mathewhe/aqua_rat huggingface dataset:
Question: In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?
(A) 11
(B) 14
(C) 12
(D) 13
(E) 10
Rationale: Explanatory Answer
Step 1: Find the first number common to both the sequences.
The first sequence: Numbers leaving a remainder of 4 when divided by 7: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, ....
The second sequence: Numbers leaving a remainder of 9 when divided by 11: 9, 20, 31, 42, 53, 64, .....
From the listing of the two sequences we can identify the first number that is a part of the both the sequences is 53.
Step 2: Compute common difference of terms common to both sequences and find number of terms.
The common difference of the first sequence is 7 and that of the second sequence is 11.
Elements common to both the sequences will have a common difference that is the LCM of 7 and 11.
77 is the LCM of 7 and 11.
Every 77th number after 53 will satisfy both the conditions.
The terms that are common to both the arithmetic sequences can be expressed as 77k + 53.
Because we are interested in the first 1000 natural numbers, k will take values from 0 to 12.
i.e., a total of 13 values.
Choice D is the correct answer.
Answer: (D) 13
Question: Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
(A) 22
(B) 24
(C) 99
(D) 27
(E) 17
Rationale: Explanation:
Less Cogs more turns and less time less turns
Number of turns required=80 × × = 24 times
Answer: B) 24
Answer: (B) 24
Question: (?)+3699+1985-2047=31111
(A) 34748
(B) 27474
(C) 30154
(D) 27574
(E) None of them
Rationale: x+3699+1985-2047=31111
=x+3699+1985=31111+2047
=x+5684=33158
=x=33158-5684
=27474
Answer is B
Answer: (B) 27474
Question: tom and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: tom always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: tom bids up first, and Bonnie follows. tom bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?
(A) 90
(B) 45
(C) 46
(D) 255
(E) 466
Rationale: Initial bid = p$
tom = p+40
Bonnie = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus A is the correct answer.
Answer: (A) 90
Question: The average weight of 20 boys sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the boys decreased by 8 kg. Find the average weight of first 20 boys?
(A) 150
(B) 154
(C) 218
(D) 182
(E) 192
Rationale: 20x + 50 = 21(x â€“ 8)
x = 218
C
Answer: (C) 218
Question: Difference between the length&breadth of a rectangle is 23m. If its perimeter is 206m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2430 m^2
(B) 2640 m^2
(C) 2520 m^2
(D) 2650 m^2
(E) 2570 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages?
(A) 12
(B) 18
(C) 20
(D) 24
(E) 36
Rationale: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*120/50=36 minutes to print 120 pages (ANSWER E)
Answer: (E) 36
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 31 kg
(B) 32 kg
(C) 33 kg
(D) 34 kg
(E) None of these
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (43 x 2) = 86 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)
Subtracting (i) from (iv), we get : B = 31.
B’s weight = 31 kg.
Answer: A
Answer: (A) 31 kg
Question: What is the ratio of 4/7 to the product 2*(7/3)?
(A) 6:49
(B) 1:3
(C) 3:21
(D) 1:7
(E) 3:49
Rationale: 4/7 / 14/3 = 6/49...
IMO option A.
Answer: (A) 6:49
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 77
(B) 77
(C) 66
(D) 55
(E) 77
Rationale: (45 * 8)/30
= (x * 6)/50
=> x =100
100 – 45
= 55
Answer:D
Answer: (D) 55
Question: The value of (0.625 * 0.0729 * 28.9)/(0.0017 * 0.025 * 8.1) is
(A) 0.3825
(B) 3.825
(C) 38.25
(D) 382.5
(E) 0.0382
Rationale: (0.625*0.0729*28.9)/(0.0017)*0.025*8.1
={(625/1000)*(729/10000)*(289/10)}/{(17/10000)*(25/1000)*(81/10)
=382.5 ANSWER:D
Answer: (D) 382.5
Question: George's drawer has 7 loose black socks, 11 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: The worst case scenario is choosing 11 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is C.
Answer: (C) 14
Question: What is the greatest prime factor of 11!10! + 10!9! ?
(A) 11
(B) 17
(C) 29
(D) 37
(E) 41
Rationale: 11!10! + 10!9! = 10!9!(11*10+1) = 10!*9!*111 = 10!*9!*3*37
The answer is D.
Answer: (D) 37
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
25p of x,10p of 2x,5p of 3x;
25p=25/100=1/4;
10p=10/100=1/10;
5p=5/100=1/20;
1x/4 + 2x/10 + 3x/20=30;
5x+4x+3x=600;
12x=600 (3*50)
x=150 answer : C
Answer: (C) 150
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 5
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
ANSWER E
Answer: (E) 6
Question: What is the perimeter of a regular polygon with sides of length 10 cm and internal angles measuring 140° each?
