mathewhe/aqua_rat huggingface dataset:
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 41, 33
(C) 42, 35
(D) 41, 35
(E) 41, 37
Rationale: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Answer: (A) 42, 33
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference D= 10k - 3 - (10k - 7)
= 4
Answer - D
Answer: (D) 4
Question: 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
(A) 2 : 5
(B) 3 : 10
(C) 4 : 5
(D) 4 : 7
(E) 5 : 11
Rationale: We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
Answer: (B) 3 : 10
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
(A) 32
(B) 20
(C) 24
(D) 16
(E) 14
Rationale: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP=x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER A
Answer: (A) 32
Question: three men invested sum. and their ratio is 5:7:6. profit is 1800.then b's share
(A) 2000
(B) 2100
(C) 700
(D) 2300
(E) 2400
Rationale: b's share =7/18*1800=700
ANSWER:C
Answer: (C) 700
Question: A group of people participate in some curriculum, 30 of them practice Yoga, 20 study cooking, 15 study weaving, 5 of them study cooking only, 8 of them study both the cooking and yoga, 5 of them participate all curriculums. How many people study both cooking and weaving?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Both cooking and weaving = 20 - (5+8+5) = 2
So, the correct answer is B.
Answer: (B) 2
Question: Three candidates contested an election and received 3834 votes, 7606 votes, and 14560 votes respectively. What percentage of the total votes did the winning candidate receive?
(A) 55%
(B) 56%
(C) 57%
(D) 58%
(E) 59%
Rationale: The total number of votes polled = (3834 + 7606 + 14560) = 26000
The winner's percentage = 14560/26000 * 100 = 56%
The answer is B.
Answer: (B) 56%
Question: (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2] = ?
(A) 1.45
(B) 2.75
(C) 26.5
(D) 265
(E) None
Rationale: Answer
Given expression = (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2]
= (69 - 42 + 2) / (45 - 25)
= 29 / 20
= 1.45
Correct Option: A
Answer: (A) 1.45
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040
Rationale: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Answer: (A) 420
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 49
(B) 44
(C) 77
(D) 25
(E) 29
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.Answer:B
Answer: (B) 44
Question: Let Q represent a set of five distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: Q = p1+p2+p3+p4+p5 = even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = even
Ans. B. 2
Answer: (B) 2
Question: A boat crossed a lake from North to South at the speed of 6 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 5 km/h that day, what was its approximate downstream speed?
(A) 12
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/5 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/5 = 1/6 + 2/3 +2/x (div. both sides by D)
=> 1.0 = .16+.66 +.16/x => x=11.98 ~12
option A
Answer: (A) 12
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
(A) 1/15
(B) 4/5
(C) 4/15
(D) 1/5
(E) 2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)
hence 1/5
D
Answer: (D) 1/5
Question: If m and n are both odd prime numbers andm < n, then how many different positive integer factors does2mnhave?
(A)  3
(B)  8
(C)  6
(D)  4
(E)  12
Rationale: m and n are both odd prime numbers- It means either m or n is not 2
and since prime numbers have only two factors - 1 and the number itself
m and n each will have (1+1)= 2 factors
Hence 2mn will have (1+1)(1+1)(1+1)= 8 factors
B is the answer
Answer: (B)  8
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 46%
(B) 57%
(C) 74%
(D) 63%
(E) 68%
Rationale: B
57%
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =(11628x100/20400)% = 57%.
Answer: (B) 57%
Question: Two trains 190 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.6 sec
(B) 18.8 sec
(C) 14.6 sec
(D) 10.8 sec
(E) 12.6 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 190 + 160 = 350 m.
Required time = 350 * 9/250 = 63/5 = 12.6 sec.
Answer: E
Answer: (E) 12.6 sec
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 1978
(B) 2707
(C) 7728
(D) 7008
(E) 7291
Rationale: 35:15 => 7:3
9600*10/100 = 960
9600 - 960 = 8640
8640*7/10 = 6048 + 960
= 7008
Answer: D
Answer: (D) 7008
Question: if p/q=3/4
then3p+7q=?
(A) 37/4
(B) 25/2
(C) 20/4
(D) 35/4
(E) 25/3
Rationale: 3p+7q=?
Divided by q,
3(p/q)+7=x
3*(3/4)+7=37/4
ANSWER:A
Answer: (A) 37/4
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 99
(B) 277
(C) 48
(D) 99
(E) 22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Answer: (C) 48
Question: If (x^2 + x - 8) ≤ x + 1, then x could be represented by which of the following?
(A) − 4 ≤ x ≤ − 3
(B) − 4 ≤ x ≤ 3
(C) − 3 ≤ x ≤ 3
(D) − 3 ≤ x ≤ 4
(E) 3 ≤ x ≤ 4
Rationale: IMO C is correct answer
solving through eqautions
x^2 +x-8<= x+1
(x+3)(x-3)<=0
Answer: (C) − 3 ≤ x ≤ 3
Question: If r and h are two positive integers and r/h = 1.60, then r can equal which one of the following?
