mathewhe/aqua_rat huggingface dataset:
Question: Seller selling an apple for Rs.16, a Seller loses 1/6th of what it costs him. The CP of the apple is?
(A) 10
(B) 12
(C) 17
(D) 18
(E) 20
Rationale: SP=16Loss=CP17Loss=CP−SP=CP−16⇒CP17=CP−16⇒16 CP17=16⇒CP17=1⇒CP=17
C
Answer: (C) 17
Question: In the Mundane Goblet competition, 6 teams compete in a “round robin” format: that is, each team plays every other team exactly once. A team gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all teams (added together) in the Mundane Goblet competition?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
Rationale: No OA yet: my method:
max points:
A B C D E F
15 12 9 6 3 0 = 45POINTS
min points
A B C D E F
5 5 5 5 5 5 = 30
45-30= 15 points ====> (A)ANS
Answer: (A) 15
Question: A six-digit number is formed by repeating a three-digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :
(A) 7 only
(B) 13 only
(C) 11 only
(D) 1001 only
(E) 1003 only
Rationale: 256256 = 256 x 1001; 678678 = 678 x 1001, etc.
So, any number of this form is divisible by 1001
ANSWER:D
Answer: (D) 1001 only
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) 276
(C) 88
(D) 27
(E) 828
Rationale: Explanation:
A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:A
Answer: (A) 1261
Question: The number of new words that can be formed by rearranging the letters of the word 'tuesday' is?
(A) 5040
(B) 7
(C) 1
(D) 5041
(E) 5039
Rationale: Number of words which can be formed
= 7! - 1 = 5040 - 1
= 5039.
Answer:E
Answer: (E) 5039
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in
(A) 15 sec.
(B) 16 sec.
(C) 18 sec.
(D) 20 sec.
(E) None
Rationale: Solution
Speed	= (63 x 5/18) m/sec
= 35/2 msec
Time taken	= (280 x 2 /35)m/sec
= 16 sec.
Answer B
Answer: (B) 16 sec.
Question: Shekar scored 76, 65, 82, 67 and 55 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
(A) 65
(B) 69
(C) 75
(D) 85
(E) 90
Rationale: Explanation :
Average= (76+65+82+67+55)/5 = 375/5 =69
Hence average=69
Answer : B
Answer: (B) 69
Question: 12, 10, x, 8
The median of the list of positive integers above is 9. Which of the following could be the average (arithmetic mean) of the list?
(A) 3
(B) 5.5
(C) 6.25
(D) 7
(E) 9
Rationale: GivenThe median of the list of positive integers above is 9
So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 9
so the sequence will be x 8 10 12
Lets say x = 6, which gives us mean = sum/4 = 9
E is correct
Answer: (E) 9
Question: The average of 9 observations was 6, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 36
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
1 to 9 = 9 * 6 = 54
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 54 = 36
Option A
Answer: (A) 36
Question: At a game of billiards,A can give B 15 points in 60 and A can give C 20 points in 60.How many points can B give C in a game of 90 ?
(A) 30 points
(B) 20 points
(C) 10 points
(D) 12 points
(E) None of these
Rationale: Solution
A : B = 60 : 45 and A : C = 60 : 40.
∴ B/C =( B/A x A/C) = (45/60 x 60/40) = 45/40 =90/80= 90 : 80
∴ B can give C 10 points in a game of 90.
Answer C
Answer: (C) 10 points
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 15 more than the first integer. Find the three integers?
(A) 7, 9, 29
(B) 7, 2, 10
(C) 7, 9, 10
(D) 9, 11,13
(E) 7, 9, 29
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 15 => x = 9
Hence three consecutive odd integers are 9, 11 and 13.
Answer:D
Answer: (D) 9, 11,13
Question: Ramesh and Neelesh start walking to meet one another from places 25 kms apart. If Ramesh walks at the rate of 2 kms an hour and Neelesh at 3 kms an hour, how many hours will it be before they meet?
