mathewhe/aqua_rat huggingface dataset:
Question: A right angled cone has its height 'h'. The cone is being cut parallel to its base at h/5 distance from its vertex. What will be the ratio of the cone and the cutting portion
(A) 1:124
(B) 1:125
(C) 1:25
(D) 1:26
(E) 1:24
Rationale: let radius of smaller cone=R
radius of bigger cone=r
height of smaller cone=h/5
height of bigger cone=h
volume of smaller cone=1/3*pi*R^2*h
volume of reamaining portion=volume of bigger cone - volume of smaller cone
i.e 1/3*pi*r^2h-1/3*pi*R^2(h/5)
from the similarity of triangle
r/R=5:1
equating value
we get 1:124
ANSWER:A
Answer: (A) 1:124
Question: 6 x 0.6 x 0.06 x 0.006 x 60 = ?
(A) 77.76
(B) 7.776
(C) 0.7776
(D) 0.07776
(E) None otf these
Rationale: Explanation:
? = 6 x 6/10 x 6/100 x 6/1000 x 60 = 77760/1000000
= 7776/100000 = 0.07776
Answer: Option D
Answer: (D) 0.07776
Question: A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Sale price of the article
II. Number of articles sold
(A) Only I is necessary
(B) Only II is necessary
(C) Either I or II is necessary
(D) Both I and II are necessary
(E) None of these
Rationale: EXPLANATION
Gain = 25% of C.P.
In order to find gain, we must know the sale price of each article and the number of articles sold.
answer is (D).
Answer: (D) Both I and II are necessary
Question: If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a − c?
(A) −220
(B) −100
(C) 100
(D) 135
(E) It cannot be determined from the information given
Rationale: (a + b)/ 2 =110 ===> a + b = 220
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) = 220 - 320 ===> a + b - b - c = - 100 ===> a - c = - 100
Answer: B
Answer: (B) −100
Question: If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey?
(A) 38km/hr
(B) 58km/hr
(C) 68km/hr
(D) 48km/hr
(E) 47km/hr
Rationale: total distance=2*120
total time=120/60+120/40=5 hours
avg=120*2/5=48km/hr
ANSWER:D
Answer: (D) 48km/hr
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) 7
(B) 6
(C) 9
(D) 5
(E) 4
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
Answer:D
Answer: (D) 5
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 315 what is the least possible value of k?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: 315 = 3*3*5*7
Thus k must include numbers at least up to the number 7.
The answer is B.
Answer: (B) 7
Question: A sum of Rs. 12500 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 4%
(B) 5%
(C) 6%
(D) 8%
(E) 14%
Rationale: S.I. = (15000 - 12500) = Rs. 2500/-
Rate = (100 * 2500) / (12500 * 4) = 5%
ANSWER:B
Answer: (B) 5%
Question: In how many ways can 9 people, A, B, C, D, E, F, G, H, I be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 3841258
(B) 39600
(C) 576822
(D) 362784
(E) 69600
Rationale: Number of total arrangements = 9!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
9! - (4!*2*2) = 362880 - (24*2*2) = 362784
Answer D
Answer: (D) 362784
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 240
(C) 250
(D) 260
(E) 270
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: Option A
Answer: (A) 230
Question: A pharmaceutical company received $3 million in royalties on the first $25 million in sales of and then $9 million in royalties on the next $130 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $25 million in sales to the next $130 million in sales?
(A) 8%
(B) 15%
(C) 35%
(D) 42%
(E) 56%
Rationale: (9/130)/(3/25) = 15/26 = 57.7% it means that 9/130 represents only 57.7%. Therefore a decrease of 42%.
Answer D
Answer: (D) 42%
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 300 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 2160.
(C) 5780
(D) 5760
(E) 6380.
Rationale: Normal Day = 300 kw/h
Stormy Day = 300*1.2=360 kw/h
3 windmills for 2 hours on stormy day
360*3*2=2160
Answer: B
Answer: (B) 2160.
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) None of these
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22
Option C
Answer: (C) 22 years
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 320
(B) 350
(C) 365
(D) 420
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: A CAN FINISH A WORK IN 12 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
(A) 4
(B) 5 1/2
(C) 6
(D) 8
(E) NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (12*1/3)=4 DAYS.
