mathewhe/aqua_rat huggingface dataset:
Question: Addison High School’s senior class has 200 boys and 160 girls. If 60% of the boys and 75% of the girls attended college, what percentage of the total class that did not attend college?
(A) 33.33
(B) 60
(C) 80
(D) 66.67
(E) 64
Rationale: Number of boys attending the college: 0.60*200 = 120
number of girls attending the college: 0.75*160 = 120
Total attending = 120+120 = 240
Total people = 200+160 = 360
% of people attending = 240/360 = 66.67%. D is the correct answer
Answer: (D) 66.67
Question: How many seconds will a 500 metre long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 30
(B) 40
(C) 50
(D) 20
(E) 15
Rationale: Dist = 500 m
relative speed = (63-3) = 60 km/hr
60*5/18 = 50/3 m/s
time taken = 500/(50/3) = 30 sec
ANSWER A
Answer: (A) 30
Question: Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is ?
(A) 2 : 3
(B) 3 : 2
(C) 3: 4
(D) 1 : 2
(E) 4 : 3
Rationale: Let us name the trains as A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer : E
Answer: (E) 4 : 3
Question: If n^2 = m^2, which of the following must be true?
(A) n = m
(B) n = -m
(C) n = |m|
(D) |n| = |m|
(E) n = -|m|
Rationale: Solution:
We are given that n^2 = m^2, and we can start by simplifying the equation by taking the square root of both sides.
√n^2 = √m^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√n^2 = √m^2 is |n| = |m|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: D
Answer: (D) |n| = |m|
Question: If n is a positive integer, what is the remainder when (6^(4n+3))(6^n) is divided by 10?
(A) 7
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 6
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =7.
A or J in this problem.
Answer: (A) 7
Question: An amount of Rs. 55000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) s. 52500; Rs. 47500
(B) s. 34375; Rs. 20625
(C) s. 72500; Rs. 27500
(D) s. 82500; Rs. 17500
(E) s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (55000 - x). Then,
(x * 9 * 1)/100 + [(55000 - x) * 11 * 1]/100 = (55000 * 39/4 * 1/100)
(9x + 605000 - 11x)/100 = 39000/4 = 10725/2
x =34375
Sum invested at 9% = Rs. 34375
Sum invested at 11% = Rs. (55000 - 34375) = Rs. 20625
ANSWER:B
Answer: (B) s. 34375; Rs. 20625
Question: The greatest number of four digits which is divisible by 10, 13, 40 and 60 is:
(A) 9200
(B) 9300
(C) 9400
(D) 7800
(E) 8700
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 13, 40 and 60 is 600.
On dividing 9999 by 7800, the remainder is 2199.
Required number (9999 - 2199) = 7800.
ANSWER :D
Answer: (D) 7800
Question: If
1 = 3
2 = 6
3 = 9
4 = 12
5 = 15
Then 9 = ?
Hint: Its a logic Riddle not a mathematical riddle
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: C
3
As stated
3=9 => 9=3
Answer is C
Answer: (C) 3
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80.The compound interest on the same sum for the same period is :
(A) Rs.81.60
(B) Rs.160
(C) Rs.1081.60
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Principal = Rs. (100×80/4×2) = Rs.1000
C.I = Rs. [{1000×(1+4/100)2−1000}] = Rs.81.60
Correct Option: A
Answer: (A) Rs.81.60
Question: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
(A) 15%
(B) 20%
(C) 40%
(D) 50%
(E) 150%
Rationale: Let rate in R = 100x
then P = 75x
G = 100y
P = 90y
Thus
75 x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%
Answer: B.
Answer: (B) 20%
Question: If a = 105 and a^3= 21 * 25 * 35 * b, what is the value of b?
(A) 35
(B) 42
(C) 45
(D) 49
(E) 63
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
25 = 5 * 5
35 = 7 * 5
so, (105)^3 = 3 * 7 * 5 * 5 * 7 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3 * 5^3 * 7^2 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 * 5 ^3 * 7^2
b = 3^2*7 = 9*7=63
Correct answer E.
Answer: (E) 63
Question: What is the scope including 1/41+1/42+1/43+......+1/50?