(A)  9
(B)  24
(C)  20
(D)  22
(E)  23
Rationale: r/h = 1.60 = 160/100 = 8/5
So, r COULD equal 24
Answer: B
Answer: (B)  24
Question: A bag contains 8 red, 7 blue and 6 green dress. If one dress is picked up randomly then ewhat is the probability that it is neither red nor green?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 3/7
(E) None of these
Rationale: Total number of dress = (8 + 7 + 6) = 21.
Let E	= event that the dress drawn is neither red nor green
= event that the dress drawn is blue.
n(E) = 7.
P(E) =	n(E)	=	7	=	1/3
n(S) 21
A
Answer: (A) 1/3
Question: A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 3 new workers. How many different ways can she assign the new workers?
(A) 2430
(B) 2640
(C) 3300
(D) 4860
(E) 5400
Rationale: whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12C3 = 220 ways.
now 3 out of 12 means total of 4 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 4*3*2*1 = 24
here alt and alt are the same: so 24/2 = 12 ways.
total ways of selecting = (selecting 3 out of 12)*arranging those teams in shifts
= 220*24 = 2640
Ans: B
Answer: (B) 2640
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
(A) 8m/s
(B) 9m/s
(C) 6m/s
(D) 4m/s
(E) 1m/s
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer: A
Answer: (A) 8m/s
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?
(A) $3,000
(B) $4,000
(C) $7,000
(D) $11,000
(E) $25,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (55/100)* (15,000 + x + 18000 )
15,000 + x = (11/20) * (33,000 + x)
300,000 + 20x = 11x + 363,000
9 x = 63,000
x = 7,000
So, Answer will be C
Answer: (C) $7,000
Question: If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
(A) Rs. 850
(B) Rs. 900
(C) Rs. 800
(D) Rs. 910
(E) Rs. 1000
Rationale: Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A)
Answer: (A) Rs. 850
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
(A) 187 min
(B) 177 min
(C) 144 min
(D) 189 min
(E) 166 min
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
Answer:C
Answer: (C) 144 min
Question: If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?
(A) x + y
(B) y – z
(C) xy + 1
(D) xyz + 1
(E) x^2 + y^2
Rationale: xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.
Answer: D.
Answer: (D) xyz + 1
Question: A rectangular tiled patio is composed of 60 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 60 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 13
(E) 8
Rationale: r*c=60 and (r+4)(c-2)=60 --> r=8 and c=7.
Answer: E.
Answer: (E) 8
Question: The average of first five prime numbers greater than 61 is?
(A) 32.2
(B) 32.98
(C) 74.6
(D) 32.8
(E) 32.4
Rationale: 67 + 71 + 73 + 79 + 83
= 373/5
= 74.6
Answer: C
Answer: (C) 74.6
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:6, the price of the cheapest item is?
(A) 2379
(B) 2889
(C) 9288
(D) 9000
(E) 7500
Rationale: Let their prices be 3x, 5x and 7x.
Then, 2x + 4x + 6x = (15000 * 3) or x = 3750.
Cost of cheapest item = 2x = Rs. 7500.
Answer: E
Answer: (E) 7500
Question: Three partners A,B,C start a business.Twice A’s capital is equal to thirce B’s capital and B’s capital is four times C’s capital.Out of a total profit of Rs.16,500 at the end of the year,B’s share is :
(A) Rs.4000
(B) Rs.6000
(C) Rs.7500
(D) Rs.6600
(E) None of these
Rationale: Solution
Let C = x.Then,B = 4x and 2A = 3 4x = 12 x or A = 6x.
∴ A : B : C = 6x : 4x : x = 6 : 4 : 1 .
So, B’s capital = Rs. (16500x4/11) = Rs. 6000. Answer B
Answer: (B) Rs.6000
Question: if N is a prime number bigger than 5. Which of the following expressions must be even?
(A) (a) (N+2)^2
(B) (b) N^2+2.
(C) (c) N(N+2).
(D) (d) (N+1)(N+2)
(E) (e) (N-2)^2
Rationale: N=11
a. 169
b. 123
c. 143
d. 180
e. 81
B
Answer: (B) (b) N^2+2.
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four pink stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
(A) 120
(B) 350
(C) 700
(D) 1,960
(E) 5,040
Rationale: Number of ways to choose 2 colors among 8 - 8c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations -8c2 * 2* 7c4 = 1960
D
Answer: (D) 1,960
Question: If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 2x^2 − x
III. (x + 1)
(A) I only
(B) II only
(C) III only
(D) I , II and III
(E) II and III only
Rationale: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 20
x=3-> 3+9 = 12 ...decreased
ST2:x= 4-> 2*16-4 = 28
x=3->2*9-3 = 15
decreased
St3: x=4-> 5
x=3->1/3 4
Ans: D
Answer: (D) I , II and III
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6years
(D) 12 years
(E) None
Rationale: Solution
Mother's age when Ayesha's brother was born	= 36 years.
