mathewhe/aqua_rat huggingface dataset:
Question: When a is divided by b the remainder is 13.When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b+d?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: In the original question, we're told that, when a is divided by b the remainder is 13
So, b must be greater than 13.
In other words, b COULD equal 14, 15, 16, 17, ....
We're also told that, c is divided by d the remainder is 12
So, d must be greater than 12.
In other words, d COULD equal 13, 14, 15, 16, ....
So, the smallest possible value of b+d is 14+13
In other words, b+d COULD equal 27
Answer:E
Answer: (E) 27
Question: The age of Somu is one-third his father's. 10 years back he was one-fifth of his father's age. What is his persent age ?
(A) 11
(B) 13
(C) 14
(D) 12
(E) 20
Rationale: Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 10 = 3x - 10/5 = x = 20
Answer : Option E
Answer: (E) 20
Question: A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?
(A) 35 min
(B) 36 min
(C) 37 min
(D) 39 min
(E) 45 min
Rationale: at start one person will tell to 2 persons, it will take 5 min, now that 1+2 = 3 persons will tell this to next 6 persons, then 1+2+6 = 9 persons will tell to next 18 persons, then 1+2+6+18 = 27 persons to 54 similarly 1+2+6+18+54 = 81 persons will tell this to 162 persons similarly 1+2+6+18+54+162 = 243 persons will tell this to 486 persons, upto this step total persons who have listened this secret = 2+6+18+54+162+486 = 728, and total time taken upto this step = 5*6 = 30 min, now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min
ANSWER:A
Answer: (A) 35 min
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 12 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19:2
(B) 18:3
(C) 11:1
(D) 11:5
(E) 11:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 15/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 15/2 + 7/2 = 11 litres
As 16 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 11 : 5
Answer:D
Answer: (D) 11:5
Question: Look at this series: J14, L16, __, P20, R22, ... What number should fill the blank?
(A) S24
(B) N18
(C) M18
(D) T24
(E) T28
Rationale: In this series, each set contains alphabet and numbers.
Alphabet increasing by 2alphabets : J L N P R
Numbers increasing by 2 : 14 16 18 20 22
Finally : J14 L16 N18 P20 R22
ANSWER:B
Answer: (B) N18
Question: After decreasing 24% in the price of an article costs Rs.1140. Find the actual cost of an article?
(A) 1500
(B) 6789
(C) 1200
(D) 6151
(E) 1421
Rationale: CP* (76/100)
= 1140
CP= 15 * 100 => CP
= 1500
Answer: A
Answer: (A) 1500
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 2888
(B) 2690
(C) 2668
(D) 9261
(E) 2312
Rationale: A = 8000(21/20)3 = 9261.Answer:D
Answer: (D) 9261
Question: A farmer is planting a row consisting of 3 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
(A) 288
(B) 576
(C) 1,024
(D) 1,152
(E) 10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
3 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *3! * 4! = 288
correct answer option A
Answer: (A) 288
Question: Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 13 sec
(B) 12 sec
(C) 16 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 12 + 6 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer:A
Answer: (A) 13 sec
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 90% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
(A) 1.8 lakh
(B) 1.5 lakh
(C) 1.9 lakh
(D) 8.1 lakh
(E) 6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.9 = 5.7 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 5.7 - 1.2 = 4.5 lakh
Average SP of all the 3 cars = 1.5 lakh
Answer: B)
Answer: (B) 1.5 lakh
Question: Due to 10% decrease in the price of sugar and John can buy 2kg more sugar in Rs100 , then find the CP of sugar?
(A) s. 5(5/9)
(B) s. 2(2/9)
(C) s. 2(1/9)
(D) s. 3(2/7)
(E) s. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 2 kg
Actual price of sugar = 10*100/((100-10 )*2) = Rs. 5(5/9)
A
Answer: (A) s. 5(5/9)
Question: Find the mean proportional between 36 & 49?
