mathewhe/aqua_rat huggingface dataset:
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 20-sided polygon have?
(A)  875
(B)  170
(C)  1425
(D)  2025
(E)  2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 20.
Plugging it in, we get 170 diagonals!
Answer (B).
Answer: (B)  170
Question: Adding 50% of x to x is equivalent to multiplying x by which of the following?
(A) 12.5
(B) 1.05
(C) 1.5
(D) 1.2
(E) 1.25
Rationale: 150x/100= 1.5*x
ANSWER:C
Answer: (C) 1.5
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.128 in 4 Years?
(A) 5%
(B) 3%
(C) 4%
(D) 9%
(E) 1%
Rationale: 128 = (800*4*R)/100
R = 4%
Answer: C
Answer: (C) 4%
Question: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: I think the order matters so I'm going w/B. I reasoned this one out.
Does "a pair of distinct letters written in alphabetical order" mean anything significant?
1 2 3 4 5 6 7 8 9 10 11 12
A B C D E AA AB AC AD AE BA BB
Answer: (B) 5
Question: A and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
(A) 30days
(B) 35days
(C) 40days
(D) 45days
(E) 50days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2
A complete remaining work in 1/2*40 = 20
Total work = 10+20 = 30days
Answer: Option A
Answer: (A) 30days
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 79. How tall is the fourth person?
(A) 85
(B) 87
(C) 89
(D) 91
(E) 93
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(79) = 316
x = 75 and the fourth person has a height of 75+10 = 85 inches
The answer is A.
Answer: (A) 85
Question: Kamal's salary was decreased by 50% and subsequently increased by 30%. How much percent does he lose?
(A) 30%
(B) 37%
(C) 65%
(D) 35%
(E) 45%
Rationale: Explanation :
Solution: let original salary = Rs. 100. new final salary = 130% of (50% of Rs.100) = Rs. (130/100 * 50/100 * 100) = Rs. 65.
.'. Decrease = 35%
Answer : D
Answer: (D) 35%
Question: A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 9:5
(B) 9:9
(C) 9:6
(D) 9:1
(E) 9:2
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
Answer: A) 9:5
Answer: (A) 9:5
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
(A) 126 sq. ft
(B) 64 sq. ft
(C) 100 sq. ft
(D) 120 sq. ft
(E) 140 sq. ft
Rationale: Explanation:
Solution 1
length =9 feet
breadth =37−9/2=14feet
Area =9×14=126 square feet
Answer: Option A
Answer: (A) 126 sq. ft
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
(A) 279
(B) 283
(C) 308
(D) 318
(E) 342
Rationale: Other number = (11 x 7700)/275 = 308.
Answer: Option C
Answer: (C) 308
Question: What is the equation of a circle of radius 6 units centered at (2, 2)?
(A) x^2 + y^2 + 6x – 4y = 23
(B) x^2 + y^2 - 6x + 4y = 23
(C) x^2 + y^2 + 6x + 4y = 23
(D) x^2 + y^2 - 6x – 4y = - 23
(E) x^2 + y^2 - 4x – 4y = 28
Rationale: the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2
=> answer = (X-2)^2+(Y-2)^2=6^2
solving,,we get the equation in answer choiceE.
Answer: (E) x^2 + y^2 - 4x – 4y = 28
Question: The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
(A) (700/107) %
(B) (107/100) %
(C) (100/107)%
(D) (7/100)%
(E) (100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $107.
We want the spendings to remain at $100.
(New consumption)*107 = 100 --> (New consumption) = 100/107 kg.
Percent decrease = Change/Original *100 = (1 - 100/107)/1*100 = 700/107%.
Answer: A.
Answer: (A) (700/107) %
Question: In how many ways letters of the word RSCUPERATE be arranged?
(A) 246577
(B) 462349
(C) 454523
(D) 564656
(E) 302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: (E) 302400
Question: 9548 + 7314 = 7362 + (?)
(A) 8300
(B) 8400
(C) 8500
(D) 8700
(E) 9500
Rationale: 9548 16862 = 7362 + x
+ 7314 x = 16862 - 7362
----- = 9500
16862
-----
E)
Answer: (E) 9500
Question: The current birth rate per thousand is 32, whereas corresponding death rate is 11 per thoudand. The net growth rate in terms of population increase in percent is given by
(A) 0.0021%
(B) 0.021%
(C) 2.1%
(D) 21%
(E) none
Rationale: Solution
Net growth on 1000 = (32 - 11) = 21.
Net growth on 100
‹=› [21 / 1000 x 100]%
= 2.1%.
Answer C
Answer: (C) 2.1%
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 18
(D) 24
(E) None of these
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 432
12R2 = 432
R2 = 36
R = 6.