(A) 1/6~1/5
(B) 1/5~1/4
(C) 1/4~1/3
(D) 1/3~1/2
(E) 1/2~1
Rationale: For Maximum value : It should be less than 1/41 + 1/41 +1/41... 10 times = 10/41 ~ 1/4
For Minimum Value : It should be greater than 1/50+ 1/50+ 1/50 .. 10 times = 10/50 = 1/5.
Thus, the answer should lie between 1/5 and 1/4. Correct ans : B.
Answer: (B) 1/5~1/4
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
(A) 2 years
(B) 3 years
(C) 5 years
(D) 4 years
(E) 1 years
Rationale: Answer: Option D
28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: (D) 4 years
Question: A can do a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together on the Dec. 15, 2000, but A left 8 days and B 12 days before the completion of the work. If C took the rest for a week then in how many days, the work was finished from the day it started ? Sol. Let the total time taken be x days.
(A) 1
(B) 70
(C) 5
(D) 7
(E) 776
Rationale: Answer:E
Answer: (E) 776
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 5%
(B) 10%
(C) 25%
(D) 40%
(E) 65%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
so 0.5+0.5*0.3=0.65
Answer:
E
Answer: (E) 65%
Question: If x^2+(1/x^2)=5, x^4+(1/x^4)=?
(A) 23
(B) 11
(C) 12
(D) 14
(E) 15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=5^2-2=23.
Thus, the answer is A.
Answer: (A) 23
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = d is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-d, -k), then what are the coordinates of the point P?
(A) (-5d, -5k)
(B) (-3d, -3k)
(C) (2d, 2k)
(D) (3d, 3k)
(E) (5d, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-d, -k), so R is at a distance of 2d from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4d and coord (3d,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3d,3k).ans D
Answer: (D) (3d, 3k)
Question: Ross has 60 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
(A) 9 ; 15.
(B) 2 ; 15.
(C) 4 ; 10.
(D) 5 ; 25.
(E) 3 ; 10.
Rationale: Total shirts = 60
Green shirts = 3/4*60 = 45, Non green shirts = 15
Shirts without button = 1/10*60 = 6, shirts with button = 24
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 15
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 15 - 6 = 6
Hence the range would be (9, 15)
Correct Option: A
Answer: (A) 9 ; 15.
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 1978
(B) 2707
(C) 7728
(D) 4200
(E) 7291
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer: D
Answer: (D) 4200
Question: What is the sum of the integers 45 through 175 inclusive?
(A) 12,295
(B) 13,000
(C) 14,300
(D) 14,410
(E) 28,820
Rationale: sum of n consecutive positive integers=n(n+1)/2..
in one case n=44 and other 175... subtract the sum to get the answer
sum of first 175 +ive numbers=175*176/2=15400..
sum of first 45 +i've numbers=45*44/2=990..
answer=15400-990=14410
ANSWER:D
Answer: (D) 14,410
Question: which of the following options must be accurate if given the equation below: h=-e^7
I. h is positive.
II. If e is negative then h is negative.
III. e is non-negative.
(A) I only
(B) II and III only
(C) I and III only
(D) II only
(E) III only
Rationale: I. h is positive --> not true;
II. If h is negative then e is negative. h is negative means that e is not zero. ;
III. e is non-negative.
Answer: D (I only).
Answer: (D) II only
Question: The side of a square has the length of 9. What is the area of the region shaded?
(A) 48-8π
(B) 48-6 π
(C) 24+6π
(D) 16+8π
(E) 64-9π
Rationale: The area of a square whose side is 9 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is E.
Answer: (E) 64-9π
Question: 2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?
(A) 39 and 31
(B) 40 and 33
(C) 42 and 33
(D) 37 and 31
(E) 35 and 32
Rationale: Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
C
Answer: (C) 42 and 33
Question: a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find b=?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: adding 1 to all equqtions.,we get them modified to the following form
(a^2+1)(b^2+1)=260
(b^2+1)(c^2+1)=1300
(c^2+1)(a^2+1)=500
by corresponding mul and div we get a=3,b=5,c=7
ANSWER:D
Answer: (D) 5
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.36 more than Jane, what was the original price of the dish?
(A)  24
(B)  34.8
(C)  37.8
(D)  42
(E)  84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.36 --> 15p - 13.5p = 36 --> p = 24.
Answer: A.
Answer: (A)  24
Question: If a population of women in a town is 50% of men . What is the population of men as a percentage of population of women ?