(A) 2 hr
(B) 3 hr
(C) 4 hr
(D) 5 hr
(E) 6 hr
Rationale: velocity of ramesh =2km/h
velocity of neelesh =3km/h
both start moving from both the end of 25km
let at time t they meet
let ramesh walks x km
than neelesh have walk =25-x km
2=x/t.......(a)
3=25-x/t.....(b)
on solving
t=5 hr.
ANSWER:D
Answer: (D) 5 hr
Question: Find the sum of 4 digit numbers which are made by 1,2,5,6
(A) 93424
(B) 93524
(C) 92324
(D) 93324
(E) 93344
Rationale: (n-1)!(1111....)(sum of digits)
(4-1)!(1111)(1+2+5+6)
93324
ANSWER:D
Answer: (D) 93324
Question: A hostel had provisions for 250 men for 48 days. If 50 men left the hostel, how long will the food last at the same rate?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 65
Rationale: A hostel had provisions for 250 men for 48 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 48
250×48=200x
5×48=4x
x=5×12=60
ANSWER D
Answer: (D) 60
Question: Robert spent $64 in buying raw materials, $125 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) A)$150
(B) B)$210
(C) C)$250
(D) D)$160
(E) E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 64+125
90% of x = 189
90x/100 = 189
x = $210
Answer is B
Answer: (B) B)$210
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) 1045
Rationale: 1015 as it is divisible by every no..
ANSWER:B
Answer: (B) 1015
Question: The number which exceeds 16% of it by 84 is :
(A) 100
(B) 52
(C) 58
(D) 60
(E) 62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =84
x-16/100x =84
x-4/25x=84
21/25x=84
x=(84x25/21)= 100
Answer A
Answer: (A) 100
Question: In how many ways can the integer 54 be expressed as a product of two different positive integers?
(A) 10
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: 54=(3^3)*2
Since 54 is not a perfect square, no of ways=4
Answer D
Answer: (D) 4
Question: On selling 13 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
(A) s. 45
(B) s. 50
(C) s. 55
(D) s. 60
(E) s. 90
Rationale: (C.P. of 13 balls) - (S.P. of 13 balls) = (C.P. of 5 balls)
C.P. of 8 balls = S.P. of 13 balls = Rs.720.
C.P. of 1 ball = Rs.720/8	= Rs.90.
Answer: Option E
Answer: (E) s. 90
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 25 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 11.79
(B) B) 8
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/25 = 9*12/5 = 21.6
Time difference = 11.79
Ans:A
Answer: (A) A) 11.79
Question: A 300 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 99
(B) 450
(C) 350
(D) 882
(E) 281
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 45 = 50/3
3(x + 300) = 2250 è x = 450m.
Answer: B
Answer: (B) 450
Question: In how many ways can the letters of the word RECPECT be arranged?
(A) 6453
(B) 9856
(C) 2520
(D) 6429
(E) 8547
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: (C) 2520
Question: 3 teenagers decided to make greetings cards to sell. Their goal was to make 60 cards. Mark made 7 times more than Paul, while John made three times more than Paul. How many did Paul make?
(A) 3
(B) 6
(C) 7
(D) 36
(E) 60
Rationale: # of cards Paul made = x
Mark = 7x
John = 3x
X + 7x+ 3x = 66
11x = 66
X = 6
ANSWER: B
Answer: (B) 6
Question: Walking with 4/5 of my usual speed, I miss the bus by 3 minutes. What is my usual time?
(A) 16 min
(B) 26 min
(C) 34 min
(D) 20 min
(E) 12 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:51 -------- 3 4 --------- ? è 12
Answer: E
Answer: (E) 12 min
Question: Fourteen years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) A)35
(B) B)34
(C) C)45
(D) D)49
(E) E)26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Fourteen years ago, P was half of Q in age
=> 2(3x – 14) = (4x – 14)
=> 6x – 28 = 4x – 14
=> 2x = 14
=> x = 7
7*x = 7*7 = 49
Answer: Option D
Answer: (D) D)49
Question: Car A runs at the speed of 70km/hr & reaches its destination in 10hr. Car B runs at the speed of 35 km/h & reaches its destination in 10h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 5
(B) 11 : 8
(C) 13 : 7
(D) 15 : 7
(E) 2 : 1
Rationale: Sol. Distance travelled by Car A = 70 × 10 = 700 km
Distance travelled by Car B = 35 × 10 = 350 km
Ratio = 700/350 = 2 : 1
Answer : E
Answer: (E) 2 : 1
Question: What is the area of a square field whose diagonal of length 14 m?
