mathewhe/aqua_rat huggingface dataset:
Question: If points A and B are (4+1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(4+1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: (A) I only
Question: In a party attended by 10 persons, each clinch their glass with every other. How many glass clinches?
(A) 45
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=10*9/2
= 45
ANSWER:A
Answer: (A) 45
Question: If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24
II. 36
III. 48
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: y needs to be divisible by 3, 8 and 12. This means that it must be the LCM of 3, 8 and 12 or a multiple of the LCM. The LCM is the smallest number which is divisible by all 3 numbers.
LCM of 3, 8 and 12 will be 3*8 = 24
Now y must be either 24 or a multiple of 24. In any case it will always be divisible by 24.
Will it be divisible by 36 necessarily? No. Say if y is 24, it will not be divisible by 36.
Will it be divisible by 48 necessarily? No. Say if y is 24, it will not be divisible by 48.
Answer (A)
Answer: (A) I only
Question: How many possible integer values are there for x if |6x - 3| < 6 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Solution: |6x-3| < 6
let 6x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =6x ==> -3<6x<9
dividing all values by +4 we have -0.5 <x < 1.5
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Answer: (B) Two
Question: If |x - 8| = x, then x=?
(A) 8
(B) 4
(C) -4
(D) 0
(E) 2
Rationale: |x - 8| = x ...(given)
x^2 - 16x + 64 = x^2
0*x^2 + 16*x -64 = 0 ....(by solving above eq. we get) , x = 4 ===> Ans - B
Answer: (B) 4
Question: At what rate percent per annum will a sum of money double in 8 years.
(A) 12.5%
(B) 13.5%
(C) 11.5%
(D) 14.5%
(E) 24.5%
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
Answer: (A) 12.5%
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 1:2. The sum of numbers is:
(A) 28
(B) 30
(C) 40
(D) 50
(E) 72
Rationale: Let the numbers be 1x and 2x.
Then, their L.C.M = 2x. So, 2x = 48 or x = 24.
The numbers are 24 and 48.
Hence, required sum = (24 + 48) = 72.
ANSWER:E
Answer: (E) 72
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: (A) 10
Question: How many multiples of 5 are there between 5 to 100?
(A) 9
(B) 18
(C) 17
(D) none of these
(E) Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.
Answer : B
Answer: (B) 18
Question: If V is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of V?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: V = 30!
8
V = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3
3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3
So we have a total of 14 three's ...
Therefore the maximum value of K can be 14 (C)
Answer: (C) 14
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 3
(II) y = 3
(III) x + y = 0
(A) II
(B) I
(C) III
(D) I&II
(E) II&III
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
A
Answer: (A) II
Question: The cost of the paint is rs.20 per kg. if 1kg of paint covers 15 sq.ft, how much will it cost to paint outside of a cube having 5 feet each side
(A) Rs.200
(B) Rs.672
(C) Rs.546
(D) Rs.876
(E) None of these
Rationale: Explanation:
surface area of a cube= 6 x 5^2 = 150 sq.ft
quantity of paint required=(150/15)=10 kg
cost of painting= 20 x 10 = Rs.200
Answer: A
Answer: (A) Rs.200
Question: Find the average of first 30 natural numbers.
(A) 20.5
(B) 15.5
(C) 19.5
(D) 19
(E) 17
Rationale: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 30 natural numbers = 30*31/2 = 465
Required average =465/30 =15.5
Answer:B
Answer: (B) 15.5
Question: If there are 56 laborers in a crew, and on a certain day, 30 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
(A) 53.6%
(B) 52.6%
(C) 54.6%
(D) 55.6%
(E) 59.6%
Rationale: 30/56*100=53.57
53.6%
correct answer A
Answer: (A) 53.6%
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 15 days
(B) 14 days
(C) 13 days
(D) 11 days
(E) 10 days
Rationale: Explanation:
x/24 + x/30 + x/40 = 1
x = 11 days
Answer: D
Answer: (D) 11 days
Question: Two horses begin running on an oval course at the same time. One runs each lap in 8 minutes; the other takes 12 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
(A) 24
(B) 12
(C) 9
(D) 4
(E) 3
Rationale: The rate of the faster horse is 1/8 lap/minute;
The rate of the slower horse is 1/12 lap/minute;
Their relative rate is 1/8-1/12=1/24 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(1/24)=24 minutes.
Answer: A.
Answer: (A) 24
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $80, what was the final price of the sweater?
