mathewhe/aqua_rat huggingface dataset:
Question: Population of a colony of ants is increasing by 20% per day. If the population on Monday was 3000, on which day of that week the population would be 5184 ?
(A) Wednesday
(B) Thursday
(C) Monday
(D) sunday
(E) tuesday
Rationale: Monday - 3000, Tuesday = 3000+(3000*.20)= 3600
wednesday = 3600+(3600*.20) = 4320
Thursday = 4320+(4320*.20) = 5184
ANSWER:B
Answer: (B) Thursday
Question: A bag contains 10 red and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 2/3
(C) 5/8
(D) 1/4
(E) 5/7
Rationale: Total number of balls = 10+6 = 16
number of white balls = 10
Probability = 10/16 = 5/8
Answer is C
Answer: (C) 5/8
Question: A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits $ 1600 each in 1st month and 7th month of a year. At the end of the year, the amount he would have gained by way of interest is?
(A) 121
(B) 50
(C) 100
(D) 160
(E) 80
Rationale: Amount = (1600)* (1 + (5/2*100))^2
Amount = 1600 * (41/40) * (41/40) = 1681 ------(for investment in 1st month) Amount = 1600 * (41/40) = 1640 -----(for investment in 7th month) Total Amount = 1681 + 1640 = 3321 Interest = 3321-3200 = 121.............. Ans -A
Answer: (A) 121
Question: If q and r are both odd numbers B, which of the following must also be odd?
(A) q – r
(B) (q + r)^2
(C) q(q + r)
(D) (qr)^2
(E) q/r
Rationale: We're told that q and r are both ODD numbers B. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: (D) (qr)^2
Question: A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 16 days
Rationale: (A+B)'s 1 day's work = 1/35+1/20 = 11/140
(A+C)'s 1 day's work = 1/35+1/55 = 18/385
work done in 2 day's = 11/140+18/385 = 48/383
48/383th work done in 2 days
work done= 383/48*2 = 16 days (approx)
ANSWER:E
Answer: (E) 16 days
Question: The words mentioned below have been arranged in a particular order.
SHOP, FEAR, BALL, DEAD
Can you find the logic behind the order?
(A) 58 > 30 > 27 > 14
(B) 58 > 30 > 27 > 15
(C) 58 > 30 > 27 > 16
(D) 58 > 30 > 27 > 17
(E) None
Rationale: Solution:
Here, the alphabets can be re-written to their corresponding numbers:
A = 1, B = 2, C = 3... and so on
SHOP = 19 + 8 + 15 + 16 = 58
FEAR = 6 + 5 + 1 + 18 = 30
BALL = 2 + 1 + 12 + 12 = 27
DEAD = 4 + 5 + 1 + 4 = 14
Now, clearly 58 > 30 > 27 > 14
Thus, the order.
Answer A
Answer: (A) 58 > 30 > 27 > 14
Question: 2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (C)
Required remainder = remainder by (13 +11)/17 = 7
Answer: (C) 7
Question: If the price of a TV is first decreased by 20% and then increased by 55%, then the net change in the price will be :
(A) 4% increase
(B) 24% increase
(C) 10% decrease
(D) 6% increase
(E) None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 155% of(80% of 100) =Rs. 155/100 * 80/100 * 100 = Rs. 124.
.'. Increase = 24%
Answer : B
Answer: (B) 24% increase
Question: Ben and Andrew are partners in a business. Ben is a working partner while Andrew is a sleeping partner. Ben gets 8% of the profit for managing the business, and the rest is divided in proportion to their capitals. If Ben invested 25000 and Andrew invested 38000, what is Ben's share in profit of 3500?
(A) 1557.8
(B) 1157.8
(C) 1540.8
(D) 3557.8
(E) 2557.8
Rationale: The amount Ben gets for managing
= 8% of Rs. 3500 = 280
Remaining profit = 3500 â€“ 280 = 3220
This is to be divided in the ratio 25000 : 38000=25: 38.
Share of Ben = 25/63 of 3220 = 1277.8
â‡’ Total share of Ben = 280 + 1277.8 = 1557.8.
Answer A
Answer: (A) 1557.8
Question: The cost of 20 articles is equal to selling price of 10. Find the gain or loss percent?
(A) 50%
(B) 100%
(C) 25%
(D) 15%
(E) 60%
Rationale: C.P. of each article be $1
C.P. of 10 articles = 10
gain% = 10/10*100 = 100%
Answer is B
Answer: (B) 100%
Question: The area of a triangle is with base 18m and height 6m?
(A) 88 m2
(B) 10 m2
(C) 66 m2
(D) 54 m2
(E) 31 m2
Rationale: 1/2 * 18 * 6 = 54 m2
Answer: D
Answer: (D) 54 m2
Question: A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 1000. He sold both the items together for Rs. 6000. What percentage of profit did he make?