(A) A)42
(B) B)61
(C) C)63
(D) D)65
(E) E)67
Rationale: Formula = √a×b
A = 36 and B = 49
√36×49 = 6 × 7 = 42
A
Answer: (A) A)42
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/3 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
(A) 12 greater
(B) 17 fewer
(C) 92 fewer
(D) 36 fewer
(E) 44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/3* 480 =160
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 160-68 =92>>> therfore answer is 92 fewer
C
Answer: (C) 92 fewer
Question: The area of a triangle is with base 4m and height 5m?
(A) 11
(B) 10
(C) 288
(D) 87
(E) 22
Rationale: 1/2 * 4 * 5 = 10 m2 ,Answer: B
Answer: (B) 10
Question: Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan?
(A) 2000
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000
=>4:5:3
=>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]
=> 12:5:6
Share of Rajan => 4600*12/23 = 2400
ANSWER:E
Answer: (E) 2400
Question: In a 200 Meter race A beats B by 35 Meters in 7 seconds. A's time over the cause is?
(A) 47 sec
(B) 40 sec
(C) 45 sec
(D) 33 sec
(E) 35 sec
Rationale: B covers 35m in 7seconds
B take time =(200*7)/35=40
A takes time =40-7=33 sec
ANSWER:D
Answer: (D) 33 sec
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 15th highest price and the 22nd lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: There were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio. Including the radio, there were 14 + 21 + 1 = 36 items sold.
The answer is C.
Answer: (C) 36
Question: If the average (arithmetic mean) of a and b is 110, and the average of b and c is 150, what is the value of a − c?
(A) −220
(B) −100
(C) 100
(D) −80
(E) It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =110 ===> a + b = 220
(b + c)/2 = 150 ===> b + c = 300
(a + b) - (b + c) = 220 - 300 ===> a + b - b - c = - 80 ===> a - c = - 80
Answer: D
Answer: (D) −80
Question: A mixture of 150 liters of wine and water contains 15% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 10
(B) 30
(C) 20
(D) 15
(E) 17
Rationale: Number of liters of water in150 liters of the mixture = 15% of 150 = 15/100 * 150 = 22.5 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (22.5 + P) and total volume of mixture is (150 + P).
(22.5 + P) = 25/100 * (150 + P)
90+4P = 150+P
P = 20 liters.
Answer: C
Answer: (C) 20
Question: If n = 5^11 – 5, what is the units digit of n?
(A) 0
(B) 1
(C) 4
(D) 6
(E) 8
Rationale: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 5^3 - 5. Now 5^3 has last digit 5. we subtract 5 from 5=0 is the answer. Option A
Answer: (A) 0
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 6
(B) 7
(C) 9
(D) 2
(E) 1
Rationale: 9 a.m.
Answer:C
Answer: (C) 9
Question: The length of a rectangle is reduced by 15%. By what % would the width have to be increased to maintain the original area?
(A) 10%
(B) 20%
(C) 17.6%
(D) 30%
(E) 35%
Rationale: Sol. Required change = (15*100)/(100-15)=17.6%
C
Answer: (C) 17.6%
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 55
(B) 65
(C) 75
(D) 85
(E) 95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
ANSWER:C
Answer: (C) 75
Question: A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?
(A) 1/2
(B) 31/36
(C) 49/54
(D) 7/8
(E) 11/12
Rationale: P(three odd digits) = 5/9*5/10*5/10 = 5/36 (first digit cannot be 0, so we have a total of 9 digits, 4 even and 5 odd).
Therefore, P(at least one even digit) = 1 - 5/36 = 31/36.
Answer B.
Answer: (B) 31/36
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 186
(B) 167
(C) 120
(D) 168
(E) 619
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C:
Answer: (C) 120
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 37
(B) 38
(C) 30
(D) 77
(E) 27
Rationale: US = 25
DS = 35
M = (35 + 25)/2
= 30
Answer:C
Answer: (C) 30
Question: How many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph?
