mathewhe/aqua_rat huggingface dataset:
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio?
(A) 16:18
(B) 16:13
(C) 16:15
(D) 16:12
(E) 16:11
Rationale: For an income of Re. 1 in 9% stock at 96, investment
= Rs. 96/9 = Rs.32/3
For an income Re. 1 in 12% stock at 120, investment
= Rs. 120/12 = Rs. 10.
Ratio of investments =(32/3) : 10
= 32 : 30 = 16 : 15
Answer: C
Answer: (C) 16:15
Question: The length of the bridge, which a train 140 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 377
(B) 367
(C) 235
(D) 245
(E) 267
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (140 + x)/30 = 25/2
x = 235 m.
Answer: C
Answer: (C) 235
Question: Find the one which does not belong to that group ?
(A) 372
(B) 630
(C) 287
(D) 192
(E) 119
Rationale: Explanation:
30 = 33 + 3, 630 = 54 + 5, 10 = 23 + 2, 520 = 83 + 8 and 130 = 53 + 5.
30, 10, 130 and 520 can be expressed as n3 + n but not 630.
Answer:B
Answer: (B) 630
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 50% play football, how many play both?
(A) 120
(B) 150
(C) 200
(D) 180
(E) 160
Rationale: n(A) = 75*600/100 = 450
n(B) = 50*600/100 = 300
n(AUB) = 600
n(AnB) = 450+300-600 = 150
Answer is B
Answer: (B) 150
Question: in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 12 people all together .how many people can sit in a bus?
(A) 52
(B) 49
(C) 95
(D) 88
(E) 93
Rationale: Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 12
Total People can seat= 81+12=93
ANSWER:E
Answer: (E) 93
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
(A) 8
(B) 7
(C) 1
(D) 9
(E) 6
Rationale: Explanation:
x/2 â€“ x/3 = 6 => x =6
3 + 6 = 9
Answer: D
Answer: (D) 9
Question: A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 2 hours
(B) 5 hours
(C) 6 hours
(D) 8 hours
(E) 3 hours
Rationale: Number of pages typed by A in one hour=32/6=16/3
Number of pages typed by B in one hour=40/5=8
Number of pages typed by both in one hour=((16/3)+8)=40/3
Time taken by both to type 110 pages=110*3/40=8 hours.
Answer : D.
Answer: (D) 8 hours
Question: In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes
(A) 16800
(B) 15800
(C) 16700
(D) 15700
(E) None of these
Rationale: Explanation:
Let the total number of votes enrolled are x.
Number of votes cast = 75% of x
Valid votes = 98% of 75% of x
Now, as 9261 is the 75% of valid casted votes so,
75% of 98% of 75% of x = 9261 [imporant]
=>75×98×75×x / 100×100×100=9261=>x=16800
Option A
Answer: (A) 16800
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,500 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
(A) 38,000
(B) 40,000
(C) 42,500
(D) 45,500
(E) 48,500
Rationale: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.5
So, answer is D.
Answer: (D) 45,500
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
(A) A)25
(B) B)30
(C) C)20
(D) D)21
(E) E)18
Rationale: M = 15
S = 15
DS = 15 + 15 = 30
Answer:B
Answer: (B) B)30
Question: A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
(A) 24/78
(B) 24/709
(C) 24/76
(D) 24/71
(E) 24/72
Rationale: Explanation:
Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles
2 marbles are drawn from 13 marbles at random. Therefore,
n(S) = 13C2 = 78 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 24/78
ANSWER:A
Answer: (A) 24/78
Question: A number is increased by 40 % and then decreased by 40 %. Find the net increase or decrease per cent.
(A) 19%
(B) 18%
(C) 17%
(D) 13%
(E) 16%
Rationale: Let the number be 100.
Increase in the number = 40 % = 40 % of 100
= (40/100 × 100)
= 40
Therefore, increased number = 100 + 40 = 140
This number is decreased by 40 %
Therefore, decrease in number = 40 % of 140
= (40/100 × 140)
= 5600/100
= 56
Therefore, new number = 140 - 56 = 84
Thus, net decreases = 100 - 84 = 16
Hence, net percentage decrease = (16/100 × 100) %
= (1600/100) %
= 16 %
Answer:E
Answer: (E) 16%
Question: If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?