(A) 80%
(B) 89%
(C) 100%
(D) 48%
(E) 10%
Rationale: The total CP = Rs. 2000 + Rs. 1000
= Rs. 3000 and SP = Rs. 6000
Profit(%) = (6000 - 3000)/3000 * 100
= 100%
Answer: C
Answer: (C) 100%
Question: R and S together can plough a field in 10 hours but by himself R requires 15 hours. How long would S take to plough the same field?
(A) 24hours
(B) 5 hours
(C) 10hours
(D) 15hours
(E) 20hours
Rationale: f R and S together can do a piece of work in x days and R alone can do the same work in y days, then S alone can do the same work in x y/ y â€“ x days.
the No. of hours required by S= 10 Ã— 20/ 20 â€“ 10 = 200/10 = 20 hours
E
Answer: (E) 20hours
Question: In a restaurant, the profit is 130% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 51%
(C) 90%
(D) 100%
(E) None of these
Rationale: Explanation :
Let C.P.= Rs. 100. Then, Profit = Rs. 130, S.P. = Rs. 230.
New C.P. = 112% of Rs. 100 = Rs. 112
New S.P. = Rs. 230.
Profit = Rs. (230 - 112) = Rs. 118.
Required percentage = (118 /230 *100) % = 51 % appox
Answer : B
Answer: (B) 51%
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
(A) 4000
(B) 5000
(C) 2000
(D) 1000
(E) 6000
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer is C.
Answer: (C) 2000
Question: If k, (k+200), (k+350), and 15*K are all multiples of S then S could equal which of the following ?
(A) 20
(B) S=25
(C) 75
(D) 100
(E) 150
Rationale: {Multiple of S} - {Multiple of S} = {Multiple of S}.
(K+200) - k = 200 = {Multiple of S}.
(K+350) - k = 350 = {Multiple of S}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Answer: (B) S=25
Question: The sum of three consecutive even numbers is 366. Find the middle number of the three?
(A) 111
(B) 123
(C) 122
(D) 152
(E) 142
Rationale: Middle number =366/3
=122
Ans C
Answer: (C) 122
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 30% of the total school population of x students, what is x?
(A) 125
(B) 173
(C) 225
(D) 250
(E) 500
Rationale: 90=x/100*30/100*x=>x^2 = 9*10000/3 = > x = 173
B
Answer: (B) 173
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 30 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 7 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A)  7
(B)  8
(C)  12
(D)  3
(E)  15
Rationale: Rate of H = 7 acres/hr
Remaining land to be harvested = 100 - 30 = 70
Rate of H and K = 70/7 = 10 acres/hr
Rate of K = 10 - 7 = 3
Answer: D
Answer: (D)  3
Question: A train crosses a platform of200 m in 15 sec, same train crosses another platform of length 300 m in 20 sec. then find the length of the train?
(A) 100m
(B) 180m
(C) 159m
(D) 250m
(E) 152m
Rationale: Length of the train be ‘X’
X + 200/15 = X +300/20
4X + 800 = 3X + 900
X = 100m
Answer:A
Answer: (A) 100m
Question: Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
(A) 4^30
(B) 2^30
(C) 1^30
(D) 3^30
(E) 6^30
Rationale: Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 4 ways...so all 30 can be divided in 4^30 ways
ANS:A
Answer: (A) 4^30
Question: John has 6 friends who want to ride in his new car that can accommodate only 5 people at a time (John plus 4 passengers). How many different combinations of 4 passengers can be formed from John's 6 friends?
(A) 3
(B) 8
(C) 10
(D) 15
(E) 20
Rationale: 6C4 = 15
The answer is D.
Answer: (D) 15
Question: The cost price of a radio is Rs.3300 and it was sold for Rs.1230, find the loss %?
(A) 62.7%
(B) 65%
(C) 88%
(D) 65%
(E) 62%
Rationale: 3300 ---- 2070
100 ---- ? => 62.7%
Answer:A
Answer: (A) 62.7%
Question: The greatest number of four digits which is divisible by 10, 16, 24 and 80 is:
(A) 9000
(B) 9420
(C) 9660
(D) 9840
(E) 9900
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10,16, 24 and 80 is 240.
On dividing 9999 by 240, the remainder is 159.
Required number (9999 - 159) = 9840.
Answer: Option D
Answer: (D) 9840
Question: Missing number in the series
4 9 20 43 90 ?