(A) 26
(B) 72
(C) 25
(D) 82
(E) 27
Rationale: Explanation:
D = 100 + 160 = 260
S = 36 * 5/18 = 10 mps
T = 260/10 = 26 sec
Answer: Option A
Answer: (A) 26
Question: Find all rational zeros of P(x) = x3*cubic* - 7x + 6.
(A) 1,2,-3
(B) 2,2,-5
(C) 1,4,-7
(D) 4,3,-1
(E) 3,3,-8
Rationale: P(x) = x3*cubic* - 7x + 6 : given
leading coefficient 1 and its factors are : +1,-1
constant term is 6 and its factors are : +1,-1,+2,-2,+3,-3,+6,-6
possible rational zeros : +1,-1,+2,-2,+3,-3,+6,-6
test : P(1) = 0, P(2) = 0 and P(-3) = 0
x = 1, x = 2 and x = -3 are the zeros of P(x).
correct answer is A) 1,2,-3
Answer: (A) 1,2,-3
Question: How much water must be added to 48 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 10 litres
(B) 12 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 48 litres of milk
= (1⁄4 × 48) litres = 12 litres.
Answer B
Answer: (B) 12 litres
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 250 meter
(C) 200 meter
(D) 480 meter
(E) 153 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A
Answer: (A) 150 meter
Question: What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?
(A) 22
(B) 32
(C) 88
(D) 29
(E) 01
Rationale: Explanation:
When the triangles are drawn in an octagon with vertices same as those of the octagon and having one side common to that of the octagon, the figure will appear as shown in (Fig. 1).
Now, we shall first consider the triangles having only one side AB common with octagon ABCDEFGH and having vertices common with the octagon (See Fig. 2).Such triangles are ABD, ABE, ABF and ABG i.e. 4 in number.
Similarly, the triangles having only one side BC common with the octagon and also having vertices common with the octagon are BCE, BCF, BCG and BCH (as shown in Fig. 3). i.e. There are 4 such triangles.
This way, we have 4 triangles for each side of the octagon. Thus, there are 8 x 4 = 32 such triangles.
Answer: B) 32
Answer: (B) 32
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:
(A) 5 %
(B) 12/11 %
(C) 2 %
(D) 5 5/11 %
(E) 10/6%
Rationale: Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % =(300/5500*100)%=5 5/11 %
ANSWER:D
Answer: (D) 5 5/11 %
Question: The product of two positive integers is 575 and their difference is 2. What is the bigger number?
(A) 21
(B) 23
(C) 25
(D) 27
(E) 29
Rationale: Let's use trial and error to find the two numbers.
27*25 = 675 (too high)
25*23 = 575
The answer is C.
Answer: (C) 25
Question: Raja and David invested in a business. They earned some profit which they divided in the ratio of 2:4. If RAM invested Rs.10, 000, the amount invested by David is:
(A) Rs. 21000
(B) Rs. 22000
(C) Rs. 20000
(D) Rs. 23000
(E) Rs. 24000
Rationale: Invested by David = 10000/2*4 = 20000
ANSWER : C
Answer: (C) Rs. 20000
Question: Some of the people in Town L are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town L, three times as many people are tall as are tall in Town L, three times as many people are both as are both in Town L, but no one is neither. If the total number of people in Town L is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town L who are neither left-handed nor tall?
(A)  23
(B)  39
(C)  72
(D)  143
(E)  199
Rationale: Yes, correct answer is indeed D.
{L}={Left} + {Tall} - {Both} + {Neither};
{Y} = 3*{Left} + 3*{Tall} - 3*{Both};
Since the total number of people in Town L is four times greater than the total number of people in Town Y, then:
{Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});
{Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town L who are neither left-handed nor tall must be a multiple of 11.
Only answer choice D, is a multiple of 11: 143=11*13.
Answer: D.