(A) 90 cm
(B) 108 cm
(C) 120 cm
(D) 132 cm
(E) 144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 140*n
from here
n = 9
So perimeter becomes 10*9= 90
Answer: A
Answer: (A) 90 cm
Question: If n = 2×3×5×7×11×13×18, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
(A) I only
(B) II only
(C) III only
(D) I and III
(E) None of the above
Rationale: Statement I: this is true.
Statement 2 this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (D).
Answer: (D) I and III
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 6n years to that after 3n years?
(A) (1+n/100)^k
(B) (1+k)^n
(C) (1+kn/100)
(D) (1+k/100)^3n
(E) (1+kn)
Rationale: Amount after 6n years will be = x ( 1 + k/100)^6n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^6n } / {x ( 1 + k/100)^3n } = (1+k/100)^3n
Hence answer will be a. (1+k/100)^3n
D
Answer: (D) (1+k/100)^3n
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
(A) 20%
(B) 26%
(C) 42%
(D) 5%
(E) 22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 5 => 5%
Answer: D
Answer: (D) 5%
Question: A can complete the job in 3 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
(A) 1/6
(B) 3/10
(C) 1/2
(D) 5/6
(E) 8/9
Rationale: 1/6=A
Answer: (A) 1/6
Question: Twelve machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2*12 =18
So we need 18-12 = 6 more machines.
Answer : D
Answer: (D) 6
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6 kmph
(B) 7 kmph
(C) 9 kmph
(D) 4 kmph
(E) 2 kmph
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: (A) 6 kmph
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 87
(B) 27
(C) 25
(D) 26
(E) 24
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
Answer: (C) 25
Question: A and B finish the job in 15 days.while A,B and C can finish it in 5 days . C alone will finish the job in
(A) 4.50 days
(B) 3.50 days
(C) 6.0 days
(D) 7.5 days
(E) 5.50 days
Rationale: Explanation:
5 = (15 * x)/(15 + x)
75+5x=15x
10x=75
X=7.5
Answer: Option D
Answer: (D) 7.5 days
Question: A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?
(A) 6
(B) 8
(C) 11
(D) 12
(E) 14
Rationale: In 4hr journey = 55*4 = 220mph
Let in the next additional hour journey = 70*x =70x mph
So, (220+70x)/(4+x)= 60
=> 220+70x = 240+60x
=> 10x = 20
=> x = 2h
So the trip is (4+x)=> 6 hours long
ANSWER:A
Answer: (A) 6
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then DUMP?
(A) 200
(B) 210
(C) 216
(D) 225
(E) 240
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
DUMP=(4+21+13+16)*4= 216
ANSWER:C
Answer: (C) 216
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy?
(A) A)36
(B) B)90
(C) C)40
(D) D)42
(E) E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=600.
6(85-G)+7G=600.
510-6G+7G=600.
G=600-510=90.
The answer is B.
Answer: (B) B)90
Question: A part of certain sum of money is invested at 8% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:6
(B) 3:2
(C) 4:3
(D) 4:1
(E) 4:2
Rationale: 12:8
= 3:2
Answer: B
Answer: (B) 3:2
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 6.
(A) 150
(B) 152
(C) 154
(D) 159
(E) 144
Rationale: D = d * Q + R
D = 17 * 9 + 6
D = 153 + 6
D = 159
ANSWER D
Answer: (D) 159
Question: If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other
(A) 34
(B) 77
(C) 12
(D) 45
(E) None of these
Rationale: Explanation:
For any this type of question, remember
Product of two numbers = Product of their HCF and LCM
So Other number =
693×1199
= 77
Answer: Option B
Answer: (B) 77
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 10.5
(B) 12.5
(C) 13.5
(D) 11.5
(E) 11
Rationale: 1000*15 = 1200*x
x = 12.5
ANSWER B
Answer: (B) 12.5
Question: Viswak was born 3 years after his father's marriage. His mother is 8 years younger than his father but 20 years older than Viswak who is 10 years old. At what age did the father get married ?
(A) 23 years
(B) 25 years
(C) 26 years
(D) 24 years
(E) 22 years
Rationale: Explanation:
Viswak's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
His father's present age = (30 + 8) years = 38 years.
His father's age at the time of Viswak's birth = (38 - 10) years = 28 years.
Therefore Viswak's father's age at the time of marriage = (28 - 3) years = 25 years.
Answer: B
Answer: (B) 25 years
Question: If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
(A) 50 km
(B) 76 km
(C) 18 km
(D) 60 km
(E) 97 km
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/15
5x - 300 =>x = 60 km.