(A) 7
(B) 1
(C) 2
(D) 3
(E) 0
Rationale: We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers.
If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number.
Again, when A is a whole number and it is equal to 0 then the whole number before that is A – 1 which means 0 – 1 = -1, which is not a whole number.
Therefore, if A is a whole number then the number before that will not always be a whole number.
Answer:B
Answer: (B) 1
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 6
(B) 5
(C) 8
(D) 9
(E) 1
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(A) 5
(B) 6
(C) 7
(D) 1
(E) 89
Rationale: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer:B
Answer: (B) 6
Question: If 6 Men or 8 Women take 6 days to complete some work, how many days will 8 Men and 4 Women working together take to complete the work?
Can anyone explain please? The OA is 9/4
(A) 1. 36/11 days
(B) 2. 2 Days
(C) 3. 9/4 days
(D) 4.5/2 days
(E) 5.3 days
Rationale: 6 men or 8 women takes 6 days to complete the work
So 6M = 8W
W = 3/4M
1 man in 1 day does 1 unit of work
so 6 M in 6 M = 36 units of work
now 8 M and 4 W = 8M + 4(3/4)M
= 8M + 3M
= 11M
Since both set do the same work
11M in n Days = 36 units of work
n = 36 /11 days.
A
Answer: (A) 1. 36/11 days
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 77, the three numbers in order are?
(A) 33, 66, and 132
(B) 33, 132, and 66
(C) 66, 33, and 132
(D) 66, 132, and 33
(E) 132, 33, and 66
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 77
7x/3 = 77
x = 33
The numbers in order are 66, 33, and 132
The answer is C.
Answer: (C) 66, 33, and 132
Question: If 6/w + 6/x = 6/y and wx = y, then the average (arithmetic mean) of w and x is
(A) 1/2
(B) 1
(C) 2
(D) 4
(E) 8
Rationale: Given: 6/w + 6/x = 6/ywx=y
Find: (w+x)/2 = ?
6(1/w + 1/x) = 6(1/y) - divide both sides by 6
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Answer: (A) 1/2
Question: Peter invests $100,000 in an account that pays 10% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 10% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
(A) $471.31
(B) $4713.10
(C) $47.13
(D) $4.71
(E) Zero
Rationale: Peters interest= $100,000*0.10 = $10,000 or $833.33 each month.
Martha’s interest, 10%/12 = 0.833% each month:
For the 1st month = $100,000*0.00833 = $833.33;
For the 2nd month = $833.33 + 0.833% of 833.33 = ~$840, so we would have interest earned on interest (very small amount);
For the 3rd month = $840 + 0.833% of 840 = ~$847;
For the 4th month = $847 + 0.833% of 847 = ~$854;
...
For the 12th month = $905 + 0.833% of 905 = ~$912.
The difference between Peters interest and Martha’s interest = ~(7 + 14 + ... + 77) = $462.
Answer: A.
Answer: (A) $471.31
Question: A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?
(A) 25 days
(B) 30 days
(C) 23 days
(D) 35 days
(E) 45 days
Rationale: Work done by B in 1 day = 1/10 - 1/14
= (7-5)/70
= 1/35
So, B alone can do the work in 35 days.
ANSWER:D
Answer: (D) 35 days
Question: Machine A working alone can complete a job in 12 hours. Machine A+B working alone can do the same job in 15 hours. How long will it take machine B working at their respective constant rates to complete the job?
(A) 80
(B) 70
(C) 60
(D) 50
(E) 90
Rationale: Machines ( A ) ( B ) (A+B)
---Time - 12 - ( - ) -(15)
---Rate 5 --- 1 -- 4
--Work 60 --60 - 60
A+B = (60/1) = 60
C
Answer: (C) 60
Question: Kim finds a 3-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
(A) 2/5
(B) 3/5
(C) 8/15
(D) 1/2
(E) 7/5
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is B
Answer: (B) 3/5
Question: Of the votes cast on a certain proposal, 62 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
(A) 280
(B) 290
(C) 300
(D) 310
(E) 320
Rationale: Let x be the total number of votes cast.