(A) 160 sq m
(B) 140 sq m
(C) 200 sq m
(D) 400 sq m
(E) 180 sq m
Rationale: d2/2 = (14 * 14)/2 = 140
ANSWER:B
Answer: (B) 140 sq m
Question: A person can row at 9 kmph and still water. He takes 6 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
(B) 28
(C) 29
(D) 54
(E) 20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 6.5
=> x/10 + x/8 = 13/2 => (4x + 5x)/40 = 13/2 => x
= 29 km.
Answer:C
Answer: (C) 29
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 40 square meters. What is the area that is covered with three layers of wallpaper?
(A) 5 Square Meters
(B) 36 Square Meters
(C) 40 Square Meters
(D) 83.3 Square Meters
(E) 120 Square Meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 40 = 80 sq m of the wallpaper overlaps in three layers. 80 sq m makes two extra layers hence the area over which it makes two extra layers is 40 sq m.
Answer (C).
Answer: (C) 40 Square Meters
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 50 sec
(B) 45 sec
(C) 55 sec
(D) 65 sec
(E) 51 sec
Rationale: C
55 sec
T = (660 + 165)/54 * 18/5
T = 55
Answer: (C) 55 sec
Question: If a = b*c, -1 < c < 0 and 8 < b, which of the following is correct?
(A) a > 7.
(B) 0 < a <8.
(C) 8 < a < 0
(D) a < -14
(E) a < -7
Rationale: b is +ve & c is -ve
Eliminate A ,B&C
For min. value max. numerator and minimize denominator
take b=8.1 & c=-0.9
a=8.1*-0.9
a<-7
Ans E
Answer: (E) a < -7
Question: In a factory, there are 50% technicians and 50% non-technicians. If the 50% of the technicians and 50% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 50%
(B) 57%
(C) 52%
(D) 22%
(E) 42%
Rationale: Total = 100
T= 50 NT= 50
50*(50/100)=25 50*(50/100)=25
25 + 25 = 50 => 100 - 50 = 50%
Answer:A
Answer: (A) 50%
Question: In how many ways can 3 men and 3 women be seated around a round table if each women is to be between 2 men.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 1-2-3-4-5-6-1 (assume this to be a closed circle)
Lets assume the position of the first man to be "fixed" at 1, then there are two remaining positions for the remaining two men: 3rd and 5th seat.
Number of ways of seating a man in 3rd seat = 2
As only one man is left, number of ways of seating a man in 5th seat is 1.
Number of ways that three men can be seated first at the round table = 1*2*1=2
There are three remaining seats 2,4, and 6.
Number of options for 2 = 3
Number of options for 4 = 2 (only 2 women are left)
Number of options for 6 = 1 (only 1 woman left)
i.e. The three women can be seated in 3! ways = 6
Total number of possibilities = 2*6 = 12
ANS:A
Answer: (A) 12
Question: If a man buys 1 liter of milk for 12 rs. and mixes it with 20% water and sells it for 15 rs then what is the %age of gain...
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Quantity after adding 20% water=1.2 liter
SP of 1.2 lit.@15 Rs./liter=15*1.2=18 Rs
CP=12 Rs/lit.
% profit=100*(18-12)/12=50
ANSWER:C
Answer: (C) 50
Question: if 1/8 of a pencil is black 1/2 of the remaining is white and the remaining 7/2 is blue find the total length of the pencil?