Answer: D
Answer: (D) 60 km
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer Q factors does 2xy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Since 2xy prime Q factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: (D) 8
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 17%?
(A) 17 per kg
(B) 17.55 per kg
(C) 16.5 per kg
(D) 16 per kg
(E) None of these
Rationale: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 117% of 3000 = (117⁄100 × 3000) = 3510
∴ Rate of S.P. of the mixture = (3510⁄200) per kg
= 17.55 per kg.
Answer B
Answer: (B) 17.55 per kg
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 1 mins
(B) 3 mins
(C) 8 mins
(D) 6 mins
(E) 4 mins
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec
= 3 mins
Answer: B
Answer: (B) 3 mins
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 57
(A) 2
(B) 57
(C) 15
(D) 31
(E) 91
Rationale: 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
Now we are getting 56 not 57.. So 57 is the wrong number of the given.
answer : B
Answer: (B) 57
Question: If C(n, 7) = C(n, 5), find n
(A) 15
(B) 12
(C) 18
(D) -1
(E) -2
Rationale: We know that C(n,r) = n! / r!(n - r)!
Now C(n,7) = C(n,5)
n! / 7! (n - 7)! = n! / 5! (n - 5)!
=> 5! (n - 5)! = 7! (n - 7)!
=> [5!] x [(n - 5)(n - 6)[(n - 7)!] = 7 x 6 x 5! x (n - 7)!
=> n2 - 11n + 30 = 42
=> n2 - 11n - 12 = 0
=> (n - 12)(n + 1) = 0
=> n = 12 or n = - 1
But n = - 1 is rejected as n is a non negative integer. Therefore, n = 12
ANSWER:B
Answer: (B) 12
Question: A sum of money at simple interest amounts to Rs. 2240 in 2 years and to Rs. 2600 in 5 years. What is the principal amount
(A) 1000
(B) 1500
(C) 2000
(D) 2500
(E) 3500
Rationale: Explanation:
SI for 3 year = 2600-2240 = 360
SI for 2 year 360/3 * 2 = 240
principal = 2240 - 240 = 2000
Answer: Option C
Answer: (C) 2000
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections Q of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
Q=3*20=60
E. 60
Answer: (E) 60
Question: A wheel rotates 10 times every minute and moves 30 cm during each rotation. How many metres does
the wheel move in two hour?
(A) 6 metre
(B) 12 metre
(C) 120 metre
(D) 876 metre
(E) 360 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 120 = 1200
:. Distance moves = (1200 *30) cms = 36000 cms
In metres = 360 metre
Answer: E
Answer: (E) 360 metre
Question: Look at this series: 31, 29, 24, 22, 17, ... What number should come next?
(A) 11
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: B
15
This is a simple alternating subtraction series, which subtracts 2, then 5.
Answer: (B) 15
Question: A Man travelled a distance of 80 km in 10 hours. He travelled partly on foot at 5 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
(A) 16 km
(B) 14 km
(C) 12 km
(D) 10 km
(E) None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 80 km
So,
5x + 10(9-x) = 80
=> 5x = 10
=> x = 2
So distance traveled on foot = 5(2) = 10 km
Answer: Option D
Answer: (D) 10 km
Question: John makes $40 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 75%
Rationale: Increase = (30/40)*100 = (3/4)*100 = 75%.
E
Answer: (E) 75%
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:20 a.m., how long will the conference last if there are a total of 6 seminars that day?
(A) hours and 15 minutes
(B) hours and 20 minutes
(C) hours and 25 minutes
(D) hours and 30 minutes
(E) hours and 35 minutes
Rationale: Well its like this S B S B S B S B S B S
the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150
Time of 1 seminar =150 /3=50 min .
So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 20 min .
Answer is B.
Answer: (B) hours and 20 minutes
Question: When n is divided by 19, the remainder is 7. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 7. Z must be divisible by which of the following numbers?
(A) 16
(B) 18
(C) 20
(D) 19
(E) 22
Rationale: N = 19 q + 7
N = 11 z + 76
Equating
19 Q + 7 = 11z+7
11z=19q
11z/19 = q
since q is an integer Z must be divisible by 19.
Hence D
Answer: (D) 19
Question: In the formula A = (2r)^3, if r is halved, then A is multiplied by ?
(A) 64
(B) 1/8
(C) 1
(D) 8
(E) 1/64
Rationale: Say r=2 => A1 = 64
when r=1; V2 = 8
V2 = 1/8*V1.
Answer : B
Answer: (B) 1/8
Question: In a 8 x 8 chess board what is the total number of squares.