0.6x = 0.4x + 62
0.2x = 62
x = 310
The answer is D.
Answer: (D) 310
Question: If [Y] denotes the least integer greater than or equal to Y and [Y] = 0, which of the following statements must be true?
(A) Y = 0
(B) 0 <= Y < 1
(C) 0 < Y <= 1
(D) -1 < Y <= 0
(E) -1 <= Y < 0
Rationale: The answer for this is 0 < = Y< = 1
However it is not available in the options. The match to the above is-1 < Y <= 0
Answer = D
Answer: (D) -1 < Y <= 0
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.27000. What will be the ratio in which they should share the profit at the end of the year?
(A) 20:9
(B) 2:1
(C) 3:2
(D) 2:3
(E) 5:3
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:27000×9
=45×12:27×9
=15×12:9×9
=20:9
Answer is A
Answer: (A) 20:9
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 28 metre of cloth ?
(A) 175 seconds
(B) 219 seconds
(C) 155 seconds
(D) 115 seconds
(E) 115 seconds
Rationale: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 28 : x => x = {\color{Blue} \frac{28\times 1}{0.128}}
=> x = 218.75
So time will be approx 219 seconds
Answer: B
Answer: (B) 219 seconds
Question: The value of x + x(x^x) when x = 5 is
(A) 15630
(B) 14000
(C) 15400
(D) 15560
(E) 15605
Rationale: Solution:
x + x(x^x)
Put the value of x = 5 in the above expression we get,
5 + 5(5^5)
= 5 + 5(5 Ã— 5 x 5 x 5 x 5 )
= 5 + 2(3125)
= 5 + 15625
= 15630
Answer: (a)
Answer: (A) 15630
Question: Find the missing number in the given sequence : 1,5,9,13,?,21,25,?
(A) 14 & 26
(B) 15 & 27
(C) 16 & 28
(D) 17 & 29
(E) 15 & 30
Rationale: 1+4=5
5+4=9
9+4=13
13+4=17
17+4=21
21+4=25
25+4=29
ANSWER:D
Answer: (D) 17 & 29
Question: An empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
(A) 3/5
(B) 5/9
(C) 9/19
(D) 4/9
(E) 2/5
Rationale: An empty wooden vessel weighs 20% of its total weight when filled with paint:
Vessel = 0.2(Vessel + Paint);
20V = V + P (so the weight of completely filled vessel is 10V)
P = 19V (so the weight of the paint when the vessels is completely filled is 9V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*20V;
P' = 9V (so the weight of the paint when the vessels is partially filled is 9V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 9V/19V = 9/19.
Answer: C.
Answer: (C) 9/19
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 3.6
(B) 7.2
(C) 8.4
(D) 10
(E) 12
Rationale: Explanation:
Speed =	(600 / 5 X60)m/sec =2 m/sec.
Converting m/sec to km/hr = (2 X 18/5)km/hr
= 7.2 km/hr.
ANSWER IS B
Answer: (B) 7.2
Question: The average of first five prime numbers greater than 10 is?
(A) 16.6
(B) 12.9
(C) 31.3
(D) 19.2
(E) 15.7
Rationale: 11 + 13 + 17 + 19 + 23 = 83/5 = 16.6
Answer: A
Answer: (A) 16.6
Question: If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?
(A) Rs.(xy/d)
(B) Rs.(xd)
(C) Rs.(yd)
(D) Rs.(yd/x)
(E) Rs.(yx)
Rationale: Cost of x metres = Rs. d.
Cost of 1 metre = Rs.	d/x
Cost of y metres = Rs.((d/x)y)
= Rs.(yd/x)
Correct answer is D
Answer: (D) Rs.(yd/x)
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 26%?