(A) $25.75
(B) $35.75
(C) $15.75
(D) $ 45.75
(E) $42
Rationale: The price with 30% off
80 - 30% of 80 = 80 - (30 / 100) *80 = 56
The price with another 25% off
56 - 25% of 56 = 56 - (25/100)* 56 = $42
correct answer E
Answer: (E) $42
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 720
(B) 740
(C) 760
(D) 780
(E) 800
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A
Answer: (A) 720
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 3 : 4 : 8
(B) 3 : 4 : 7
(C) 3 : 4 : 2
(D) 3 : 4 : 1
(E) 3 : 4 : 5
Rationale: A : B : C = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 144 : 192 : 336
= 3 : 4 : 7.
Answer: B
Answer: (B) 3 : 4 : 7
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum R of all the digits of the integers from 0 to 99 inclusive?
(A) 450
(B) 810
(C) 900
(D) 1000
(E) 1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just R=900:the answer is C.
Answer: (C) 900
Question: The overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X?
(A) 11
(B) 15
(C) 12
(D) 17
(E) 18
Rationale: E
18
(X + Y) â€“ (Y + Z) = 18
X â€“ Z = 18
Answer: (E) 18
Question: How many positive factors do 150 and 90 have in common?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 150 and 90 is 30
Number of factors of 30 = 8
Answer :A
Answer: (A) 8
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
(A) 1:3
(B) 3:1
(C) 2:3
(D) 3:2
(E) 3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
= (27x + 17 y)/(x+y) = 23
= (27x + 17 y)/ = 23(x+y)
= 4x = 6y
=x/y = 6/4 = 3/2 i.e 3:2
Answer :D
Answer: (D) 3:2
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 7
(B) 8
(C) 12
(D) 14
(E) 16
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12
Question: A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?
(A) SEVEN 7
(B) 8
(C) 9
(D) 15
(E) 17
Rationale: 2) The average of the new group of numbers is 35 7/17. The denominator of THAT fraction tells us that the total number of terms in the new list MUST be a multiple of 17:
17, 34, 51, 68, 85, etc.
3) Since we're removing 1 number from a list of consecutive positive integers, we could quickly limit down the possible number of terms in the ORIGINAL list:
If new = 17, old = 18, but the numbers from 1 to 18 would NOT have an average in the mid-30s (it would be much smaller). ELIMINATE this option.
If new = 34, old = 35, but we run into the same problem. The average won't match here either. ELIMINATE this option.
If new = 51, old = 52, same problem here. ELIMINATE this option.
If new = 68, old = 69....HERE we have a group of numbers that might just be what we're looking for.
In theold group, the average is themiddle term= 35, which is REALLY close to the new average once we remove a number.
Now, we just have to figure out which of the 5 answers was removed (and that changed the new average to 35 7/17). There are a couple of ways to do this math, but I'm going to use the answers to save myself some steps:
Sum of 1 to 69, inclusive = 69(35) = 2415
Remove Answer B....2415 - 8 = 2407
New average = 2407/68 = 35 27/68
Now, we can compare 27/68 to 7/17
27/68 and 28/68
This is REALLY close, but is not the answer. Eliminate B. The answer is either A or C.
Since 28/68 is a BIGGER fraction than 27/68, we need the sum (of the 68 integers) to be BIGGER...which means we need to remove a SMALLER number.
Final Answer:
A
Answer: (A) SEVEN 7
Question: If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?
(A) 8
(B) 9
(C) 16
(D) 23
(E) 24
Rationale: (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y.
Thus (16 # y) = 1 implies that 16=yq+1 --> 15=yq--> y is a factor of 15. The factors of 15 are 1, 3, 5, and 15. Now, y cannot be 1, since 16 divided by 1 yields the remainder of 0 not 1.
Therefore the sum of all the possible values of y is 3+5+15=23.
Answer: D.
Answer: (D) 23
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 33∘, the temperature of Friday was :
(A) 41∘
(B) 39∘
(C) 38∘
(D) 30∘
(E) None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 33. So T+W+Th=(152-33)=119
T+W+Th+F=(4×40)=160
F = (160-119)=41∘
Correct Option: A
Answer: (A) 41∘
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
(A) 2/7
(B) 3/7
(C) 5/49
(D) 6/49
(E) 30/343
Rationale: The number of ways to select w, x, and y is: 7*7*7=343
The number of ways to choose three different numbers from the set is 7C3=35.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 35/343 = 5/49
The answer is C.
