mathewhe/aqua_rat huggingface dataset:
Question: If y > 0, (2y)/5 + (3y)/10 is what percent of y?
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: can be reduced to 2y/5+3y/10 =2y/5=70%
D
Answer: (D) 70%
Question: [( 3.242 x 15 ) / 100] = ?
(A) 0.045388
(B) 4.5388
(C) 453.88
(D) 473.88
(E) 0.04863
Rationale: Answer
Multiplying 3.242 x 15=4.863
Now divide 4.863 by 100
So, 4.863 ÷ 100= 0.04863
∴ Shift the decimal two places to the left as 100
Correct Option: E
Answer: (E) 0.04863
Question: The manufacturing cost of a shoe is Rs.200 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
(A) s 222
(B) s 246
(C) s 220
(D) s 210
(E) s 217
Rationale: Explanation :
Total cost of a watch = 200 + (500/100) = 205.
Gain = 20% => SP = 1.2CP = 1.2 X 205 = 246
Answer : B
Answer: (B) s 246
Question: My friend collects antique stamps. she purchased two, but found that she needed to raise money urgently. So she sold them for Rs. 800 each. On one she made 20% and on the other she lost 20%. How much did she gain or lose in the entire transaction?
(A) 66.66
(B) 66.69
(C) 66.68
(D) 66.67
(E) 66.65
Rationale: Explanation:
Selling prices were given. Assume that on the first stamp she made profit and on the second stamp she made loss.
So cost prices of the both stamps = 800120%+80080%800120%+80080% = 1666.66
So She incurred a loss of 66.66 rupees.
Answer: A
Answer: (A) 66.66
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 2999
(B) 3000
(C) 2777
(D) 2999
(E) 17212
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer:B
Answer: (B) 3000
Question: Look at this series: 90, 88, 86, 84, 82, 80, 78, 76, ... What number should come next?
(A) 72
(B) 70
(C) 77
(D) 74
(E) 78
Rationale: Explanation:
In this series, each number 2 is subtracted to arrive at the next number.
Answer: Option D
Answer: (D) 74
Question: The average price of three items of furniture is Rs. 12000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
(A) 2379
(B) 2889
(C) 9288
(D) 7200
(E) 28311
Rationale: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (12000 * 3) or x = 2400.
Cost of cheapest item = 3x = Rs. 7200.
Answer: D
Answer: (D) 7200
Question: The smallest number which when diminished by 6, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1014
(C) 1022
(D) 1032
(E) 1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+6
= 1008 + 6
= 1014
Answer: B
Answer: (B) 1014
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 50 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(A) 250
(B) 300
(C) 350
(D) 400
(E) 500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 50 meters, thus second time she runs 2*50 = 100 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters, thus the circumference is 100 + 150 = 250 meters.
Answer: A.
Answer: (A) 250
Question: If 50% of x is 20 less than 5% of 500, then x is?
(A) 50
(B) 100
(C) 75
(D) 25
(E) 10
Rationale: 50% of x = x/2 ; 5% of 500 = 5/100 * 500 = 25
Given that, x/2 = 25 - 20 => x/2 = 5 => x = 10.
Answer: E
Answer: (E) 10
Question: The value of x + x(xx) when x = 2 is:
(A) 10
(B) 16
(C) 18
(D) 36
(E) 64
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (A)
Answer: (A) 10
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?
(A) 1000
(B) 1300
(C) 1450
(D) 1540
(E) 2000
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
and 5x art books = 2000
E
Answer: (E) 2000
Question: What will be the remainder when 13^36 is divided by 2196?
(A) 0
(B) 1
(C) 12
(D) 2195
(E) 5
Rationale: In such Qs, best is to get the dividend and divisor in some friendly figures..