(A) 100 ml
(B) 60 ml
(C) 120 ml
(D) 130 ml
(E) 150 ml
Rationale: we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*26/100 = 130 ml (30ml is de old concentration +100 ml (newly added)
Answer D
Answer: (D) 130 ml
Question: A room of 6m 00cm long and 8m 00cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 12
(B) 200
(C) 600
(D) 800
(E) 20
Rationale: Explanation:
area of the room = 600 * 800 sq cm
size of largest square tile = H.C.F of 600cm and 800cm= 200cm
area of 1 tile = 200*200 sq cm
no. of tiles required = (600*800) / (200 *200) = 12
Answer: A) 12
Answer: (A) 12
Question: Which of the following is not divisible by 3?
(A) 10394
(B) 15363
(C) 29340
(D) 30753
(E) 41715
Rationale: Divisibility rule of 3: The sum of the digits of the number should be divisible by 3
Option A: 10394, Sum = 17. Not divisible by 3. Hence the number 10394 is also not divisible by 3
Option B: 15363, Sum = 18, Divisible by 3
Option C: 29340, Sum = 18, Divisible by 3
Option D: 30753, Sum = 18, Divisible by 3
Option E: 41715, Sum = 18, Divisible by 3
Correct Option: E
Answer: (E) 41715
Question: A 21% stock yielding 10% is quoted at :
(A) 83.33
(B) 210
(C) 112
(D) 120
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 21, money invested = Rs.(100/10X21) = Rs. 210.
âˆ´ Market value of Rs. 100 stock =Rs. 210
Answer B
Answer: (B) 210
Question: Five years ago, the ratio of ages of P and Q was 3:2. Ten years from now, the ratio of their ages will be 6:5. What is P's age at present?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: 2(P-5)/3 = (Q-5). Then Q = 2(P-5)/3 + 5
5(P+10)/6 = Q+10
5(P+10)/6 = 2(P-5)/3 +15
5P+50 = 4P + 70
P = 20
The answer is A.
Answer: (A) 20
Question: Two persons start running simultaneously around a circular track of length 500 m from the same point at speeds of 16 kmph and 20 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) 50
(D) 32
(E) 38
Rationale: Time taken to meet the first time = length of track/relative speed
= 500/ (16+20) (5/18)
= 500/36 *(18/5) = 50 sec.
Answer : C
Answer: (C) 50
Question: If a < b < c , which of the following must be true?
(I) a > b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
(A) I only
(B) None
(C) II only
(D) III only
(E) II and III
Rationale: (I) a < b^2. Not necessarily true fractions: try a=1 and b=2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: B.
Answer: (B) None
Question: If TIER is written as 7168 and BRAIN is written as 28415, how is RENT coded ?
(A) 3653
(B) 8657
(C) 2977
(D) 2790
(E) 2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 6 8 2 4 5
Thus, the code for RENT is 8657.
ANSWER:B
Answer: (B) 8657
Question: A person want to give his money of $4500 to his 4 children A,B,C,D in the ratio 2:4:5:4. What is the A+B share?
(A) $1000
(B) $2000
(C) $1800
(D) $1500
(E) $1600
Rationale: A's share = 4500*2/15 = $600
B's share = 4500*4/15 = $1200
A+B = $1800
Answer is C
Answer: (C) $1800
Question: 3,5,9,15,23,33,__
(A) 45
(B) 55
(C) 65
(D) 34
(E) 25
Rationale: 5=3+2
9=5+4
15=9+6
23=15=8
33=23+10
Similarly 33+12=45
ANSWER:A
Answer: (A) 45
Question: A manâ€™s current age is (2/5) of the age of his father. After 14 years, he will be (1/2) of the age of his father. What is the age of father at now?
(A) 40
(B) 45
(C) 38
(D) 50
(E) 70
Rationale: Let, fatherâ€™s current age is A years.