Answer: (C) 5/49
Question: How many positive integers e less than 30 have no common prime factor with 30?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: e=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: (D) 8
Question: If A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :
(A) ratio 20 : 35 : 63
(B) 35 : 36 : 63
(C) 30 : 35 : 65
(D) 25 :34: 68
(E) None of these
Rationale: A : B = 4 : 7
B : C = 5 :9 = 5*7/5 : 9 *7/5 = 7 : 63/5
A : B : C = 4 : 7 : 63/5 = 20 : 35 : 63
ANSWER: A
Answer: (A) ratio 20 : 35 : 63
Question: 17 balls are numbered 1 to 17. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
(A) 1/7
(B) 3/14
(C) 5/23
(D) 7/34
(E) 9/41
Rationale: P(1st ball is even) = 8/17
P(2nd ball is also even) = 7/16
P(both balls are even) = 8/17 * 7/16 = 7/34
The answer is D.
Answer: (D) 7/34
Question: A train crosses a platform of 140 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 190
(B) 88
(C) 77
(D) 62
(E) 52
Rationale: Length of the train be â€˜Xâ€™
X + 140/15 = X + 250/20
4X + 560 = 3X + 750
X = 190m
Answer: A
Answer: (A) 190
Question: Out of 7 consonants and 4 vowels, how many words of 4 consonants and 2 vowels can be formed?
(A) 25900
(B) 151200
(C) 210
(D) 120
(E) 720
Rationale: Required selection = select 4 consonants from 7 and 2 vowels frm 4
= 7C4 * 4C2
= 210
As we have to form 6 letter word the above combination of consonants and vowels can be done in 6! = 720 different ways
Required no. of ways = 210 * 720
= 151200
Ans - B
Answer: (B) 151200
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 50 and n is not prime, what is the greatest possible value of f(n)?
(A) 48
(B) 35
(C) 31
(D) 32
(E) 28
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 48 = 2*2*2*2*3. This is not a product of distinct prime numbers. Hence incorrect
Option B: 35 = 5*7. This is a product of distinct prime numbers.
Rest all the options are smaller that 35.
Correct Option: B
Answer: (B) 35
Question: A cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
(A) 8.1
(B) 8.9
(C) 8.6
(D) 8.3
(E) 9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 8 miles per hour
Time = t1 = Distance/ Speed = x/8
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 10 miles per hour
Time = t2 = Distance/ Speed = x/10
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/10 + x/8 = x (1/10 + 1/8) = =9x/40
Speed = 2x/(9x/40) = 80/9
= 8.9
Answer : B
Answer: (B) 8.9
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2781
(C) 2278
(D) 2081
(E) 2721
Rationale: Explanation:
(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: (A) 2000
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2888
(C) 2771
(D) 1261
(E) 1121
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) 1000
Question: In some language, 'COLLEGE' is written as 'FSOPHKH' and 'SCHOOL' is wriiten as 'VGKSRP'. Then What is for "STUDENT"??
(A) VXWHHRW
(B) VXXHIRW
(C) VXWHIRX
(D) VXXHHRW
(E) VXXHHRS
Rationale: In 'college' and "school'
1) odd letters has +3 letters more from the alphabets
2) even letter has +4 letters from the alphabets
ODD LETTERS EVEN LETTERS
-----------------------------
S--->V T--->X
U--->X D--->H
E--->H N--->R
T--->W
ANSWER:D
Answer: (D) VXXHHRW
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ l0) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years. Answer: C
Answer: (C) 35
Question: 4.036 divided by 0.02 gives :
(A) 10.09
(B) 1.06
(C) 10.06
(D) 201.8
(E) 100.9
Rationale: = 4.036/0.02
= 403.6/2
= 201.8
Answer is D.
Answer: (D) 201.8
Question: The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
(A) 22
(B) 29
(C) 88
(D) 28
(E) 11
Rationale: Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1
= 29.
Answer:B
Answer: (B) 29
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 80 terms?
(A) 1
(B) 21
(C) 40/41
(D) 80/81
(E) 160/161
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a80 = 1/80 - 1/81
The sum of these terms is 1-1/81 = 80/81
The answer is D.