(A) 100%
(B) 120%
(C) 200%
(D) 150%
(E) 180%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
Men = 10
Women = 5
We're asked for the number of Men, as a percentage of the number of Women.
M/W %= 10/5 = 200%
Answer is C
Answer: (C) 200%
Question: A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?
(A) Rs. 4000
(B) Rs. 4056
(C) Rs. 4060
(D) Rs. 4100
(E) Rs. 4150
Rationale: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
Answer: (B) Rs. 4056
Question: Train X and train Y pass one another traveling in opposite directions. Twenty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
(A) 28
(B) 40
(C) 55
(D) 72
(E) 80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 20 min i.e 20/60 hr
using RTD table, (2R+30) * 20/60 = 100 ==> R= 135 miles/hr
So the rate of train X is 165 miles/hr (since R+30)
The distance traveled by Train X in 20 min is R*T = 165 * 20/60 = 55 miles (C)
Answer: (C) 55
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 44 minutes is:
(A) 86.6 km
(B) 46.6 km
(C) 35.9 km
(D) 35.6 km
(E) 26.6 km
Rationale: Speed downstream = (42 + 7) = 49 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×49 = 35.9 km
ANSWER:C
Answer: (C) 35.9 km
Question: A man buys 60 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
(A) 7.6 %
(B) 7.7 %
(C) 29.13 %
(D) 33.6 %
(E) 37.82 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 60 pens = Rs. 46
S.P. of 60 pens = 99% of Rs. 60 = Rs. 59.4
Profit % = (Profit /C.P.) x 100
Profit% = (13.4/46) x 100 = 29.13%
ANSWER: C
Answer: (C) 29.13 %
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
(A) 64.98
(B) 64.29
(C) 53.98
(D) 64.1
(E) 22.13
Rationale: n:
S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000]
= Rs. 464.10 Difference
= (464.10 - 400)
= Rs. 64.10
Answer:D
Answer: (D) 64.1
Question: Two faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
(A) 1/36
(B) 1/18
(C) 1/32
(D) 1/54
(E) None of these
Rationale: Probability of getting yellow color = P(Y) = 2/6 = 1/3
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/3 x 1/3 x 1/6 = 1/54
ANSWER:D
Answer: (D) 1/54
Question: A big container is 30% full with water. If 36 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
(A) 36 liters
(B) 40 liters
(C) 45 liters
(D) 54 liters
(E) 80 liters
Rationale: A big container is 30% full with water and after 36 liters of water is added, the container becomes 75% full. Hence these 36 liters account for 45% of the container, which means that the capacity of it is 36/0.45=80 liters.
OR: if the capacity of the container is x liters then: 0.3x+36=0.75x --> x=80 liters.
Answer: E.
Answer: (E) 80 liters
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 13
(D) 15
(E) 16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
Rationale: Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
= 5 men and 10 women can complete the work in 7 days Answer : Option C
Answer: (C) 7
Question: A couple decides to have 3 children. If they succeed in having 3 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 2 boys?
(A) 3/4
(B) 1/2
(C) 5/8
(D) 1
(E) 1/4
Rationale: Sample space = 2^3 = 8
Favourable events = {bgg}, {bgb}, {bbb}, {ggg}, {gbg},
Probability = 5/8 = 5/8.
Ans (C).
Answer: (C) 5/8
Question: The average of first five multiples of 3 is
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Solution
Average	= 3(1+2+3+4+5) / 5
= 45 / 5.
= 9.
Answer C
Answer: (C) 9
Question: In how many years, Rs. 200 will produce the same interest @ 5 % as Rs. 900 produce in 2 years @ 3 ½ %?
(A) 6.3 years
(B) 8.2 years
(C) 9 years
(D) 12 years
(E) None of these
Rationale: Explanation:
P = Rs 900, R = 3 ½ % = 7/2 %, T = 2 years.