Answer: Option B
Answer: (B) 6
Question: Which of the following describes all values of x for which 4–x^2 >= 0?
(A)  x >= 1
(B)  x <= –1
(C)  0 <= x <= 1
(D)  x <= –1 or x >= 1
(E)  –2 <= x <= 2
Rationale: 4 - x^2 >=0
means x^2 - 4 <=0
=> (x-2)(x+2) <= 0
=> -2 <= x <= 2
Answer - E
Answer: (E)  –2 <= x <= 2
Question: AMS employs 7 professors on their staff. Their respective probability of remaining in employment for 10 years are, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years all 7 of them still work in AMS is ?
(A) 0.19
(B) 0.018144
(C) 0.1
(D) 0.16
(E) none of these
Rationale: Asking atleast 6 of them continue ,
it has 3 cases.
1 all 7 professors continue.
all 7 continues - 0.3*0.4*.0.5*0.6*0.7*0.8*0.9 =0.018144
B
Answer: (B) 0.018144
Question: Jegan has 10 pairs of shoes; each pair is a different color. If Jegan randomly selects 2 shoes without replacement from the 20 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/15
(B) 1/41
(C) 1/35
(D) 1/12
(E) 1/19
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 20 shoes = 20/20 = 1
Probability of selecting the next shoe (out of 19 available) having the same color = 1/19 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/19=1/19.
E is the correct answer.
Answer: (E) 1/19
Question: The fourth proportional to 12, 15 and 20 is?
(A) 21
(B) 66
(C) 25
(D) 99
(E) 26
Rationale: (15*20)/12 = 25
Answer: C
Answer: (C) 25
Question: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:
(A) 25%
(B) 33 1/3 %
(C) 50%
(D) 66 2/3 %
(E) none
Rationale: Let C.P. of each pen be Re. 1.
Then, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.
Gain % = 4/8 * 100 = 50%
ANSWER:C
Answer: (C) 50%
Question: If m/35 is an integer, then each of the following must be an integer EXCEPT
(A) 3
(B) 7/2
(C) 4
(D) 5
(E) 6
Rationale: Now plug m =35 into the answer choices:
A. (35- 28)/7 =1. This is an integer
B. (35+ 21)/7 = 8. This is an integer
C. 14(35)/98 = 7. This is an integer
D. (35^2 - 49)/49 =24. This is an integer
E. (35+ 14)/14 = 7/2. This is NOT an integer
Answer: B
Answer: (B) 7/2
Question: Visitors to show were charged Rs.5 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 2: 5: 13
2x 5x 13x
5 7.5 2.5
10x + 37.5x + 32.5x = 80x/20x
Average = 4
ANSWER:D
Answer: (D) 4
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 277
(B) 299
(C) 245
(D) 200
(E) 211
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.Answer: C
Answer: (C) 245
Question: A jar contains 9 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
(A) 1/49
(B) 1/16
(C) 1/28
(D) 1/3
(E) 1/2
Rationale: Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 9C3 = 84.
Probability of choosing 3 red = 3C3/9C3 = 1/84.
Probability of choosing 3 green = 3C3/9C3 = 1/84.
Probability of choosing 3 blue = 3C3/9C3 = 1/84.
Required probability = 1+1+1/84 = 3/84 = 1/28. Ans (C).
Answer: (C) 1/28
Question: A MAN wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 12 rows the number of trees in each row is 24 if there are 6 more rows find the number of trees in each row?
(A) A)63
(B) B)8
(C) C)48
(D) D)32
(E) E)33
Rationale: Required number of trees
= 12/36 * 24= 8.
ANSWER:B
Answer: (B) B)8
Question: If 2<m<6<m<11, then what is the greatest possible positive integer difference of m and n?
(A) 3
(B) 8
(C) 5
(D) 6
(E) 7
Rationale: Let x=2.1 and y=10.1
Greatest possible difference=10.1-2.1=8
Answer B
Answer: (B) 8
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 8 months
(B) 7 months
(C) 6 months
(D) 10 months
(E) 5 months
Rationale: Let B joined for x months. Then
85000×12:42500×x=3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
⇒850×4=425x
⇒x=8
Answer is A.
Answer: (A) 8 months
Question: Every student at Zarcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Zarcy School?
(A) 63
(B) 69
(C) 74
(D) 82
(E) 86
Rationale: total number of students at Zarcy School The answer is 86 or any multiple of 43.E
Answer: (E) 86
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
(A) 50
(B) 99
(C) 77
(D) 61
(E) 21
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer: A
Answer: (A) 50
Question: If the cost price of 20 articles is same as the selling price of 25 articles. Find the gain or loss percentage?