Father's age when Ayesha's brother was born
= (38+4) years.
= 42 years.
Required difference	= (42-36)
= 6 years.
Answer C
Answer: (C) 6years
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
(A) 6 days
(B) 10 days
(C) 15 days
(D) 20 days
(E) 25 days
Rationale: Explanation:
Work done by X in 4 days = (1/20 * 4) = 1/5
Remaining work = (1 - 1/5) = 4/5
(X + Y)'s 1 day work = (1/20 + 1/12) = 2/15
Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in (15/2 * 4/5) = 6 days.
Hence, total time taken = (6 + 4) = 10 days.
ANSWER IS B
Answer: (B) 10 days
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(46)-A(45)?
(A) 2^22+1
(B) 2^45
(C) 2^23+1
(D) 2^24
(E) 2^23+1
Rationale: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A46-A45= 2^45
B is the answer
Answer: (B) 2^45
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 997
(C) 266
(D) 289
(E) 179
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: Question: What is the remainder when Q=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
(A)  0
(B)  25
(C)  49
(D)  81
(E)  100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when Q=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: (D)  81
Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Rs. 15
(B) Rs. 15.70
(C) Rs. 19.70
(D) Rs. 20
(E) Rs. 20.70
Rationale: Let the amount taxable purchases be Rs. x.
65 of x =30/100
X = (30/100)x(100/6)
= 5
Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
answer : C
Answer: (C) Rs. 19.70
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
(A) 6.09%
(B) 6.08%
(C) 6.1%
(D) 6.07%
(E) 6.05%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly
=100 x (1 + 3/100)^2 = 106.09
Therefore Effective rate = (106.09 - 100)% = 6.09%
Answer A) 6.09%
Answer: (A) 6.09%
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
5 ~ 2 ~ 7 ~ 4 = ____
(A) 2410
(B) 2910
(C) 2940
(D) 3749
(E) 4470
Rationale: A
2410
2410
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
5 ~ 2 ~ 7 ~ 4 = [first digit of (5 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (5 * 4)]
= 2410
Thus 2410 is the missing number.
Answer: (A) 2410
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters Q long?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 3
Rationale: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m=Q, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Answer: (B) 1
Question: E=(429)^2 * 237 * (1243)^3 is thrice of ?
(A) 33605 * 31960 * (1243)^2
(B) 33654 * 538219 * (1243)^2
(C) 33891 * 533247 * (1243)^2
(D) 34122 * 532004 * (1243)^2
(E) 34606 * 534572 * (1243)^2
Rationale: E=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Answer: (C) 33891 * 533247 * (1243)^2
Question: Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 7 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: A={4,5,6,7,8,9,10,11,12}
B={6,7,8,9,10,11,12...}
Thus we see that there are 9 distinct integers that are common to both. D is the correct answer.
Answer: (D) 9
Question: If the average (arithmetic mean) of the four numbers 5, 15, 30, and (N + 1) is 30, then N =
(A)  19
(B)  20
(C)  69
(D)  78
(E)  292
Rationale: 5+15+30+N+1= 30x 4 = 120
=>N +51 = 120
=>N=69
Answer C
Answer: (C)  69
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
(A) 3:4
(B) 2:5
(C) 6:7
(D) 4:6
(E) 5:2
Rationale: Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
ANSWER A
Answer: (A) 3:4
Question: The present population of a town is 10000. Population increase rate is 10% p.a. Find the population of town after 2 years?
(A) 10000
(B) 11100
(C) 15000
(D) 12100
(E) 14520
Rationale: P = 10000
R = 10%
Required population of town = P(1 + R/100)^T
= 10000(1 + 10/100)^2
= 10000(11/10)^2
= 12100
Answer is D
Answer: (D) 12100
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 35
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: P Ã· 44 = 432
=> P = 432 * 44 = 19008
P / 35 = 19008 / 35 = 543, remainder = 3
B
Answer: (B) 3
Question: Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 6H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 6.93H
(E) 1.21D
Rationale: before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=6H
final value: 6.93H
Ans Is D
Answer: (D) 6.93H
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
(A) 144
(B) 36
(C) 124
(D) 32
(E) 38
Rationale: Time taken to meet the first time = length of track/relative speed
= 400/ (15 +25) (5/18)
= 400/40 *(18/5) = 36 sec.
Answer : B
Answer: (B) 36
Question: The product of digit is a Factor of a two digit number.No of such digit are:
(A) 3
(B) 5
(C) 9
(D) 27
(E) 25
Rationale: 11, 1*1=1
12 , 1*2=2
15 ,1*5=5
24 ,2*4=8
36 , 3*6=18
so Ans is 5
ANSWER:B
Answer: (B) 5
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent R of thatbeforeJuly 1 last year?
(A) 90%
(B) 99%
(C) 100%
(D) 101%
(E) 110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before R= [0.9n (1.1x)]/xn= 0.99 or 99%.B
Answer: (B) 99%