13^36=(13^3)^12=2197^12=(2196+1)^12
when (2196+1)^12 is divided by 2196, all terms in the expansion are divisible by 2196 except 1^12, so the remainder will be 1
ANSWER:B
Answer: (B) 1
Question: On decreasing the price of a colour TV by 10%, its sale is increased by 15%. The effect on the revenue is?
(A) 4.5% decrease
(B) 4.5 % increase
(C) 16% decrease
(D) 16% increase
(E) none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-10 + 15 + ( -10 x 15)/100]% or 3.5%
ANSWER:3..5
Answer: (E) none of these
Question: A company produces 120000 bottles of water everyday. If a case can hold 12 bottles of water .How many cases are required by the company to hold its one day production
(A) 2000
(B) 4500
(C) 5000
(D) 8000
(E) 10000
Rationale: Number of bottles that can be held in a case = 12
Number of cases required to hold 120000 bottles = 120000/12=10000 cases.
So the answer is E =10000
Answer: (E) 10000
Question: If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?
(A) a. 8
(B) b. 9
(C) c. 12
(D) d. 7
(E) e. 27
Rationale: Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D
Answer: (D) d. 7
Question: Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?
(A) 2100 miles.
(B) 2200 miles.
(C) 2300 miles.
(D) 2400 miles.
(E) 2100 miles.
Rationale: E
2100 miles.
Each vowel equivalent to 500 and each consonant equivalent to -200
Answer: (E) 2100 miles.
Question: The average weight of 12 persons is 50 kg. On replacing a man whose weight is 53 kg. with a new man, new average becomes 49 kg. The weight of the new man is:
(A) 22
(B) 41
(C) 37
(D) 29
(E) 11
Rationale: Explanation:
Sum of the weights of all 12 persons = 12 × 50 = 600
Sum of the weights of all 12 persons after replacement = 12 × 49 = 588
The difference is because of one person with 53 kg is replaced by another one. So his weight must be 53 - 12 = 41
AnswerB
Answer: (B) 41
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 12. What is the total number of students in the school?
(A) 72
(B) 80
(C) 25
(D) 150
(E) 100
Rationale: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 12 + 2/3 of 12
80/100x = 20
x = 25.
Answer: Option C
Answer: (C) 25
Question: Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.
(A) 2
(B) 4
(C) 6
(D) 7
(E) 9
Rationale: Sol. use formula (xy / x+y)
So nearest value for 3.93 = 4
Answer: Option B
Answer: (B) 4
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(A) 35
(B) 62
(C) 68
(D) 35
(E) 32
Rationale: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1
= 55 - 15 - 10 + 2 = 32
Answer: E
Answer: (E) 32
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 70 watch exactly two channels. How many watch exactly one channel?
(A) 185
(B) 180
(C) 165
(D) 190
(E) 195
Rationale: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 70 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 -70 - 2x
x = 25
250 = n(Exactly 1 channel) + 70 + 25
n(Exactly 1 channel) = 165
Answer (C)
Answer: (C) 165
Question: N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?
(A) 5
(B) 6
(C) 1
(D) 2
(E) 3
Rationale: DETAILED SOLUTION
To begin with, the question should read "find the 44th digit".
Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.
So, a number comprising 42 2's would be a multiple of 13, so would a number comprising 36 2's. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.
CORRECT ANSWER B
Answer: (B) 6
Question: The present ages of three persons are in proportions
4 :7 :9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)
(A) 8, 20, 28
(B) 16, 28, 36
(C) 20, 35, 45
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let their present ages be 4x,7x and 9x years respectively.
Then, (4x-8)+(7x-8)+(9x-8)	= 56
20x = 80
x= 4.
Their present ages are 16,28,36 years .
Answer B
Answer: (B) 16, 28, 36
Question: Rose & Raylene goes to same place for work daily from same house & they work for five days a week. Rose saves 10 minutes on a day than Raylene in her trip. In a month, how much time Rose saves compared to Raylene in traveling? Take in a month there are four weeks (20 working days)
(A) 3 hours & 20 minutes
(B) 3 & 10
(C) 3 hours
(D) 2 hours & 20 minutes
(E) 2 hours & 30 minutes
Rationale: For each day rose saves 10 minutes so for a week 50 minutes (10*5) & which gives a month 200 minutes (50*4).