Answer: (D) 80/81
Question: A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 5/21
(B) 9/21
(C) 7/21
(D) 6/21
(E) 8/21
Rationale: Required probability = (5C3 . 5C1)/10C4 = (10 * 5)/210
= 5/21
Answer:A
Answer: (A) 5/21
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
(A) 11
(B) 12
(C) 10
(D) 13
(E) 10.5
Rationale: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
Ans- C
Answer: (C) 10
Question: If 25th of August in a year is Thursday, the number of Mondays in that month is
(A) 4
(B) 5
(C) 2
(D) 3
(E) 1
Rationale: Explanation:
Given that 25th August = Thursday
Hence 29th August = Monday
So 22nd,15th and 8th and 1st of August also will be Mondays
Number of Mondays in August = 5
Answer: Option B
Answer: (B) 5
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 7 hats randomly out of the drawer and returning each hat before taking out the next one?
(A) 3/4
(B) 5/8
(C) 9/16
(D) 17/32
(E) 35/64
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/128
There are 7C3 = 35 such cases so we need to multiply this by 35.
P(exactly 3 red hats) = 35*1/128 = 35/128
Clearly the probability of getting exactly 3 blue hats will also be 35/128.
The sum of the probabilities is 35/128+35/128 = 70/128 = 35/64
The answer is E.
Answer: (E) 35/64
Question: Set A contains all the even numbers between 12 and 50 inclusive. Set B contains all the even numbers between 112 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 2000
(B) 2550
(C) 5050
(D) 6275
(E) 11325
Rationale: Set A contains 12,14 , 16 ... 50
Set B contains 112 , 114 , 116 ... 150
Number of terms in each set = 20
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*20 = 2000
Answer A
Answer: (A) 2000
Question: A person incurs 20% loss by selling a watch for $1000. At what price should the watch be sold to earn 20% profit?
(A) $1000
(B) $950
(C) $1500
(D) $1150
(E) $1250
Rationale: Let the new selling price be $x
(100-loss%): (1st S.P.) = (100+gain%):(2nd S.P.)
(100-20)/1000 = (100+20)/x
x = 120*1000/80 = 1500
Answer is C
Answer: (C) $1500
Question: What is the greatest power that 4 can be raised to so that the resulting number is a factor of 24!?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: the number of 4s in 24!= 24/4=6..
ans E
Answer: (E) 6
Question: A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is?
(A) 5 5/9
(B) 5 5/7
(C) 5 5/2
(D) 5 5/8
(E) 5 5/1
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 3 years.
Rate = (100 * x) / (x * 6 * 3) = 5 5/9 %.
Answer:A
Answer: (A) 5 5/9
Question: Two pipes can fill a tank in 10 hours and 12 hours. While the 3rd pipe empties the full tank in 20hours. If all the 3 pipes are open in how much time will the tank be filled?
(A) 6hr
(B) 5hr
(C) 7hr 30min
(D) 8hr 20min
(E) 9hr
Rationale: Net part filled in 1 hour = 1/10 + 1/12 - 1/20 = 8/60 = 2/15
The tank will be full in 15/2 hours = 7hr 30min
Answer is C
Answer: (C) 7hr 30min
Question: A particular parking garage is increasing its rates by 25 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
(A) 15%
(B) 18%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.25P = x*P
N*x = x/1.25 = 0.8x, thus a 20% reduction.
The answer is C.
Answer: (C) 20%
Question: Which pair of numbers has least and maximum frequency in the given sequence?
8 7 5 6 4 5 8 3 8 6 7 2 3 5 8 3 5 7 6 4 7 6 5
(A) 3 and 8
(B) 4 and 5
(C) 2 and 6
(D) 2 and 5
(E) 2 and 7
Rationale: frequency means how many times the number occured in the given series
here they asked about least and max frequency
so in the given pair 2 occurs 1 time and 5 occurs 5 times
ANSWER:D
Answer: (D) 2 and 5
Question: What is the diference between the place value and face value of 3 in the numeral 1375?
(A) 295
(B) 297
(C) 300
(D) 310
(E) 312
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
B
Answer: (B) 297
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^6) – (109)?
(A) 2
(B) 5
(C) 18
(D) 19
(E) 25
Rationale: (21)(3^6) is divisible by 3 but 109 is not divisible by 3.
Therefore (21)(3^6) - 109 is not divisible by 3 and thus not divisible by 18.
The answer is C.
Answer: (C) 18
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 299
(B) 288
(C) 240
(D) 775
(E) 2321
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. Answer: C
Answer: (C) 240