answer: A) 500
Answer: (A) 500
Question: If 40! × 40!/40^n is an integer, what is the largest possible value of n?
(A) 24
(B) 10
(C) 7
(D) 3
(E) 1
Rationale: 40! × 40!/40^n is an integer.
Or 40! × 40!/(4^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 40! = [40/5] + [40/25] = 5
Since there are 2 20!'s, power of 5 in the numerator = 2*5 = 10
Hence the largest value of b for which 40! × 40!/40^n is integer = 10
Correct Option : B
Answer: (B) 10
Question: If the GCD of two distinct numbers (not equal, both integers, greater than 1) is 3, then which of the following can be true? A. They are prime.
B. They are odd.
C. They do not have a common prime factor.
D. They do not have a common factor other than 3.
(A) Only A
(B) Only B
(C) Only C
(D) Only D
(E) Only A and D
Rationale: The GCD of two distinct numbers (not equal, both integers, greater than 1) is 3 means that they don't share factors greater than 3. Allowed factors are 1, 2, and 3. Defined factors are 1 and 3.
A. They are not prime. 3 is the only prime number that is divisible by 3, so one number can be prime but the other number cannot be.
B. They can be odd. For example: 9 has factors of 1 and 3 (1 x 3 x 3), and 15 has factors of 1, 3, and 5 (1 x 3 x 5). 9 and 15 are both odd and have a GCD of 3.
C. They do have a common prime factor. That prime factor is 3.
D. They have a common factor other than 3. Both numbers have common factors of 3 and 1.
Therefore only (B) is correct.
Answer: (B) Only B
Question: 60 + 5 * 12 / (180/3) = ?
(A) 60
(B) 120
(C) 13
(D) 61
(E) None of these
Rationale: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
ANSWER IS D
Answer: (D) 61
Question: Find the odd man out. 125, 127, 130, 135, 142, 153, 165
(A) 165
(B) 142
(C) 153
(D) 130
(E) 125
Rationale: Explanation :
Prime numbers 2, 3, 5, 7, 11, 13 are added successively. Hence, 165 is wrong
Answer : Option A
Answer: (A) 165
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB > CD
(B) XB < YD
(C) AX > XB
(D) CY < XB
(E) AX > AB
Rationale: A--X------B
C-----Y---D
CY < XB.
Answer: D.
Answer: (D) CY < XB
Question: If p is the product of the integers from 1 to 32, inclusive, what is the greatest integer k for which 3^k is a factor of p?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 32! has 3, 6, 9,....30 as factors, which are 10 multiples of 3.
We need to add 4 more to 10 because of 9, 18, and 27.
The answer is C.
Answer: (C) 14
Question: A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage?
(A) 25%
(B) 18%
(C) 20%
(D) 40%
(E) 45%
Rationale: 100(1000-800)/800 = 25%
Profit percentage = 25%
ANSWER A
Answer: (A) 25%
Question: Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)P can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C)  500
(D)  300
(E)  240
Rationale: In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,P if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
Answer: (E)  240
Question: If a certain sample of data has a mean of 31.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (27.0; 36.5)
(B) (24.5; 38.0)
(C) (28.0; 32.5)
(D) (26.5; 35.0)
(E) (29.0; 32.5)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 26 and 36 are within 2.5 standard deviations from the mean.
The answer is B.
Answer: (B) (24.5; 38.0)