CORRECT OPTION:A
Answer: (A) 4
Question: On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) 12%
Rationale: Explanation:
Difference between C.I and S.I for 2 years = 36.30
S.I. for one year = 330.
S.I. on Rs 330 for one year = 36.30
So R% = \frac{100*36.30}{330*1} = 11%
Option D
Answer: (D) 11%
Question: In a group of 800 people, 1/5 play at least one instrument, 64 play two or more. What is the probability that one student play exactly one instrument?
(A) 3/25
(B) 3/125
(C) C)2/25
(D) 3/25
(E) 1/5
Rationale: P(playing 2 or more instruments) = 64/800 = 2/25.
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 2/25 = 3/25.
Answer A.
Answer: (A) 3/25
Question: Dhoni can read m pages in 2 minutes. At this rate, how long will it take him to read n pages?
(A) (2/m)*n
(B) (3/m)*n
(C) (4m)*n
(D) (6/m)*n
(E) (8/m)*n
Rationale: m page in 2 mins
i.e. 1 page in 2/m mins
i.e. n pages in (2/m)*n
Answer: option A
Answer: (A) (2/m)*n
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 650 m
(B) 600 m
(C) 200 m
(D) 300 m
(E) 350 m
Rationale: Explanation:
2(l + 100) = 600 => l = 200 m
ANSWER IS C
Answer: (C) 200 m
Question: How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=32/51 ?
(A) 6
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 2. So, one more solution, where a=b is not possible.
So, answer will be C.
Answer: (C) 2
Question: How many positive integers W between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
(A) 3
(B) 16
(C) 75
(D) 24
(E) 26
Rationale: 1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E.
Answer: (E) 26
Question: If x is negative, which of the following must be positive ?
I. x^2
II. (-1) x
III. 1/x
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: x=-ve
I. x^2
will be positive
II. (-1) x
=-ve*-ve= +ve
will be positive
III. 1/x
=1/-ve =-ve
will be negative
Answer B
Answer: (B) I and II only
Question: The mean of 50 observations was 36. It was found later that an observation 47 was wrongly taken as 23. The corrected new mean is
(A) 35.24
(B) 36.16
(C) 36.22
(D) 36.48
(E) None
Rationale: Solution
Correct sum = (36x50+47-23)
= 1824.
âˆ´ Correct mean = 1824 / 50
= 36.48.
Answer D
Answer: (D) 36.48
Question: The ratio of red boxes to blue boxes in a certain warehouse is 10 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
(A) 37
(B) 74
(C) 70
(D) 148
(E) 244
Rationale: Ratio = R/B = 10/25 or R = 10/25 B -----------(1)
2R/B+150 = 10/25*1/2 = 1/5 or we can say that 10R=B+150 -------------(2)
solving (1) and (2) we get
B=50 and R = 20
so total boxes is B + R = 50+20=70
Hence C. 70 is the correct answer
Answer: (C) 70
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 152 m
(B) 726 m
(C) 688 m
(D) 150 m
(E) 176 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150 m
Question: A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 400
(B) 540
(C) 500
(D) 520
(E) 589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.
Answer: Option A
Answer: (A) 400
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 100 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
(A) 250/3
(B) 500/3
(C) 300
(D) 480
(E) 600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 100 then Y = 300
ANSWER:C
Answer: (C) 300
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(34)-A(33)?
(A) 2^22+1
(B) 2^23
(C) 2^23+1
(D) 2^33
(E) 2^23+1
Rationale: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A34-A33= 2^33
answer : D
Answer: (D) 2^33
Question: Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 4 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
(A) 60
(B) 72
(C) 84
(D) 90
(E) 216
Rationale: E is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+4T) = 9T ==> T = 2/5 ==> 24 minutes
To travel double distance, 2(2+4T) = 9T ==> 4 ==> 240 minutes
Difference, 216 minutes
E
Answer: (E) 216
Question: If x < 12, then it must be true that...
(A) -x < -12
(B) -x - 2 < 14
(C) -x + 2 < -10
(D) x + 2 < 10
(E) x - 6 < 17
Rationale: A. -x < -12 --> x>12. Not true.
