mathewhe/aqua_rat huggingface dataset:
Question: The lengths of the diagonals of a rhombus are 20 and 48 meters. Find the perimeter of the rhombus?
(A) 150 merters
(B) 125 meters
(C) 96 meters
(D) 104 meters
(E) 152 meters
Rationale: Below is shown a rhombus with the given diagonals. Consider the right triangle BOC and apply Pythagora's theorem as follows
BC 2 = 10^2 + 24^2
and evaluate BC
BC = 26 meters.
We now evaluate the perimeter P as follows:
P = 4 * 26 = 104 meters.
Answer is D
Answer: (D) 104 meters
Question: At present, the ratio between the ages of Arun and Deepak is 4:7. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 17 years
(B) 35 years
(C) 18 years
(D) 12 years
(E) 19 years
Rationale: Let the present ages of Arun and Deepak be 4x and 7x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 7x
= 35 years.
Answer:B
Answer: (B) 35 years
Question: A survey was sent to 90 customers, 15 of whom responded. Then the survey was redesigned and sent to another 50 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 5%
(C) 8%
(D) 28%
(E) 63%
Rationale: Rate of first survey = 15/90
Rate of second survey = 9/50
% Response rate increase (9/50-15/90)/(15/90) = 8%
Answer is C = 8%
Answer: (C) 8%
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 135?
(A) 136*136
(B) 136*137
(C) 272
(D) 136
(E) 137
Rationale: The least common multiple of two numbers greater than 135 is 2(136) = 272, where the two distinct integers are 136 and 272.
The answer is C.
Answer: (C) 272
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 99 widgets produced in the first hour of operation are not inspected by either inspector?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90/15)+1 =7
Total : 19+32 -7=44
hence, widgets not inspected: 99-44=55
Option E
Answer: (E) 55
Question: The famous Denali Star train starts from anchorge & travels towards fair banksat speed 50 mph.After some time another train Glacier Discovery Train( At parallel track) at fair banks And moves towards Anchorge at a speed of 70 mph. Both the trains Denali star & Glacier discovery have a length 1/6 miles each .After the trains meet how many seconds will faster train take to overtake the slower one?
(A) 10 sec
(B) 11 sec
(C) 12 sec
(D) 13 sec
(E) 14 sec
Rationale: total distance = (1/6)+(1/6) = 1/3 miles
relative speed = (50+70) mph = 120 mph
time taken = (1/3)/(120) hours = 10 seconds
ANSWER:A
Answer: (A) 10 sec
Question: in a triangle sides of triangle are ac=ln(n),
ab=ln(8),bc=ln(50).
what is the possible value of n?
(A) 394
(B) 395
(C) 385
(D) 398
(E) 399
Rationale: sum of 2sides of the triangle should be greater than the third side
therefore,ln(50)+ln(8)>ln(n)
Now according to the log property;log(a)+log(b)=log(a*b)
So,ln(50*8)>ln(n)
400>n;
Bt the options are;
390,395,392and 398.
So 0 and 400 wont be included,so the ans is 398.
ANSWER:D
Answer: (D) 398
Question: What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Unit digit in (6374)1793 = Unit digit in (4)1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
A)
Answer: (A) 0
Question: If the list price of a book is reduced by Rs 5 then a person can buy 2 more books for Rs 300.the original cost of the book is
(A) 25
(B) 30
(C) 15
(D) 20
(E) 22
Rationale: A list price
B No of book
AxB = 300
(A-5)x(B+2) = 300
2A-5B+AB-10=300
2A-5B=10
(2A-10)A=300x5
AA-5A = 150x5 = 750
A=30
ANSWER:B
Answer: (B) 30
Question: how many positive integers less than 1960 are such that the product of their digits is 10.