(A) 175
(B) 185
(C) 190
(D) 195
(E) 180
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
so 90*2+5=185
ANSWER:B
Answer: (B) 185
Question: There are 4 sections with 7 questions each. If three questions are selected from each section, the chance of getting different questions is________
(A) 23456
(B) 45678
(C) 42875
(D) 40000
(E) 16000
Rationale: we have to select three questions from each section so the chances are 7C4. 7C4.7C4=42875
ANSWER:C
Answer: (C) 42875
Question: A trader bought a car at 20% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 72%
(C) 12%
(D) 82%
(E) 36%
Rationale: Original price = 100
CP = 80
S = 80*(170/100) = 136
100 - 136 = 36%
Answer:E
Answer: (E) 36%
Question: If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river?
(A) (7 , 3) km/hr
(B) (7 , 9) km/hr
(C) (3 , 3) km/hr
(D) (7 , 5) km/hr
(E) (7 , 7) km/hr
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x – y
x = (Ds + Us) / 2
y = (Ds – Us) / 2
In the above problem Ds = 10 ; Us = 4
x = (10 + 4) / 2 = 14/2 = 7 km/hr
y = (10 - 4)/2 = 6/2 = 3 km/hr
ANSWER: A
Answer: (A) (7 , 3) km/hr
Question: Arithmetic mean and standard deviation of a certain normal distribution are 11.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
(A)  10.5
(B)  11
(C)  11.5
(D)  12
(E)  8.5
Rationale: The value which is exactly two SD below the mean is: mean-2*SD=11.5-2*1.5=8.5.
Answer: E.
Answer: (E)  8.5
Question: If x, y, and z are positive integers and 3x = 5y = 8z, then the least possible value of x + y + z is
(A) 45
(B) 79
(C) 50
(D) 55
(E) 60
Rationale: given 3x=5y=8z
x+y+z in terms of x
= x+(3x/5)+(3x/8) = 79x/40
now checking with each of the answers and see which value gives a minimum integer value.
A x = 40/79*45 , not an integer
C,D,E can be ruled out similarly.
B is minimum value as x = 79*40/79 = 79
Answer is B
Answer: (B) 79
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is
(A) 15
(B) 20
(C) 25
(D) 30
(E) 32
Rationale: Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
ANSWER:D
Answer: (D) 30
Question: If there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
(A) 72 min
(B) 62 min
(C) 70 min
(D) 74 min
(E) 120 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
100x+100*2x=180
x=180/300
x=0.6
time taken for type A problem=100*2*0.6=120min
ANSWER:E
Answer: (E) 120 min
Question: Two trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 26 km/hr
(B) 17 km/hr
(C) 60 km/hr
(D) 77 km/hr
(E) 96 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(160 + 160)/8 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5
= 96 km/hr.
Answer:E
Answer: (E) 96 km/hr
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
(A) 110
(B) 120
(C) 130
(D) 195
(E) 200
Rationale: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Answer: (D) 195
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.9 sec
(C) 8.9 sec
(D) 6.9 sec
(E) 5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 200/40
= 5 sec.
Answer: E
Answer: (E) 5 sec
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 231 the Other is
(A) 330
(B) 300
(C) 270
(D) 250
(E) 350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/231 = 300
Answer is B.
Answer: (B) 300
Question: In an examination, a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer. If he attempts all 100 questions and secures 300 marks, the number of questions he attempts correctly, is:
(A) 150
(B) 250
(C) 400
(D) 300
(E) 100
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (100 â€“ x).
3x â€“ 2(100 â€“ x) = 300 or 5x = 500 or x = 100.
ANSWER:E
Answer: (E) 100
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) Rs. 3642.40
(B) Rs. 3868.80
(C) Rs. 4216.20
(D) Rs. 4082.40
(E) None of these
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
ANSWER:D
Answer: (D) Rs. 4082.40
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 30 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 28 sec
(B) 37 sec
(C) 21.6 sec
(D) 23 sec
(E) 27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 400 / (20 + 30)5/18 = 300* 18 / 50 * 5 = 21.6 seconds.
Answer : C
Answer: (C) 21.6 sec
Question: 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?
(A) 7
(B) 9
(C) 18
(D) 45
(E) None of these
Rationale: Let the total number of children be x.
Then, x × (20 % of x) = 405
⇔ 1⁄5 x2 = 405 ⇔ x2 = 2025 ⇔ x = 45
∴ Number of sweets received by each child
= 20% of 45 = 9
Answer B
Answer: (B) 9
Question: In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?
I) k=0
II) k=−1
III) k=−3
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I and III only
Rationale: Please format the question properly.
Per the question, x^2+kx+1=0 with k=constant.
For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges.
B is the correct answer.