Then, Manâ€™s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 14 ]= (1/2)(A + 14)
2(2A + 70) = 5(A + 14)
A = 70
E
Answer: (E) 70
Question: At a meeting of 9 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
(A) 24,640
(B) 27,820
(C) 30,240
(D) 33,120
(E) 36,580
Rationale: 9 people can be arranged around a table in 8! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 8 units around a table is 7!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 8! - 2*7! = 6*7! = 30,240
The answer is C.
Answer: (C) 30,240
Question: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the total amount of money that the student earned for the 20 days?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2
(A) (1) $120
(B) (2) $320
(C) (3) $378
(D) (4) $240
(E) (5) $296
Rationale: 4+7+4+3+2 = 20
The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.
1st to 2nd term = 48 (2 days)
3rd to 5th term = 70 (3 days)
6th to 9th term = 80 (4 days)
10th to 16th term = 84 (7 days)
17th to 20th term = 96 (4 days)
total amount earned = 48+70+80+84+96
= 378
Pick C
Answer: (C) (3) $378
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 and 33
(B) 42, 36
(C) 44, 33
(D) 44, 36
(E) None of these
Rationale: Explanation :
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
Answer : Option A
Answer: (A) 42 and 33
Question: The digit in unit's place of the product (459 ×46×28×484) is 2, the digit in place of * is
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: Solution
(9×6×4)	= 216.
In order to obtain 2 at the unit place, we must multiply 216 by 2 or 7.
Answer C
Answer: (C) 7
Question: A cricket bat is sold for $850, making a profit of $205. The profit percentage would be
(A) 24%
(B) 25%
(C) 32%
(D) 36%
(E) 40%
Rationale: 205/(850 - 205) = 205/645 = 41/129=32%.
Answer: C.
Answer: (C) 32%
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?
(A) 78
(B) 90
(C) 36
(D) 34
(E) 23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/12 => x = 25
Speed of each train = 25 m/sec.
= 25 * 18/5 =90 km/hr.
Answer: Option B
Answer: (B) 90
Question: The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Write equation in N as follows
N + 1/N = 78/15
Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
correct answer A
Answer: (A) 5
Question: Which of the following no must added to 5678 to give a remainder of 35 when divided by 460?
(A) 955
(B) 797
(C) 618
(D) 980
(E) 680
Rationale: To get a remainder of 35 while dividing by 460 , the number should have 5 at the unit digit. 5678 ends with 8. so amongst the options the number which when added with 5678 gives 5 at the unit place will be the ans. Here 797+5678=6475 , so (b) is the correct option.
ANSWER:B
Answer: (B) 797
Question: An article costing rs.160 is sold at 5% discount on a mark-up price. What is the selling price after
discount?
(A) 106
(B) 116
(C) 126
(D) 136
(E) 152
Rationale: Rs. 136
160-(160*15/100)=160*95/100=152
ANSWER:E
Answer: (E) 152
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 45-sided polygon have?
(A)  875
(B)  945
(C)  1425
(D)  2025
(E)  2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 45.
Plugging it in, we get 945 diagonals!
Answer (B).
Answer: (B)  945
Question: Dany bought a total of 22 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
(A) 4
(B) 10
(C) 7
(D) 8
(E) 13
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 22. Hence
X + Y = 22
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 22
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 22 - X. Substitute y by 22 - x in the second equation and solve
0.25 X + 0.15 (22 - X) = 4.2
X(0.25 - 0.15) + 3.3 = 4.2
0.1 X = 0.9
X = 9 and Y = 22 - 9 = 13
correct answer E
Answer: (E) 13
Question: A shipment of 8 TV sets contains 3 black and white sets and 5 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
(A) 1/7
(B) 1/4
(C) 9/14
(D) 11/28
(E) 13/28
Rationale: 5/8 * 4/7 = 20/56
1-(20/56) = 36/56 = 9/14
Answer C
Answer: (C) 9/14
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 30, find the number?
(A) 11201
(B) 12102
(C) 12081
(D) 12108
(E) 10126
Rationale: D
12108
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 30 => b = 10
So a = 12 and b = 8
Hence the three digit number is: 12108
Answer: (D) 12108