(A) 220
(B) 230
(C) 280
(D) 220
(E) 240
Rationale: 1960 is divisible by 10 ( or 2*5) = 196
196 is divisible by 4 = > 49
49 = 7 *7
hence 1960 is divisible by 2,4,5, 7 ,7
if there were only one 7,
i.e if the problem were 280
C
Answer: (C) 280
Question: Express the following as a fraction 56%
(A) 13/50
(B) 17/30
(C) 11/25
(D) 14/25
(E) 14/19
Rationale: 56% = 56/100
= 14/25
Answer is D.
Answer: (D) 14/25
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:99
(B) 82:31
(C) 32:45
(D) 34:89
(E) 35:21
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer:C
Answer: (C) 32:45
Question: What is the least number which when divided by 5, 6, 9 and 12 leaves remainder 4 in each care?
(A) 130
(B) 140
(C) 156
(D) 184
(E) 196
Rationale: Explanation:
LCM of 5, 6, 9 and 12 is 180
Required number = 180 + 4 = 184
Answer: Option D
Answer: (D) 184
Question: In given series 56, 72, 90, 110, 132, 150 only one number is incorrect. Find out that wrong number
(A) 140
(B) 150
(C) 120
(D) 170
(E) 160
Rationale: The numbers are
7 x 8=56
8 x 9=72
9 x 10=90
10 x 11=110
11 x 12=132
12 x 13=156
So, 150 is wrong.
ANSWER:B
Answer: (B) 150
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of two hammers and two wrenches is one-third that of 8 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer?
(A) 1/2
(B) 2/3
(C) 1
(D) 3/2
(E) 2
Rationale: x be the weight of a hammer and y be the weight of a wrench.
(2x+2y)=1/3*(8x+5y)
3(2x+2y)=(8x+5y)
6x+6y=8x+5y
y=2x
Ans - E
Answer: (E) 2
Question: Two pipes A and B can fill a cistern in 15 and 20 minutes respectively, and a third pipe C can empty it in 30 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/4 min
(B) 12 min
(C) 17 1/7 min
(D) 17 1/8 min
(E) 17 5/7 min
Rationale: 1/15 + 1/20 - 1/30 = 5/60 = 1/12
12/1 = 12
Answer:B
Answer: (B) 12 min
Question: Express a speed of 72 kmph in meters per second?
(A) 10 mps
(B) 76 mps
(C) 20 mps
(D) 97 mps
(E) 16 mps
Rationale: 72 * 5/18
= 20 mps
Answer:C
Answer: (C) 20 mps
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
(A) 1/7
(B) 1/2
(C) 1/6
(D) 1/3
(E) 1/1
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer:B
Answer: (B) 1/2
Question: In a class, 6 students can speak Gujarati, 15 can speak Hindi and 6 can speak Marathi. If two students can speak two languages and one student can speak all the three languages, then how many students are there in the class
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: n(AUBUC)=6+15+6-2-2-2+1=22
ANSWER:B
Answer: (B) 22
Question: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?
(A)   3
(B)   3.5
(C)   4
(D)   4.5
(E)   5
Rationale: Let total time= t
F travelled at rate 10mph for t/3 time and 5mph for 2t/3 time
d= s1t1+s2t2
30= 10*t/3 + 5*2t/3
30= 20t/3
t= 4.5
D is the answer
Answer: (D)   4.5
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
(A) 3 days
(B) 2 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: C
5 days
WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer: (C) 5 days
Question: A trumpet section includes two musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
(A) 240
(B) 125
(C) 120
(D) 100
(E) 2
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are two possible musicians who could be placed in the first chair. To determine the number of possible orderings, we multiply these numbers, which we can express as 2!. Now 2! = (2)(1) = 2=E
Answer: (E) 2
Question: George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: George 1 day work= 1/30
Mark 1 day work= 1/45
George 15 day work= 15*1/30 =1/2
Work remaining= 1-1/2 =1/2
George + Mark 1 day work= 1/30 + 1/45 =1/18
Number of day required to complete 1/2 work= (1/2)/(1/18)= 9 days
So total days required to complete the work is 15+9= 24 days.