B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.
C. -x + 2 < -10 --> x>12. Not true.
D. x + 2 < 10 --> x<8. Not true, consider x=10.
E. x - 6 < 17 --> x<23. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.
Answer: E.
Answer: (E) x - 6 < 17
Question: Find the slope of the line perpendicular to the line y = (1/3)x - 7
(A) -1
(B) -4
(C) -3
(D) 0
(E) -5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 3. If m is the slope of the line perpendicular to the given line, then
m × (1/3) = -1
Solve for m
m = - 3
correct answer C)-3
Answer: (C) -3
Question: A train passes a man standing on the platform. If the train is 240 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 16 sec
(B) 14 sec
(C) 9 ½ sec
(D) 8 ½ sec
(E) 12 sec
Rationale: D = 240
S = 72 * 5/18 = 20 mps
T = 240/20 = 12 sec
Answer: E
Answer: (E) 12 sec
Question: A’s speed is 21/19 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 2/21
(B) 2/19
(C) 1/11
(D) 1/7
(E) 1/5
Rationale: Let D be the full distance.
Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (21v/19) = xD/v
(19/21)*D/v = x*D/v
x = 19/21
B should have a head start of 2/21 of the full distance.
The answer is A.
Answer: (A) 2/21
Question: Find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm?
(A) 210 cm2
(B) 150 cm2
(C) 168 cm2
(D) 198 cm2
(E) 987 cm2
Rationale: 1/2 * 28(9 + 6)
= 210 cm2
Answer: A
Answer: (A) 210 cm2
Question: In how many different ways can the letters of the word 'PROFILE' be arranged in such a way that the vowels occupy only the odd positions ?
(A) 720
(B) 550
(C) 670
(D) 625
(E) 576
Rationale: Number of ways of arranging the vowels =4P3=4!=24.
Also, the 4 consonants can be arranged at the remaining 4 positions.
Number of ways of these arrangements =4P4=4!=24.
Total number of ways =(24*24)=576.
Answer is E
Answer: (E) 576
Question: The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 19/35
(C) 19/36
(D) 18/33
(E) 18/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 4/5 * 4/7 + 1/5 * 3/7
= 16/35 + 3/35 = 19/35
Answer: B
Answer: (B) 19/35
Question: Ragav took a bus from home to market, that travels at 40 kmph. While walking back at 4 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 30 kmph. Find the average speed.
(A) 6.5 kmph
(B) 12.0 kmph
(C) 28.5 kmph
(D) 18.5 kmph
(E) none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/40, by walking =x/4, by cycling = x/30 hours
:. Average speed = Total Distance/Total time
= 4x / x/20 + x/4 + x/30
= 4 *60 / 3+15+2
= 12.0
ANSWER:B
Answer: (B) 12.0 kmph
Question: The cricket team of 11members is 27yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 21
(B) 22
(C) 23
(D) 25
(E) 24
Rationale: Let the average age of the whole team be x years.
11x - (27 + 30) = 9 (x - 1)
=> 11x - 9x = 48
=> 2x = 48
=> x = 24.
So, average age of the team is 24 years.
E
Answer: (E) 24
Question: The largest 4 digit number exactly divisible by 88 is:
(A) 9944
(B) 9955
(C) 9966
(D) 6677
(E) 9958
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
Answer:A
Answer: (A) 9944
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
(A) 4 : 3
(B) 3 : 2
(C) 6 : 5
(D) 7 : 6
(E) None of these
Rationale: Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6
ANSWER:D
Answer: (D) 7 : 6
Question: |x+3| – |2-x| = |8+x| How many solutions will this equation have?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 2
C
Answer: (C) 2
Question: Which natural number is nearest to 8485, which is completely divisible by 75 ?
(A) 7845
(B) 8475
(C) 2540
(D) 3520
(E) 6540
Rationale: 75) 8485 (113
75
---
98
75
----
235
225
---
10
Required number = (8485 - 10) // Because 10 < (75 - 10)
= 8475.