(A) 7.33cm
(B) 6.33cm
(C) 5.33cm
(D) 9.33cm
(E) 8.33cm
Rationale: (1/8)p + (1/2)p + (7/2)= p
on solving the above for p we get 9.333
Now checking for the answer:
9.333/8=1.166 cm
9.333/2=4.665 cm
now 1.166+4.665+(7/2) = 9.33cm
ANSWER:D
Answer: (D) 9.33cm
Question: Given a spinner with four sections of equal size labeled W, B, C, and D, what is the probability of NOT getting an W after spinning the spinner two times?
(A) 15/16
(B) 9/16
(C) 1/2
(D) 1/4
(E) 1/8
Rationale: The probability of NOT getting an W after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Answer: (B) 9/16
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
(A) -33
(B) 34
(C) -34
(D) 35
(E) 33
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: In how many different ways can the letters of the word "BICYCLE" be rearrangement?
(A) 5040
(B) 5045
(C) 5140
(D) 5010
(E) 5020
Rationale: Option 'A'
The total number of arrangements is
7P7 = 7! = 5040
Answer: (A) 5040
Question: 71
a3
+1b
___
98
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
(A) 25
(B) 54
(C) 43
(D) 45
(E) 04
Rationale: 1+3+b=8
b=4
7+a+1=8
a=0
ab=04
ans=E
Answer: (E) 04
Question: An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest, is
(A) 10:28 am
(B) 10:30 am
(C) 10:31 am
(D) None of above
(E) Cannot be determined
Rationale: Explanation:
L.C.M. of 60 and 62 seconds is 1860 seconds
1860/60 = 31 minutes
They will beep together at 10:31 a.m.
Sometimes questions on red lights blinking comes in exam, which can be solved in the same way
Option C
Answer: (C) 10:31 am
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 220
(B) 175
(C) 145
(D) 200
(E) 362
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: D
Answer: (D) 200
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?
(A) 1/100
(B) 1/121
(C) 1/45
(D) 1/56
(E) 3/72
Rationale: =1/n - 1/(n+1)
=1/n(n+1)
Only answer choice that satisfies above equation is D
1/7*8
ANSWER:D
Answer: (D) 1/56
Question: Two dice are thrown together. What is the probability that the sum of the number on the two faces is divisible by 4?
(A) 2/9
(B) 1/9
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Clearly n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 4.
E= {(1,3), (2,2), (2,6), (3,1), (3,5), (4,4), (5,3), (6,2), (6,6)}
n(E) = 9
Hence, P(E) = n(E)/n(S) = 9/36 = 1/4
ANSWER:C
Answer: (C) 1/4
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1.75, then the 3rd term is which of the following?
(A) −1.5
(B) −1
(C) 0
(D) 0.5
(E) 4
Rationale: First = 1.75
Second = 2*1.75-1 = 2.5
Second = 2*2.5-1 = 4
Answer: option E
Answer: (E) 4
Question: The average of first five prime numbers greater than 20 is?
(A) 32.9
(B) 32.7
(C) 32.8
(D) 32.2
(E) 32.1
Rationale: 23 + 29 + 31 + 37 + 41 = 161/5
= 32.2
Answer:D
Answer: (D) 32.2
Question: List I: 4, 6, 8, 10
List II: x, 4, 6, 8, 10
(A) 7
(B) 4
(C) 3
(D) 5
(E) 2
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: A
Answer: (A) 7
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) 228
(B) 480
(C) 267
(D) 288
(E) 276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer: B
Answer: (B) 480
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) 80000
(B) 60000
(C) 50000
(D) 75000
(E) 90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
=1/3 x = 1/2 (150000 - x)
=x/3 + x/2 = 75000
=5x/6 = 75000
=x = 75000 x 6 /5	= 90000
Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
Answer is B.
Answer: (B) 60000
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 6 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 21 : 50
(B) 3 : 10 : 10
(C) 4 : 8 : 5
(D) 32 : 35 : 25
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 6x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 6x × 140% :
8x × 125% = 36 : 84 : 100
= 18 : 21 : 50
Answer A
Answer: (A) 18 : 21 : 50
Question: The spinner shown is divided into 6 sections of equal
size. What is the probability of landing on a section that
contains the letter P using this spinner?