200 minutes = 3 hours 20 minutes
Answer: A
Answer: (A) 3 hours & 20 minutes
Question: Goldenrod and No Hope are in a horse race with 9 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
(A) 362880
(B) 181440
(C) 120000
(D) 24000
(E) 21000
Rationale: All 9 horses can finish the race in 9! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 9!/2=181440 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: B.
Answer: (B) 181440
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 10?
(A) 100
(B) 120
(C) 250
(D) 200
(E) 160
Rationale: Then, 10% of x= 10
(10/100)x = 10
x = (10*100*)/10= 100
Answer is A
Answer: (A) 100
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and four different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
(A) 719/720
(B) 1/24
(C) 2/233
(D) 3/543
(E) 1/720
Rationale: 4 ties and 4 shirts...
red tie can take any of 4 shirts..
orange can take any of the remaining 3 shirts
yellow any of remaining 2..
and so on till last indigo chooses the 1 remaining..
Total ways= 4*3*2*1=24
out of this 720, ONLY 1 way will have same colour tie and shirt..
prob = 1/720
B
Answer: (B) 1/24
Question: The speed of a boat in still water is 18 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 14 minutes is
(A) 1.6 km
(B) 2 km
(C) 5.1 km
(D) 4 km
(E) None of these
Rationale: Explanation:
Speed downstreams	=(18 + 4)kmph
= 22 kmph.
Distance travelled	= (22 x 14/60)km
= 5.1km
Option C
Answer: (C) 5.1 km
Question: The average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 120 kg
(B) 130 kg
(C) 137 kg
(D) 190 kg
(E) None
Rationale: Solution
Total weight increased	= (10 x 7.2)kg
= 72 kg.
Weight of new person	= (65 + 72)kg
= 137 kg.
Answer C
Answer: (C) 137 kg
Question: A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1420. If a door and 2 windows occupy 8 sq. m, find the height of the room.
(A) 4 m
(B) 4.5 m
(C) 5 m
(D) 5.5 m
(E) 6 m
Rationale: Explanation:
Let breadth = x m, length = 3x m, height = H metres.
Area of the floor = (Total cost of carpeting)/(Rate/m2)=(270/5)m2=54m2.
x× (3x/2) = 54 =>x2 = (54×2/3) = 36 <=> x = 6.
So, breadth = 6 m and length =(3/2)×6 = 9 m.
Now, papered area = (1420/10)m2 = 142 m2.
Area of 1 door and 2 windows = 8 m2.
Total area of 4 walls = (142 + 8) m2 = 150 m2
2×(9+ 6)× H = 150 <=> H = 150/30 = 5 m.
Answer: Option C
Answer: (C) 5 m
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?
(A) 388
(B) 700
(C) 277
(D) 500
(E) 271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 – 6x/100 = 83
x/100 = 7
=> x = 700.Answer: B
Answer: (B) 700
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 900. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 922.50. What is the value of X?
(A) 9000
(B) 6000
(C) 5000
(D) 4000
(E) 3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=45,000.
Now, put the value of X = 9000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 9000+5% of 9000= 9450.
2nd year, Amount = 9450 + 5% of 9450 = 9922.50.
We can see after 2 years Interest = 9922.50-9000= 922.50. hence, it satisfies the question. Hence A is the correct answer
Answer: (A) 9000
Question: Walking at 1/3th of its usual speed a cab is 20mnts late. Find its usual time to cover the journey?