Answer: (D)  143
Question: If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. a = 0
III. b < a
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: a has to equal a squared, and that only works if a is 1. There are no positive integers less than 1, so I and III are correct.
Answer : A
Answer: (A) I only
Question: A regular 10 sided area is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
(A) 48 degrees
(B) 54 degrees
(C) 72 degrees
(D) 84 degrees
(E) 72 degrees
Rationale: its a regular 10 sided so divide the globe by 10.
= 360/10
=36
36 would be the angle at O.
Angles at A and B are equivalent, so
36 + 2x = 180
2x = 144
x = 72
Angles OAB and OBA will be 72 degrees each.
E
Answer: (E) 72 degrees
Question: If p is a natural number and p! ends with w trailing zeros, then the number of zeros that (5p)! ends with will be
(A) a) (p+w) trailing zeros
(B) b) (5p+y) trailing zeros
(C) c) (5p+5y) trailing zeros
(D) d) (p+5y) trailing zeros
(E) e) none of them above
Rationale: Let p = 1. p! = 1! = 1, which means w= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + w
Answer (A).
Answer: (A) a) (p+w) trailing zeros
Question: 841, 784, 729, 676, 625, ?
(A) 576
(B) 529
(C) 484
(D) 441
(E) 400
Rationale: Explanation :
The pattern is 29^2, 28^2, 27^2, 26^2, 25^2, ...
So next number is 24^2 = 576
Answer : Option A
Answer: (A) 576
Question: If a,b are positive integers and a/b=67.75 which of the following could be the value of b?
(A) 1. 25
(B) 2. 26
(C) 4. 20
(D) 4. 27
(E) 5. 30
Rationale: Given a/b = 67.75.
this is 67 and 3/4 = 271/4
Since a and b are integers we know that whatever is the value of b, it must be divisible by 4 completely(to make a an integer)
Ans:C
Answer: (C) 4. 20
Question: Rs.1210 were divided among A,B,C so that A : B = 5 : 4 and B : C = 9 : 10.Then,C gets :
(A) Rs.340
(B) Rs.400
(C) Rs.450
(D) Rs.475
(E) None
Rationale: Solution
A : B = 5 : 4, B : C = 9 : 10 =(9x4/9) :(10x4/90 = 4 : 40/9
∴ A : B : C = 5 : 4 : 40/9 = 45 : 36 : 40 .
Sum of ratio terms =(45+36+40) = 121
∴ C’s share = Rs.(1210x40/121)= Rs. 400.
Answer B
Answer: (B) Rs.400
Question: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
Rationale: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21
ANSWER:A
Answer: (A) 2/21
Question: if p is number greater than 99 ,e is the probability of divisiblity of any even whole number p, and O is the probablity of any odd whole number divisible by p , w is probablity of any whole number divisible by p.
(A) w=2e
(B) e=w/2
(C) o=w/2
(D) either (b) or (c)
(E) none
Rationale: for eg any even whole number take e=2,
any odd whole number take o=3,
any whole number take w=6
for eg the number which is divisible by 2,3,6 is=642
so take option c;
o=w/2 which means 3=6/2 ->3=3;
ANSWER:C
Answer: (C) o=w/2
Question: In how many ways can the letters D, I, G, I be arranged so that the two I's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 6
(E) 128
Rationale: 1 D
2 I
1 G
1 T
Number of ways these letters can be arranged = 4!/2! (2! to account 2 same Is) = 12
Consider 2 Is as 1 entity and thus the number of arrangements for (II)DG = 3! =6
Total allowed cases = 12-6 =6
D is the correct answer.
Answer: (D) 6
Question: If December 3rd, 1999 is a Friday, what day is January 4th, 2000?
(A) Tuesday
(B) Wednesday
(C) Friday
(D) Saturday
(E) Sunday
Rationale: There is difference of 32 days from Dec. 3rd 1999 to Jan. 4th 2000.
32/7 has a remainder of 4.