ANSWER B
Answer: (B) 8475
Question: For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
(A) 26m
(B) 32m
(C) 24m
(D) 28m
(E) None of these
Rationale: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/28 = 8m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 4 seconds
Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres
ANSWER: B
Answer: (B) 32m
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) 14000
(B) 18000
(C) 19000
(D) 20000
(E) 25000
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
ANSWER A
Answer: (A) 14000
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 3. If the sum of the first and the last number is 13. What is the last numbers?
(A) 4
(B) 2
(C) 6
(D) 7
(E) 8
Rationale: A + B + C = 18
B + C + D = 9
A + D = 13
A – D = 9
A + D = 13
2D = 4
D = 2
ANSWER:B
Answer: (B) 2
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 1 m x 2 m x 20 cm?
(A) 5600
(B) 6000
(C) 237
(D) 7200
(E) 8600
Rationale: Number of bricks =Volume of the wall/Volume of 1 brick =	(100 x 200 x 20)/(25 x 11.25 x 6) = 237.
Answer: Option C
Answer: (C) 237
Question: A garrison of 2000 men has provisions for 65 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
(A) 1977
(B) 1893
(C) 1979
(D) 3000
(E) 1278
Rationale: 2000 ---- 65
2000 ---- 50
x ----- 20
x*20 = 2000*50
x = 5000
2000
-------
3000
Answer: D
Answer: (D) 3000
Question: If -3x+5y=48 and 3x-2y=6, what is the product of x and y?
(A) 252
(B) 428
(C) 464.
(D) 200
(E) 642
Rationale: Given -3x+5y=48 ---Eq 1
3x -2y =6 -- Eq 2
Sum both eqns we get 3Y = 54 => Y = 18
Sub 2Y in eq 2 => 3X - 36 = 6.
=> X = 14
Now XY = 14 * 18 = 252
Option A is correct answer.
Answer: (A) 252
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 8 1/2 sec
(B) 8 1/9 sec
(C) 8 5/2 sec
(D) 4 1/2 sec
(E) 5 1/2 sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer:A
Answer: (A) 8 1/2 sec
Question: There are 10 women and 3 men in Room A. One person is picked at random from Room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?
(A) 13/21
(B) 49/117
(C) 40/117
(D) 15/52
(E) 5/18
Rationale: If M picked from room A, room B probability of picking W is 4/9
If W picked from room A, room B probability of picking W is 3/9
Conditional Probability
P(W in B and M picked in A) = P(W given M picked in A)*P(M picked in A) = 10/13*4/9
P(W in B and W picked in A) = P(W given W picked in A)*P(W picked in A) = 3/13*3/9
Sum 49/117
Ans.B
Answer: (B) 49/117
Question: If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 110
(B) 130
(C) 150
(D) 170
(E) 190
Rationale: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.
The number of ways to select 2 lines from 20 lines is 20C2 = 190
The answer is E.
Answer: (E) 190
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 22
(B) 30
(C) 99
(D) 77
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: B
Answer: (B) 30
Question: In a friendship gang Angel has 3 gang, in how many ways can he invite one or more of the gang to his house?
(A) 58
(B) 5
(C) 12
(D) 9
(E) 7
Rationale: Angel can select one or more than one of his 8 gang.
=> Required number of ways = 2^3 – 1= 7.
E
Answer: (E) 7
Question: Solution X is 10% chemical A and 90% chemical B by volume. Solution Y is 20% chemical A and 80% chemical B by volume. If a mixture of X and Y is 12% chemical A, what percent of the mixture is Solution X?
(A) 80%
(B) 75%
(C) 70%
(D) 65%
(E) 60%
Rationale: The volume of the mixture be X+Y.
0.1X +0.2Y=0.12(X+Y)
X=4Y
X/(X+Y)=4/5=80%.
The answer is A.
Answer: (A) 80%
Question: If xy is an integer, which of the following must also be an integer?
I. x/y
II. y/x
III. y
(A) I alone
(B) II alone
(C) III alone
(D) None of the above
(E) I and II
Rationale: Lets take X = 8/3 and Y = 3/2
Then XY = 4 which is an integer.
But X/Y = 8/3 divided by 3/2 = 16/9 --> Not an integer.
Y/X = 3/2 divided by 8/3 = 9/16 --> Not an integer.
Y alone is 3/2. Not an integer.
Hence D. None of the above.
Answer: (D) None of the above