(A) 20% Loss
(B) 30% Loss
(C) 40% Gain
(D) 40% Loss
(E) 50% Loss
Rationale: Explanation:
20 cp = 25 sp
Cost price CP = 25
Selling price SP = 20
Formula = (SP-CP)/CP * 100 = (20 - 25)/25 * 100 = 20 % Loss
Answer: Option A
Answer: (A) 20% Loss
Question: Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 25 shoppers liked all three juices, how many shoppers took the taste test?
(A) 1,300
(B) 1,000
(C) 900
(D) 700
(E) 650
Rationale: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(300) + 3*(25) = 1000
I = 325
Total number of shoppers who took the taste test = I + II + III = 325 + 300 + 25 = 650
Answer: E
Answer: (E) 650
Question: A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $2440 had it been put at the rate of interest compounded annually?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: We can form equations as following:
Initial amount = P, Total amount after interest = T, Interest per year = I
T = P+I
Given T1 = P+2I = 1400T2 = P+ 5I = 2000
From this we get, P = 1000I = 200 $
Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)
consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ after 3rd yer it is 600$ , after 4th years it is 800$ after 5th years it is 1000$and after 6th year it is 1200$.
To get a 1040 $ compound interest the duration have to be > 4 year and < 6 years.
Only option fitting : Option A.
Answer: (A) 5
Question: A parking space have 5 different slots. 5 cars has to arrange in 5 slots. But there are exactly 3 cars between 2 specified cars. In how many ways cars can be arranged?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: we arranged 2 specified cars in 2 slots = 2!
remaining 3 cars in 3 slots = 3!
number of ways = 2!*3! = 12
correct option is B
Answer: (B) 12
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.75
(B) 3.75
(C) 4.5
(D) 5.5
(E) 6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40 = 3.75 sec.
Answer: Option B
Answer: (B) 3.75
Question: If the sum of a set of 7 different positive prime numbers is an even number, which of the following prime numbers must be in the set?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 7 different prime numbers, whose sum is even
If we include 2, we will have 6 odd prime numbers and one even.
This sum would be even
If we exclude 2, we will have 7 odd numbers.
This sum would be odd
Hence 2 is included.
Option A
Answer: (A) 2
Question: A company pays 15.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
(A) 25
(B) 31
(C) 18
(D) 19
(E) 01
Rationale: Explanation:
Dividend on 1 share = (15.5 * 50)/100 = Rs.7.75
Rs.25 is income on an investment of Rs.100
Rs.7.75is income on an investment of Rs. (7.75 * 100)/25 = Rs.31
ANSWER: B
Answer: (B) 31
Question: The 42 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=42
solving for x you get 6
Answer B
Answer: (B) 6
Question: Three workers have a productivity ratio of 2 to 3 to 5. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 12 to 1
(B) 6 to 1
(C) 25 to 6
(D) 1 to 6
(E) 1 to 5
Rationale: The fastest worker who does 6 units of job worked for all 10 hours, so he did 5*10=50 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 50 to 12, or 25 to 6.
Answer: C.
Answer: (C) 25 to 6
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
(A) It increases by 8%
(B) It decreases by 8%
(C) No change in revenue
(D) It increases by 10%
(E) None
Rationale: Explanation:
100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
ANSWER IS B
Answer: (B) It decreases by 8%
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
(A) 2/3
(B) 2/9
(C) 1/3
(D) 1/9
(E) 1/10
Rationale: Total number of outcomes possible when a die is rolled = 6
Hence n(S) = 6 * 6 =36
E = Getting a sum of 9 when the two dice fall = {(3,6),(4,5),(5,4),(6,3)}
hence n(E) = 4
=>4/36 = 1/9
ANSWER D
Answer: (D) 1/9
Question: The value of land increases by p% during June and decreases by q% during July. If the value of the land is the same at the end of July as at the beginning of June, what is q in terms of p?
(A) 100p/(100+p)
(B) 200p/(100+2p)
(C) p(2+p)/(1+p)2
(D) p(200+p)/10000
(E) 2p/p+2p
Rationale: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer B: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
A
Answer: (A) 100p/(100+p)
Question: if you put $1500 into the bank with a interest rate of 5% and left the money there for 4 years how much interest do you get at the end of the 4 years?