(A) 238
(B) 204
(C) 678
(D) 169
(E) 161
Rationale: Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares"
i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6
So Substituting 8 in the above formula we get 204
Answer:B
Answer: (B) 204
Question: Two circular signs are to be painted. If the radius of the larger sign is three times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
(A) 3
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: Let R be the radius of the smaller sign.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(3R)^2=9piR^2=9A.
Since the area is 9 times larger, we need 9 times more paint for the larger sign.
The answer is B.
Answer: (B) 9
Question: If 20 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -third less time?
(A) a. 4
(B) b. 8
(C) c. 10
(D) d. 12
(E) e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 20 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 20*36 machine-days of work. So the job requires 20*36 days of machine work in total. We instead want the job done in 1/3 less time, so in 24 days. So we'll need 20*36/24 = 30 machines, or 10 additional machines.
C
Answer: (C) c. 10
Question: In terms of percentage profit, which among following the best transaction.
(A) C.P. 36, Profit 17
(B) C.P. 50, Profit 24
(C) C.P. 40, Profit 19
(D) C.P. 60, Profit 29
(E) C.P. 70, Profit 39
Rationale: Explanation:
Hint: Calculate profit percent as
Profit% = (profit/cost) * 100
ANSWER IS D
Answer: (D) C.P. 60, Profit 29
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
(A) 18 days
(B) 20 days
(C) 24 days
(D) 30 days
(E) 32 days
Rationale: 2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
ANSWER:C
Answer: (C) 24 days
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
(A) 14028
(B) 14029
(C) 14027
(D) 14000
(E) 14298
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: (D) 14000
Question: Two cars A and B are running towards each other from different places 88 km apart. If the ratio of the speeds of the cars A and B is 5 : 6 and the speed of the car B is 90 km per hour then after how long will the two meet each other?
(A) 2263 minutes
(B) 24 minutes
(C) 32 minutes
(D) 36 minutes
(E) None of these
Rationale: Speed of the car A = 5⁄6 × 90 = 75 km/hr
\ Reqd time = 88/90+75×60=32minutes
Answer C
Answer: (C) 32 minutes
Question: If A can do a work in 8 days and B can do the same work in days,in how many days A and B together can finish the work
(A) 3 3/7
(B) 4 3/7
(C) 5 3/7
(D) 6 3/7
(E) None of these
Rationale: no of days taken to finish the work=8*6/(8+6)
Instead of solving this directly take the LCM of 8 and 6
8*6/(8+6)=LCM(8,6)/(LCM(8,6)/8 + LCM(8,6)/6)=24/(3+4)=24/7=3 3/7
Answer A
Answer: (A) 3 3/7
Question: On Saturday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up p percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of p?
(A) 20%
(B) 30%
(C) 33 1⁄3%
(D) 40%
(E) 50%
Rationale: Let Original price be O
Saturday price = 0.8 x O
Monday price = 1.P x 0.8x O
Monday price is 20 percent higher than original.price
So 1.P x 0.8 X O = 1.2 x O
1.P = 1.5
Hence P = 50 %
ANSWER:E
Answer: (E) 50%
Question: The ratio of length of two refill is 9:8.2nd refill got damaged when only half length of 2nd refill get used.The ratio of total no. of pages written by both refill.
(A) 8:3
(B) 6:5
(C) 9:8
(D) 9:4
(E) 5:4
Rationale: the no. of page written is directly proportional to length of refill.
so, initial no. of page to be write =9x,8x.
now,2nd refill only can write 4x page
so new ratio of page written =9x/4x=9:4.
answer D
Answer: (D) 9:4
Question: if {x+y}/{x-y}= 4/3 and x≠0, then what percentage (to the nearest integer) of x+3y is x–3y ?
(A) 40%
(B) 30%
(C) 55%
(D) 36%
(E) None of these
Rationale: Explanation :
=>(x+y)/(x-y)=4/3.
=>(x/y)+1/(x/y)−1=4/3.
Cross-multiplying this equation yields
=>3x/y+3=4x/y−4.
Solving for x/y yields x/y=7.
Now, the percentage of x+3y the expression x−3y makes is
=>x−3y /x+3y∗100
Dividing both the numerator and the denominator of the expression by y, gives:-
=>((x/y)−3/(x/y)+3))×100.
=>((7−3)/(7+3))×100.
=>40%.
Answer : A
Answer: (A) 40%
Question: How long does a train 200 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 82.1 sec
(B) 12.1 sec
(C) 16.1 sec
(D) 13.1 sec
(E) 16.6 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 200 + 132 = 332 m.
Required time = 332/20 = 16.6 sec.
Answer:E
Answer: (E) 16.6 sec