ANSWER:B
Answer: (B) 24
Question: There are 54 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 1) 4
(B) 2) 7
(C) 3) 17
(D) 4) 21
(E) 5) 27
Rationale: x -> Golf Club
2x -> Tennis Club
y -> both
x+2x-y = 51
3x - y =51
multiples of 3 greater than 51
57
60
63
66
69
72 - 21 = 51
IMO (D)
Answer: (D) 4) 21
Question: The average age of 3 girls is 16 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
(A) 12 years
(B) 7 years
(C) 9 years
(D) 10 years
(E) 8 years
Rationale: Total age of 3 boys = 16*3 =48
ratio of their ages = 1:2:3
Age of the youngest =48*1/6 = 8 years
Answer is E
Answer: (E) 8 years
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 12 and 13. The larger of the two numbers is:
(A) 299
(B) 278
(C) 322
(D) 231
(E) 121
Rationale: Clearly, the numbers are (23 * 12) and (23 * 13). Larger number
= (23 * 13) = 299.
Answer: A
Answer: (A) 299
Question: One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
(A) 1.00 minutes
(B) 1.20 minutes
(C) 1.50 minutes
(D) 1.85 min
(E) 2.00 minutes
Rationale: By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore, answer 1.85 minutes will be correct. Answer-D
Answer: (D) 1.85 min
Question: A, B two inlet pipes takes 15,18 minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank respectively. In what time the tank be filled if all of them are operated together?
(A) 11 minutes
(B) 10 minutes
(C) 12 minutes
(D) 13 minutes
(E) 14 minutes
Rationale: LCM=90
No of days= [90/(90/15 + 90/18 - 90/45)
= [90/(6+5-2)]
= [90/9]
= 10 minutes
ANSWER:B
Answer: (B) 10 minutes
Question: A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 95 km/hr
(B) 50 km/hr
(C) 54 km/hr
(D) 55 km/hr
(E) 56 km/hr
Rationale: Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
ANSWER: A
Answer: (A) 95 km/hr
Question: If y is 50 percent greater than x, then x is what percent less than y?
(A) 20%
(B) 25%
(C) 33%
(D) 50%
(E) 67%
Rationale: y = 1.5x
x = y/1.5 = 10y/15 = y - (1/3)*y
1/3 is about 33%.
The answer is C.
Answer: (C) 33%
Question: The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?
(A) 28%
(B) 25%
(C) 24%
(D) 23%
(E) 27%
Rationale: explanation:
15 CP = 20 SP
20 --- 5 CP loss
100 --- ? => 25% loss
Answer: B
Answer: (B) 25%
Question: q, b, c, and d are positive integers. If the remainder is 9 when q is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?
(A)  20
(B)  19
(C)  18
(D)  16
(E)  15
Rationale: When q is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Answer: (E)  15
Question: If Juan takes 15 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 15x/y
(B) 15y/x
(C) x/(15y)
(D) 15/(xy)
(E) xy/15
Rationale: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/15 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/15 seconds)
Time = (x yards) x (15 seconds/y yards)
Time = 15x/y seconds
Answer A.
Answer: (A) 15x/y
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 3 + 3 = ??
(A) 11
(B) 12
(C) 5
(D) 14
(E) 18
Rationale: 5
ANSWER:C
Answer: (C) 5
Question: If t > a and L < a, which of the following cannot be true?
(A)  d + L = 14
(B)  d - L = 7
(C)  d - L = 1
(D)  a - t = 9
(E)  a + d = 9
Rationale: Is the answer D?
If t>a, then t-a>0 (always positive). The converse would be a-t<0 (always negative). Option D states that a-t=9, which can never be true.
Answer: (D)  a - t = 9
Question: Walking 6/7 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 28 m
(B) 20 m
(C) 22 m
(D) 23 m
(E) 24 m
Rationale: Speed Ratio = 1:6/7 = 7:6
Time Ratio = 6:4
1 -------- 6
4 --------- ?
