mathewhe/aqua_rat huggingface dataset:
Question: If xy ≠ 0 and x^2y^2 − xy = 20, which of the following could be y in terms of x?
I. 5/x
II. -4/x
III. 3/x
(A) I only
(B) II only
(C) I and II only
(D) I and III
(E) II and III
Rationale: (x^2)(y^2) – xy - 20 = 0
(xy – 5)(xy + 4) = 0
xy – 5 = 0 or xy + 4 = 0
xy = 5 or xy = -4
Since we need y in terms of x, we can isolate y in both of our equations.
y = 5/x or y = -4/x
Answer: C
Answer: (C) I and II only
Question: A can run 2.7 km distance in 1 min 20 seconds, while B can run this distance in 1 min 30 sec. By how much distance can A beat B?
(A) 90 m
(B) 30 m
(C) 120 m
(D) 300 m
(E) 190 m
Rationale: A takes time 1.20 minutes=80sec
B takes time 1.30 minutes=90sec
diffrence= 90-80=10sec
now we are to find distance covered in 10 sec by B
90sec=30m
1sec=30m
10sec=10x30=300m
ANSWER:D
Answer: (D) 300 m
Question: 3x^2 - 13x + 12 =
(A) (3x-4)(x-2)
(B) (3x-4)(x+2)
(C) (3x-4)(x-3)
(D) (3x-2)(x+4)
(E) none of above
Rationale: 3x^2 - 13x + 12
= 3x^2 - 9x - 4x + 12
= 3x (x - 3) - 4 (x-3)
= (3x-4) (x-3)
Option C
Answer: (C) (3x-4)(x-3)
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
(A) 62 degrees
(B) 64 degrees
(C) 65 degrees
(D) 66 degrees
(E) 67 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8. Answer: B
Temperature on the 5th day = 8x = 64 degrees.
Answer: (B) 64 degrees
Question: A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 10 days, B can complete the job in 2 days and C can complete the job in 5 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
(A) 4/3 days
(B) 5/4 days
(C) 4/5 days
(D) 20days
(E) 14 days
Rationale: Let the total number of cans to be prepared be 10.
The number of cans prepared by A in 1 day = 1.
The number of cans prepared by B in 1 day = 5.
The number of cans prepared by C in 1 day = 2.
Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 8.
Therefore, the number of days taken to complete the whole work = 10/8 = 5/4 days.
ANSWER:B
Answer: (B) 5/4 days
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) 28,008
(B) 28,006
(C) 28,005
(D) 28,000
(E) 28,001
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000.Answer:D
Answer: (D) 28,000
Question: What should come in place of question mark (?)?
138.009 + 341.981 – 146.305 = 123.6 + ?
(A) 210.85
(B) 120.85
(C) 220.085
(D) 120.085
(E) None of these
Rationale: ? = 138.009 + 341.981 – 146.305 – 123.60
∴ ? = 210.085
Answer E
Answer: (E) None of these
Question: Find the smallest number of five digits exactly divisible by 16,24,36 and 54.
(A) 10368
(B) 10638
(C) 10836
(D) 10863
(E) None of them
Rationale: Smallest number of five digits is 10000.
Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432,
On dividing 10000 by 432,we get 64 as remainder.
Therefore, Required number = 10000 +( 432 – 64 ) = 10368.
Answer is A.
Answer: (A) 10368
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 286
(B) 278
(C) 255
(D) 150
(E) 200
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 12) m
= 200 m.
Answer:E
Answer: (E) 200
Question: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a +4) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
(A) 80
(B) 75
(C) 70
(D) 60
(E) 65
Rationale: 1/2bh=1/2(2a+1)(2a+4)
Now 4a-5=2a+4
2a=9
Therefore,
A(0,0); B(0,13); C(10,13)
1/2*10*13=65
Answer: E
Answer: (E) 65
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) 1/208
(B) 1/228
(C) 1/229
(D) 1/20
(E) 1/213
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
Answer:D
Answer: (D) 1/20
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 610 m long?
(A) 22
(B) 89
(C) 85
(D) 278
(E) 291
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 610)/10 = 85 sec.
Answer: C
Answer: (C) 85
Question: When 19 is divided by positive integer j, the remainder is 4. For how many values of j is this be true?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: When 19 is divided by j, the remainder is 4 i.e. 5 kiwis left over after grouping, so j must be greater than 5.
It also means that 15 is completely divisible by j.