(A) $15
(B) $150
(C) $300
(D) $250
(E) $125
Rationale: p= 1500
r=0.05
I=(1500)(0.05)(4)=$300
ANSWER: $125
Answer: (E) $125
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 30 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A)  15 seconds
(B)  18 seconds
(C)  25 seconds
(D)  30 seconds
(E)  45 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+30
for Cristina=C=5*t
@t=15, N=75 C=75 right answer
ans:A
Answer: (A)  15 seconds
Question: A sum amounts to Rs.3969 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
(A) s.3600
(B) s.5000
(C) s.4500
(D) s.4800
(E) s.5800
Rationale: CI=3969,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
3969=P[21/20]^2
3969[20/21]^2
3600
ANSWER:A
Answer: (A) s.3600
Question: A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k2,k42, where k represents a digit that occurs twice, how many values could n have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 10
Rationale: 1k2k42
Taking sum of the numericals = 1 + 2 + 4 + 2 = 9
We require the values of K such that they are also divisible by 3
102042
132342
162642
192942
Answer = 4 = D
Answer: (D) 4
Question: How many bricks, each measuring 50 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
(A) 6400
(B) 2400
(C) 5500
(D) 7400
(E) 3200
Rationale: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (50 x 11.25 x 6) = 3200
ANSWER:E
Answer: (E) 3200
Question: If the production cost in a certain company for first 1 lac item is Rs 20 lac and thereafter Rs 10 for each item. What is the minimum numbers of items that must be manufactured in order to get a cost of Rs 15 per item ?
(A) 12 per item
(B) 13 per item
(C) 14 per item
(D) 15 per item
(E) 16 per item
Rationale: If x lac items are to be manufactured , then
15x = 20+(10*(x-1)
x= 2
so 2 lac items must be manufactured in order to get a cost of Rs 15 per item
ANSWER:D
Answer: (D) 15 per item
Question: How much time will take for an amount of Rs. 410 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 4 years 4 months
(B) 4 years
(C) 3 years
(D) 9 years
(E) 5 years
Rationale: Time = (100 * 81) / (410 * 4.5)
= 4 years 4 months
Answer: A
Answer: (A) 4 years 4 months
Question: The youngest of 4 children has siblings who are 2, 7, and 11 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 25, what is the age of the youngest sibling?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: x + (x+2) + (x+7) + (x+11) = 100
4x + 20 = 100
4x = 80
x = 20
The answer is D.
Answer: (D) 20
Question: Two pipes A and B can separately fill a tank in 20 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 590 liters
(B) 540 liters
(C) 820 liters
(D) 900 liters
(E) 580 liters
Rationale: 1/20 + 1/15 - 1/x
= 1/15
x = 12
20 * 45 = 900
Answer:D
Answer: (D) 900 liters
Question: In 40 litres of a mixture, the ratio of milk to water is 7:1. In order to make the ratio of milk to water as 3:1, the quantity of water that should be added to the mixture will be?
(A) Rs. 1000
(B) Rs. 1200
(C) Rs. 1400
(D) Rs. 1600
(E) Rs. 2500
Rationale: Explanation:
Total simple interest received , I = Rs.1600
Principal , p = 7000
period, n = 5 years
Rate of interest, r = ?
Simple Interest,
I
=
p
n
r
100
I=pnr100
⇒
1600
=
7000
×
5
×
r
100
⇒
r
=
1600
×
100
7000
×
5
=
160
35
=
32
7
%
⇒1600=7000×5×r100⇒r=1600×1007000×5=16035=327%
By rule of alligation,
Rate of interest % from part1	Rate of interest % from part2
6	4
Net rate of interest %
32
7
327
32
7
−
4
=
4
7
327−4=47
6
−
32
7
=
10
7
6−327=107
=> Part1 : part2
=
4
7
:
10
7
=
4
:
10
=
2
:
5
=47:107=4:10=2:5
Given that total amount is Rs.7000. Therefore, the amount lent at 6% per annum (part1 amount)
=
7000
×
2
7
=Rs. 2000
D)
Answer: (D) Rs. 1600
Question: find the next term in the series 1, 0, -2, -3, 8, 95
(A) 683
(B) 684
(C) 685
(D) 686
(E) 687
Rationale: Its N! - N^2
1 - 1^2 = 0
2! - 2^2 = -2
3!(6) - 3^2 = -3
4!(24) - 4^2 = 8
..
..
6!(720) - 6^2 = 684
ANSWER:B
Answer: (B) 684
Question: In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled?
(A) 1200
(B) 1400
(C) 1600
(D) 1500
(E) 1540
Rationale: Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)
20 % = 60 % - 40 %
20% -----> 280 (20×14 = 280 )
100% -----> 1400 (100×14 = 1400)
Option 'B'
Answer: (B) 1400
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
(A) 1820
(B) 6758
(C) 6000
(D) 2582
(E) 2972
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000
= 6000
Answer:C
Answer: (C) 6000
Question: A man has Rs. 496 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 93
(C) 96
(D) 97
(E) 99
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 496
16x = 496
x = 31.
Hence, total number of notes = 3x = 93.
B
Answer: (B) 93