(A) 10m
(B) 15m
(C) 20m
(D) 25m
(E) 12m
Rationale: New speed = 1/3th of usual speed
New time = 3 of usual time
3 UT - UT = 20m
2UT = 20m
UT = 10m
Answer is A
Answer: (A) 10m
Question: If n is an integer and n^4 is divisible by 10, which of the following could be the remainder when n is divided by 10?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: option 1
Remainder 2 means 10+2=12
n^4= 12^4= 12*12*12*12/10 is not an integer
option 2
Remainder 5 means 10+5=15
n^4= 15^4= 15*15*15*15/10 is not an integer
option 3
Remainder 6 means 10+6=16
n^4= 16^4= 16*16*16*16/10 is not an integer
option 4
Remainder 8 means 10+8=18
n^4= 18^4= 18*18*18*18/10 is not an integer
option 5
Remainder 10 means 10+10=20
n^4= 20*20*20*20/10 is an integer means n^4 is divisible by 10 if we take n=10
so E is correct
Answer: (E) 10
Question: If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
(A) 12 years
(B) 18 years
(C) 16 years
(D) 14 years
(E) 19 years
Rationale: Explanation:
The sum P becomes 3P in 4 years on compound interest
3P = P(1+R/100)4
â‡’ 3 = (1+R/100)4
Let the sum P becomes 81P in n years
81P = P(1+R/100)n
â‡’ 81 = (1+R/100)n
â‡’ (3)4 = (1+R/100)n
â‡’ ((1+R/100)4)4 = (1+R/100)n
â‡’ (1+R/100)16 = (1+R/100)n
n=16
i.e, the sum will become 81 times in 16 years
ANSWER IS C
Answer: (C) 16 years
Question: 15.06 * 0.00000001 = ?
(A) 15060000
(B) 0.001506
(C) 0.01506
(D) 1.506e-07
(E) None of these
Rationale: Explanation:
Clearly after decimal 10 digits should be there.
Option D
Answer: (D) 1.506e-07
Question: Jansi went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20 p. coins as she originally had one rupee notes. She actually came back with about one-third of what she had started out with.
How much did she spend and exactly how much did she have with her when she started out ?
(A) 9.6
(B) 10.6
(C) 11.0
(D) 9.4
(E) 8.1
Rationale: A
9.60
Let us assume that originally Jansi had X rupees and Y 20 paise coins. Going shopping she had (100X + 20 Y) paise.
She returned with only (100 Y + 20 X) paise.
This last sum, as we know, is one-third of the original and therefore
3(100 Y + 20 X) = 100 X + 20 Y Simplifying we have X = 7 Y
If Y is 1 thenX is 7. Assuming this so Jansi had 7.20 rupees when she set out for shopping.
This is wrong because Jansi actually had about 15 rupees.
Let us see now what we get if Y = 2. Then X = 14. The original sum was 14.40 rupees which accords with the condition of the problem.
If we assume that Y = 3 then the sum will be too big — 21.60 rupees.
Therefore the only suitable answer is 14.40 rupees.
After shopping Jansi had 2 one rupee notes and 14 twenty Paise coins.
This is actually l/3rd of the original sum 1,440:3 = 480. Jansi's purchases, therefore, cost 14.40 — 4.80 = Rs 9.60
Answer: (A) 9.6
Question: If d is a number such that –2 ≤ d ≤ 2, which of the following has the largest possible absolute value?
(A) 3d – 1
(B) x^2 + 1
(C) 3 – x
(D) x – 3
(E) x^2 – x
Rationale: Ans is A .. leads to the max value of 7 for d = -2
Answer: (A) 3d – 1
Question: The smallest prime factor of 899 is xx. Which of the following is true of xx?
(A) 1<x≤7
(B) 7<x≤14
(C) 14<x≤21
(D) 21<x≤28
(E) 28<x≤35
Rationale: 899 = 900 - 1
=30^2−1^2
= (30+1)(30-1)
= 31 * 29
29 is the smallest factor
ANSWER:E
Answer: (E) 28<x≤35
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 10 per square m?