Therefore,
S.I. = PRT/100
S.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63
Now, P = Rs. 200, S.I. = Rs. 63, R = 5 %
Time = ((100 x 63) / (200 x 5) ) years = 6.3 years
ANSWER A
Answer: (A) 6.3 years
Question: In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
(A) 16.67%
(B) 25%
(C) 20.45%
(D) 31.56%
(E) 40%
Rationale: Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67%
Answer is A
Answer: (A) 16.67%
Question: At what price must an article costing Rs.57 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 69.5
(C) 62.3
(D) 62.1
(E) 75
Rationale: CP = 57
SP = 57*(125/100) = 71.25
MP*(95/100) = 71.25
MP = 75
Answer:E
Answer: (E) 75
Question: If the diameter of circle R is 20% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
(A) 5%
(B) 10%
(C) 15%
(D) 14%
(E) 4%
Rationale: Let diameter of circle R , dr = 20
and diameter of circle S , ds = 100
Radius of circle R , Rr = 10
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (10/50)^2 = (2/10)^2
=4%
Answer :E
Answer: (E) 4%
Question: If 3^e- 3^(e-1) = 162 then e(e-1) =
(A) 12
(B) 16
(C) 20
(D) 30
(E) 81
Rationale: It seems like you were really close but you solved for e - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of e(e -1), e.g. (3)(4) = 12. Even then, had you figured e has to be a little bigger (plugging in 4 for e gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (e - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as the only other answer with consecutive integers as factors is far too big.
Answer: (C) 20
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 6 + 16 * 8)] = 13 years. Answer: C
Answer: (C) 13
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 40, 68 kmph
(B) 40, 30 kmph
(C) 90, 60 kmph
(D) 40, 60 kmph
(E) 20, 60 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph
Answer: D
Answer: (D) 40, 60 kmph
Question: A woman has three blouses of different colors, two skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
(A) 8
(B) 12
(C) 16
(D) 10
(E) 18
Rationale: total ways = 3*2*2=12..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =12-2=10..
D
Answer: (D) 10
Question: How many halves are there in one-fourth?
(A) 0.02
(B) 12
(C) 32
(D) 0.7
(E) 0.5
Rationale: divide 1/4 by 1/2
=1/4÷1/2
=1/4*2/1
=2/4
=0.5.
Answer is E.
Answer: (E) 0.5
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) 50
(B) 88
(C) 77
(D) 66
(E) 51
Rationale: A+B+C = 500
A+C = 200
B+C = 350
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A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: (A) 50
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 10%?
(A) 25%
(B) 28%
(C) 21%
(D) 30%
(E) 32%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 10% increase A surface = 6* ((1.1a)^2) = 6*1.21*a^2
The increase in the surface area = (6*1.21*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.21-1))/(6*a^2) = 1.21-1=0.21 = 21%
Answer : C
Answer: (C) 21%
Question: In a colony of 50 residents, the ratio of the number of men and women is 3:2. Among the women, the ratio of the educated to the uneducated is 1:3. If the ratio of the number of education to uneducated persons is 4:6, then find the ratio of the number of educated and uneducated men in the colony?
(A) 1:1
(B) 3:2
(C) 1:3
(D) 2:5
(E) 5:7
Rationale: Number of men in the colony = 3/5 (50) = 30
Number of women in the colony = 2/5 (50) = 20
Number of educated women in the colony = 1/4 (20) = 5
Number of uneducated women in the colony = 3/4 (20) = 15
Number of educated persons in the colony = 4/10 (50) = 20
As 5 females are educated, remaining 15 educated persons must be men.
Number of uneducated men in the colony = 30 - 15 = 15
Number of educated men and uneducated men are in the ratio 15:15 => 1:1
Answer:A
Answer: (A) 1:1
Question: Two dice are tossed. The probability that the total score is a prime number is:
(A) 5/5
(B) 5/9
(C) 5/1
(D) 5/7
(E) 5/12
Rationale: n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }
n(E) = 15
The total cases are 6 * 6 * 6 = 216.
The probability = 15/36 = 5/12.
Answer: E
Answer: (E) 5/12
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z<(x − 1)/y
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)
(A) I only
(B) I and II
(C) II and III
(D) II only
(E) None of these
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z<(x − 1)/y --> 2/3 < 1/3 --> False
II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False
III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False
Answer: E
Answer: (E) None of these
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 638
(B) 738
(C) 375
(D) 98
(E) 8303
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer:C
Answer: (C) 375
Question: Ten stickers numbered 1 to 10 are placed in a bowl, mixed up thoroughly and then one sticker is drawn
randomly. If it is known that the number on the drawn sticker is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 4/7
(C) 5/7
(D) 7/11
(E) 9/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
B)
Answer: (B) 4/7