Jan. 4th is: Friday + 4 days = Tuesday
The answer is A.
Answer: (A) Tuesday
Question: There are 14 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 91
(B) 30
(C) 45
(D) 60
(E) 90
Rationale: 10 players are there.
two players play one game with one another.
so 14C2=14*13/2
=91
SO OPTION A is correct
Answer: (A) 91
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 360 miles apart, at what time will the trains pass each other?
(A) 12:58pm
(B) 12:49pm
(C) 12:55pm
(D) 1:00pm
(E) 1:05pm
Rationale: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 360-40=320 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
320/400>>> 48 Minutes to meet
12:10+48 minutes = 12:58 or Answer A
Answer: (A) 12:58pm
Question: How many four-digit integers exist such that all their digits are odd?
(A) 80
(B) 100
(C) 120
(D) 125
(E) 625
Rationale: so last digit can be filled in 5 ways- 1,3,5,7,9
there are 5 possibilities. The answer is 5∗5*5*5=625
The correct answer is E
Answer: (E) 625
Question: How many numbers between 11 and 90 are divisible by 7?
(A) 7
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: The required numbers are 14,21,28,...........,84.
This is an A.P with a=14,d=7.
Let it contain n terms
then T =84=a+(n-1)d
=14+(n-1)7
=7+7n
7n=77 =>n=11.
ANSWER C 11
Answer: (C) 11
Question: Noelle walks from point A to point B at an average speed of 6 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 7 kilometers per hour?
(A) 6.75
(B) 7
(C) 7.25
(D) 7.5
(E) 8.4
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
7= 2*6*x/6+x
x= 8.4
E is the answer
Answer: (E) 8.4
Question: 0.014×0.014= ?
(A) 0.000196
(B) 0.00196
(C) 19.6
(D) 196
(E) NONE
Rationale: Solution
Sum of decimals places= 6.
14×14	= 196.
= s0.014×0.014
= 0.000196
Answer A
Answer: (A) 0.000196
Question: The salaries of A,B,C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(A) 3 : 3 : 10
(B) 10 : 11 : 20
(C) 23 : 33 : 60
(D) Cannot be determined
(E) None of these
Rationale: Let A = 2k, B = 3k and C = 5k.
A’s new salary = 115⁄100 of 2k = (115⁄100 × 2k) = 23⁄10k
B’s new salary = 110⁄100 of 3k = (110⁄100 × 3k) = 33⁄10k
C’s new salary = 120⁄100 of 5k = (120⁄100 × 5k) = 6k
∴ New ratio = 23k⁄10 : 33k⁄10 : 6k = 23 : 33 : 60
Answer C
Answer: (C) 23 : 33 : 60
Question: A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water?
(A) 86
(B) 67
(C) 30
(D) 15
(E) 32
Rationale: US = 25
DS = 39
M = (39 + 25)/2
= 32
Answer: E
Answer: (E) 32
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.150
(B) Rs.180
(C) Rs.200
(D) Rs.220
(E) Rs.250
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
E)
Answer: (E) Rs.250
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 22
(B) 20
(C) 88
(D) 71
(E) 11
Rationale: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
\Answer: B
Answer: (B) 20
Question: How many different positive integers exist between 10^2 and 10^3, the sum of whose digits is equal to 2?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 101
110
200
total no. is 3
A
Answer: (A) 3
Question: what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?
(A) 1 or 7
(B) 3 or 21
(C) 4 or 28
(D) 2 or 14
(E) 2 or 15
Rationale: since the chord length=2sqrrt(r^2-d^2)
chord length=32,r=20 then we get d=12
chord length=24,r=20 then we get d=16
then we add/subtract we get 4 or 28
ANSWER:C
Answer: (C) 4 or 28
Question: Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
(A) nine hundred thirty
(B) 870
(C) 450
(D) 330
(E) 220
Rationale: A
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer: (A) nine hundred thirty