=> 24 m
ANSWER:E
Answer: (E) 24 m
Question: If .003^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
(A) 0
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 0.003^4= (3*10^-3)^4 = 81*10^-12 = 0.81*10^-10 which would have 10 zeros to the right of the decimal point. The answer is D.
Answer: (D) 10
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 $56 more. What was his original selling price?
(A) $880
(B) $950
(C) $1100
(D) $1240
(E) $1360
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 = 56
0.07 = 56
P = 800
The original selling price was 800*1.1 = 880.
The correct answer is A.
Answer: (A) $880
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.28 %
(B) 56.25 %
(C) 56.28 %
(D) 46.25 %
(E) 56.21 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer: B
Answer: (B) 56.25 %
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 100 barrels of oil?
(A) 2
(B) 3
(C) 4
(D) 18
(E) 180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 100 barrels they will take a bit less than 100 mins which will be more than 1 hrs but less than 2 hrs.
Answer (A)
Answer: (A) 2
Question: In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?
(A) 1880
(B) 2400
(C) 2880
(D) 3424
(E) None
Rationale: Solution
They have to be arranged in the following way: | L | T | L | T | L | T | L | T | L | The 5 lions should be arranged in the 5 places marked ‘L’. This can be done in 5! ways. The 4 tigers should be in the 4 places marked ‘T’. This can be done in 4! ways. Therefore, the lions and the tigers can be arranged in 5!*4!= 2880 ways
Answer C
Answer: (C) 2880
Question: The operation # is defined for all nonzero d and y by d#y = d + d/y. If a>0, then 1#(1#a) =
(A) a
(B) a+1
(C) a/(a+1)
(D) (a+2)/(a+1)
(E) (2a+1)/(a+1)
Rationale: d#y = d + d/y. If a>0, then 1#(1#a) =
You can see that a stands for y and 1 stands for d. I like to work with numbers so I did d=1 a=2 and a=y so y=2
1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in a, which is 2:
A. a --> 2
B. a+1 --> 2+1=3
C. a/(a+1)-->2/(2+1)=2/3
D. (a+2)/(a+1)-->(2+2)/(2+1)=4/3
E. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3
So E is the answer.
Answer: (E) (2a+1)/(a+1)
Question: A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?
(A) 30 seconds
(B) 32 seconds
(C) 34 seconds
(D) 36 seconds
(E) 38 seconds
Rationale: Explanation:
Speed of train relative to jogger = (45-9) = 36 kmph
= 36*(5/18) = 10 m/sec
Distance to cover = 240 + 120 = 360 metres
Time = Distance/Speed
So,
Time=360/10=36 Seconds
ANSWER IS D
Answer: (D) 36 seconds
Question: Can you replace the question mark with the correct number, given the pair of numbers exhibits similar relationship?
? : 3839 :: 11 : 1209
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Solution
16
Formular used :
pow(x,3) - pow(x,2) - 1
11*11*11 - 11*11 - 1
1331 - 121 - 1
1209
Similarly, we can solve
pow($x,3) - pow($x,2) - 1 = 3839
This condition holds true for number-16
Answer B
Answer: (B) 16
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl ande 2 boys are selected is:
(A) 21/46
(B) 25/117
(C) 1/50
(D) 3/25
(E) 7/15
Rationale: Let S be sample space and E be event of selecting 1 girl and 2 boys
Then n(S)=25c3
=2300
n(E)=10c1x15c2=1050
P(E)=2300/1050=21/46
ANSWER A 21/46
Answer: (A) 21/46
Question: A bowl contains pecans, cashews, and almonds in a ratio of 3 : 4 : 6, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
(A) II only
(B) I,II only
(C) III only
(D) I,III only
(E) I only
Rationale: i. The ratio 2 : 3 is the same as the given ratio 4 : 6. If one pecan were removed, the new ratio would be 2 : 4 : 6, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : E
Answer: (E) I only
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 8
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?