Answer: (B) III only
Question: When 200 is divided by positive integer x, the remainder is 2. What is the remainder when 398 is divided by x?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: f200/x leaves a reminder 2 then (200-2) i.e. 198 is divisible by x
So (200+198)/x leaves a reminder rem(200/x)+rem(198/x)=> 2+0=2
Answer :A
Answer: (A) 2
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.5 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
(A) a. 150
(B) b. 300
(C) c. 600
(D) d. 1,200
(E) e. 2,400
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.5 = 300
Answer: B
Answer: (B) b. 300
Question: A group of students was interviewed for that if it was asked whether or not they speak Spanish and / or English. Among those who speak Spanish, 15 speak English well, while 45 of them do not speak English. If 70% of students do not speak Spanish, how many students were surveyed?
(A) 200
(B) 220
(C) 230
(D) 210
(E) 215
Rationale: Number of students who speak Spanish are 45 + 15 = 60
Of total students, the percentage of students who do not speak Spanish was 70% --> percentage of who do is 30%
60-------30%
x ------- 100%
x = 60*100/30 = 200 = number of all students
Answer is A
Answer: (A) 200
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 2 hours?
(A) 2.4.
(B) 3.2.
(C) 4.2.
(D) 5.5.
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 2 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 2 = 3.2 desks
B is the correct answer.
Answer: (B) 3.2.
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 6 years?
(A) 5x (1+n/100)^5 - x
(B) 6x (1+n/100)^4 - x
(C) x (1+n/100)^6 - x
(D) 2x (1+n/100)^7 - x
(E) 4x (1+n/100)^8 - x
Rationale: Amount after 6 years compounded yearly = x (1+n/100)^6
Thus profit = Final amount - original principle = x (1+n/100)^6 - x . Answer : C
Answer: (C) x (1+n/100)^6 - x
Question: If 140/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is E.
Answer: (E) I, II and III
Question: The current in a river is 6 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
(A) 69 miles
(B) 88 miles
(C) 96 miles
(D) 91 miles
(E) 112 miles
Rationale: Upstream Speed = 20-6=14 mph
Downstream Speed = 20+6 = 26 mph
D/14 + D/26 = 10 hours
Solving for D we get D=91
Answer: D
Answer: (D) 91 miles
Question: How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards?	(1 mile = 1,160 yards)
(A) 2
(B) 5
(C) 4
(D) 3.61
(E) 4.3
Rationale: speed = 9 miles/hr = 4.4 yard/s = 29.33 yards/min
distance = 106 yards
time = distance/speed
=106/29.33
=3.61 minutes
ans - D
Answer: (D) 3.61
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 200
(B) 220
(C) 240
(D) 150
(E) 260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 30 = 15
x + 300 = 450
x = 150 m.
Answer: Option D
Answer: (D) 150
Question: Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?
(A) 120
(B) 150
(C) 200
(D) 270
(E) 420
Rationale: To make a triangle, you need 2 checkpoints from one track and 1 from the other. You cannot have all 3 from the same track since then the points will be in a line (assuming straight line of track)
You select 2 checkpoints from the first track and one from the second or two from the second track and one from the first.
6C2 * 10C1 + 10C2 * 6C1 = 150 + 270 = 420
Answer (E)
Answer: (E) 420
Question: Seller selling an apple for Rs.20, a Seller loses 1/6th of what it costs him. The CP of the apple is?
(A) 10
(B) 12
(C) 21
(D) 18
(E) 20
Rationale: SP=20Loss=CP21Loss=CP−SP=CP−20⇒CP21=CP−20⇒20 CP21=20⇒CP21=1⇒CP=21
C
Answer: (C) 21
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 240
(B) 140
(C) 230
(D) 130
(E) 125
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 – 65x/100 = 21
5x = 2100
x = 140.
Answer B.
Answer: (B) 140
Question: 4.509/10.02 =
(A)  0.45
(B)  0.3505
(C)  0.3509
(D)  0.351
(E)  0.3527
Rationale: 4.509 / 10.02
4509 / 1002 = 4.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.45. Answer: A
Answer: (A)  0.45
Question: An 80-liter solution of cool-drink is made from 10% jasmine water. If 8 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine?
(A) 12%
(B) 14%
(C) 16%
(D) 18%
(E) 20%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.1(80) + 8) / 100 = 16/100 = 16%
The answer is C.
Answer: (C) 16%
Question: The ratio of two numbers is 2 : 3 and their H.C.F. is 6. Their L.C.M. is
(A) 48
(B) 22
(C) 36
(D) 27
(E) 67
Rationale: Explanation:
Let the numbers be 2x and 3x. Then, their H.C.F. = x. So, x = 6.
So, the numbers 12 and 18
L.C.M. of 12 and 18 = 36
Option C
Answer: (C) 36
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 80/13 hours
(C) 30/19 hours
(D) 30/13 hours
(E) 31/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours.
Answer: D
Answer: (D) 30/13 hours
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 200 %
(B) 75 %
(C) 150 %
(D) 50 %
(E) 70%
Rationale: Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage =(295/420*100)%=1475/21%=70%
Answer:E
Answer: (E) 70%