(A) 3/6
(B) 4/6
(C) 5/6
(D) 2/6
(E) 1/6
Rationale: The spinner has 6 sections in total and 2 of these sections contain the letter P.
Sections are equal to one another in size and thus they are each equally likely to be landed on.
Therefore, the probability of landing on a section that contains the letter P is 2/6 .
correct answer D
Answer: (D) 2/6
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 6
(B) 9
(C) 3
(D) 5
(E) 2
Rationale: x * 1 = 3 * 5/3
x = 5
Answer:D
Answer: (D) 5
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 50,000
(E) 52,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*500= 50,000 light bulbs are present.
D is the answer
Answer: (D) 50,000
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.6 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
(A) a. 150
(B) b. 300
(C) c. 600
(D) d. 1,200
(E) e. 360
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.6 = 360
Answer: E
Answer: (E) e. 360
Question: The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP?
(A) 35%
(B) 65%
(C) 75%
(D) 90%
(E) 100%
Rationale: Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area of RR is less than the surface area of sphere PP
16k−4k=12k16k−4k=12k
Now,
=12k16k×100=12k16k×100
=75%=75%
Thus surface area of sphere RR is less than the surface area of sphere P by 75%
C
Answer: (C) 75%
Question: One number will be chosen randomly from each of the sets below . If x represents the chosen member of Set X and y represents the chosen member of Set Y, what is the probability that x/yx/y will be an integer?
X = {9, 10, 11, 12}
Y = {2, 3, 4, 5}
(A) 1/16
(B) 3/8
(C) 1/2
(D) 3/4
(E) 15/16
Rationale: (x, y), for which x/y = integer:
(9; 3)
(10; 2)
(10; 5)
(12; 2)
(12; 3)
(12; 4)
6 pairs out of 4*4 = 16, so the probability is 6/16 = 3/8.
Answer: B.
Answer: (B) 3/8
Question: A vessel of capacity 30 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 14.7
(B) 2.9
(C) 38.3
(D) 78.3
(E) 79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 30, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(30 - 9)/30]^2 (30) = 14.7 litres.
Answer: Option A
Answer: (A) 14.7
Question: If a car had traveled 10 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 30 km, at what speed did it travel?
(A) 20 kmh
(B) 25 kmh
(C) 30 kmh
(D) 35 kmh
(E) 40 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
30/x - 30/(x + 10) = 1/2
Substitute the value of x from the options. --> x = 20 --> 30/20 - 30/30 = 3/2 - 1 = 1/2
Answer: A
Answer: (A) 20 kmh
Question: If a = 1 and b = -2, then (2a^2 + b)(r + y) + (a + b)(r - y) =
(A) 0
(B) 2x
(C) y - r
(D) x - y
(E) x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(r+y)=y-r => Smash C
Answer: (C) y - r
Question: A man's age is 125% of what it was 10 years ago, but 8313% of what it will be after 10 years. What is his present age?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let the age before 10 years =x. Then,
125x100=x+10⇒125x=100x+1000⇒x=100025=40
Present age =x+10=40+10=50.
Answer is C.
Answer: (C) 50
Question: What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Answer: (A) 3
Question: (500 + 200)x (2+3)Ã— 4 Ã— (3 + 2) = ?
(A) 17500
(B) 70000
(C) 14000
(D) 65000
(E) 82000
Rationale: (500 + 200) Ã— 5Ã—4x5 = ?
or, ? = 700 Ã—5x 4 Ã— 5 = 70000
Answer B
Answer: (B) 70000
Question: If Reneesh earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased?
(A) 1/4
(B) 1/5
(C) 7/100
(D) 3/25
(E) 1/20
Rationale: Perhaps it is also easy to just translate the % into fractions:
6%: 6/100 = 3/50
7%: 7/100
8%: 8/100 = 4/50 =2/25
9%: 9/100
Only 7/100 exists in the answer choices, so ANS C
Answer: (C) 7/100