(A) 1/2
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Given rate at which A & B works at normal pace to complete 1 widget is (1/3).
Hence A's rate = B's rate = half of (1/3).
Hence A's rate is (1/6), so to complete 1 widget A requires 6 hours.
ANSWER:A
Answer: (A) 1/2
Question: The wages earned by Robin is 49% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
(A) 23%
(B) 18.75%
(C) 30%
(D) 50%
(E) 32.88%
Rationale: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $149 and $160 respectively.
Charles earns $49 more than Robin who earns $149.
Therefore, Charles' wage is 49/149*100 = 32.88%.
The correct choice is (E)
Answer: (E) 32.88%
Question: Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be:
(A) 9% less than N
(B) 11% less than N
(C) Equal to N
(D) 9% greater than N
(E) 11% greater than N
Rationale: Correct answer is (A).
This year, the price of a building is price1=P/N.
If this price increases by 50% it becomes Price2=P/N*1.1
Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N
Which is 9% less than N.
Answer: (A) 9% less than N
Question: If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 6 time the part of C .Find the ratio among their parts.
(A) 1:2:4
(B) 1:4:1
(C) 8:4:1
(D) 12:6:1
(E) 4:3:2
Rationale: By the assumptions as mentioned we have A=2B and B=6C. So A=2(6C) and we get A=12C. We have, therefore, A:B:C = 12C:6C:C. By cancelling the ratio with C we have 12:6:1. The answer is, therefore, D.
Answer: (D) 12:6:1
Question: At present the ratio between the ages of Arun and Deepak is 2:3. After 5years, Arun's age will be 25 years. What is the age of Deepak at present?
(A) 20 years
(B) 30 years
(C) 15 years
(D) 25 years
(E) 28 years
Rationale: Let the present ages of Arun and Deepak be 2x years and 3x years respectively
2x+5 = 25
2x = 20
x = 10
Deepak's age = 3x = 30years
Answer is B
Answer: (B) 30 years
Question: It takes Machine A 32 minutes to fill a water tank.Another Machine B takes 6 minutes to fill the same water tank. If both machines are put to work , how long would it take to fill same water tank?
(A) 3.0 minutes
(B) 4.5 minutes
(C) 5.1 minutes
(D) 6.0 minutes
(E) 6.5 minutes
Rationale: By guess it is clear that the time taken will be less than 6 minutes and around 5 Therefore, answer 5.1 minutes will be correct. Answer-C
Answer: (C) 5.1 minutes
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 15 years.
(A) 5:2
(B) 1:5
(C) 1:2
(D) 5:1
(E) None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗3/100) /(P∗R∗15/100)]
=3PR /15PR=1:5
Option B
Answer: (B) 1:5
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?
(A) 2%
(B) 3%
(C) 5%
(D) 7%
(E) None
Rationale: increase in the population in 10 years
=
262500
−
175000
=
87500
=262500−175000=87500
percent increase in the population in 10 years
=
87500
175000
×
100
=
8750
175
=
50
%
=87500175000×100=8750175=50%
average percent increase of population per year
=
50%/10
=
5%
Option C
Answer: (C) 5%
Question: A train runs across a post in 15 seconds and across a platform of length 100m in 25 seconds. Determine the length of this train:
(A) 137
(B) 150
(C) 287
(D) 167
(E) 172
Rationale: Explanation:
Let us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.
A pole is assumed as a point object.
=>Time taken by the train to pass the pole= x/y
=>15=x/y
=>y=x/15
Now, the train passes the platform which is 100 m in length in 25 seconds.
=>x+100/y=25
=>x+100/25=y
Equating speed generated from both cases:
x+100/25=x/15
Therefore x = 150 metres.
ANSWER: B
Answer: (B) 150