(A) s.9500
(B) s.50000
(C) s.57000
(D) s.60000
(E) s.62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 10 * 950
= Rs.9500
A
Answer: (A) s.9500
Question: 220, 218, 214, 208, 200, 190, ?
(A) 176
(B) 174
(C) 178
(D) 180
(E) 172
Rationale: 220
220 - 2 = 218
218 - 4 = 214
214 - 6 = 208
208 - 8 = 200
200 - 10 = 190
190 - 12 = 178
Answer is C.
Answer: (C) 178
Question: The total marks obtained by a student in Mathematics and Physics is 20 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 26
(C) 20
(D) 28
(E) 22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 20 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (20 + 20) / 2 = 20.Answer:C
Answer: (C) 20
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(4) - f(2), in terms of k?
(A)  1
(B)  k
(C)  2k
(D)  k^2 + k
(E)  k^2 - k
Rationale: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(4) and f(2):
f(4) = k(4) - k^2 = 4k - k^2
f(2) = 2k - k^2
f(4)-f(2)=2k.. Answer C
Answer: (C)  2k
Question: What is the area of a triangle with the following vertices L(1, 2), M(5, 1), and N(3, 5) ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: E.
Answer: (E) 7
Question: Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 5 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2008, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?
(A) 2015
(B) 2014
(C) 2013
(D) 2016
(E) 2017
Rationale: chart starting at 2010:
A+K=13
L=0.
Then I added 9 to a+k for each year and 14 to L for each year.
2011:AK=22 L=14
2012:AK=31 L=28
2013:AK=40 L=42
thus, 2013 is the correct answer. => C
Answer: (C) 2013
Question: A sum of Rs. 3000 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 75%
(B) 90%
(C) 55%
(D) 60%
(E) 50%
Rationale: S.I. = (9000 - 3000) = Rs. 6000
Rate = (100 * 6000) / (3000* 4)
= 50%
Answer: E
Answer: (E) 50%
Question: Train A and Train B began traveling towards each other from opposite ends of a 420-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
(A) 5:40 PM
(B) 6:00 PM
(C) 7:20 PM
(D) 8:00 PM
(E) 9:20 PM
Rationale: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 35) =420/60 = 7 hours
Trains started at 1:00 PM, there they will meet at 8:00 PM
Option D
Answer: (D) 8:00 PM
Question: A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job?
(A) 6
(B) 8
(C) 3
(D) 4
(E) 0
Rationale: Explanation:
Use formula For a work Members Ã— days = constant
8 Ã— 3 = 4 Ã— a
a = 6
so answer is 6 days
Answer: A
Answer: (A) 6
Question: There are two cars. One is 100 miles north of the other. Simultaneously, the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 15 miles per hour. How many miles apart are the cars after 3 hours?
(A) 125
(B) 150
(C) 200
(D) 225
(E) 250
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 75 and a height of 100. The hidden pattern here is a 3/4/5 right triangle (the 75 lines up with the '3' and the 100 lines up with the '4'). In this way, you can deduce that each side is '25 times' bigger than it's corresponding side:
3/4/5 becomes
75/100/125
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer: A
Answer: (A) 125
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 22 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken in 10 minutes ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 20
Rationale: a must be an integer as it is the number shoots at a rate of 22sec/shoot
3*60 + 22a = 10*60
22a = 420
a = 19
The total number of shoots -->1 +19 = 20 and
21th shoot will be taken at 620 seconds which is above 10 minutes
ANSWER: E
Answer: (E) 20
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 25%. Staff are allowed a further 20% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.6D
(B) 0.7D
(C) 0.5D
(D) 0.8D
(E) 0.9D
Rationale: Effective discount = a + b + ab/100 = - 25 - 20 + (-25)(-20)/100 =-40
Sale price = D * ( 1 - 40/100)
Sale price = .6 * D
Answer (A)
Answer: (A) 0.6D