Factors of 15 are 1, 3, 5, and 15.
Out of these, j can be 15.
Answer is (A).
Answer: (A) 1
Question: If n is the product of the integers from 1 to 9, inclusive, how many different prime factors greater than 1 does n have?
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Rationale: n = 1*2*3*4*5*6*7*8*9
The prime factors of n are 2, 3, 5, and 7.
There are 4 prime factors.
The answer is A.
Answer: (A) Four
Question: In 1940, a correspondent proposed the following question:
A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900?
(A) 14
(B) 24
(C) 34
(D) 44
(E) 54
Rationale: He was 44 years old.
From the question you know the man died between 1900 and 1940. We also know his age at death (x) is one twenty-ninth of the year of his birth (29x). If you add his age at death to the year he was born you get the year he died (30x). Only one year between 1900 and 1940 is divisible by 30, 1920 (the year he died). The year he was born can now be found: 1920 * (29/30) = 1856. So in 1900 he was (1900 - 1856) = 44 years old.
Answer: (D) 44
Question: In two digit number, the digit in the unit’s place is four times the digit in ten's place and sum of the digits is equal to 10. What is the number?
(A) 14
(B) 18
(C) 20
(D) 28
(E) 30
Rationale: Sol.
Let the ten’s digits be x. Then, unit’s digit = 4x.
∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2.
So, ten’s digit = 2, unit’s digit = 8.
Hence, the required number is 28.
Answer D
Answer: (D) 28
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour?
(A) 73
(B) 15
(C) 12
(D) 83
(E) 28
Rationale: Explanation:
T = 11/45 * 60 = 15
Answer: Option B
Answer: (B) 15
Question: The simple interest on a sum of money will be Rs.500 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 700
(B) 800
(C) 900
(D) 1000
(E) 1100
Rationale: P --- 10 ---- 500
P --- 5 ----- 250
3P --- 5 -----750
------
=> 1000
ANSWER:D
Answer: (D) 1000
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 72 6/7%
(B) 82 6/7%
(C) 22 6/7%
(D) 42 6/7%
(E) 82 2/7%
Rationale: Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: (D) 42 6/7%
Question: A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
(A) 28
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Option B
Answer: (B) 18
Question: Calculate the percentage profit or loss if a trader bought the apples at 5 per rupee and sells 4 apples per rupee.
(A) 11 %
(B) 34 %
(C) 25 %
(D) 15 %
(E) 35 %
Rationale: Let he total number of oranges bought by the shopkeeper be 12.
If he buys 5 a rupee, his CP = 4
He selling at 4 a rupee, his SP = 5
Profit = SP - CP = 5 - 4 = 1
Profit Percent = 1/4 * 100 = 25 %
Answer: C
Answer: (C) 25 %
Question: In a class there are 20 boys and 23 girls. In how many ways can a boy and a girl be selected?
(A) 508
(B) 460
(C) 800
(D) 570
(E) 503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 23 girls in 23 ways
We select a boy and girl in 20 * 23 ways i.e., = 460 ways.
Answer:B
Answer: (B) 460
Question: A man bought 40 shares of Rs. 80 at 5 discount, the rate of dividend being 12 1/2%The rate of interest obtained is
(A) 13.33%
(B) 15.5%
(C) 14%
(D) 14.25%
(E) 14.95%
Rationale: Explanation :
Face Value of a share = Rs.80
He bought each share at Rs.80 - Rs.5 = Rs.75
Number of shares = 40
Dividend = 12 1/2%=25/2%
Dividend per share = 80×25/2/100=Rs.10
Total dividend = (40 × 10)
ie, He got a dividend of (40 × 10) for an investment of Rs.(40 × 75)
Interest obtained = 40×10×100/40×75=13.33%
Answer : Option A
Answer: (A) 13.33%
Question: A rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) s.3988
(B) s.3900
(C) s.4500
(D) s.3922
(E) s.3928
Rationale: Area = (l + b – d) d
(100 + 60 – 10)10 => 1500 m2
1500 * 3
= Rs.4500
Answer:C
Answer: (C) s.4500
Question: There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
(A) 11660
(B) 11700
(C) 11760
(D) 11800
(E) 11850
Rationale: Explanation:
We need to select 5 men from 8 men and 6 women from 10 women
Number of ways to do this
= 8C5 × 10C6
= 8C3 × 10C4 [∵ nCr = nC(n-r)]
=
(
8
×
7
×
6
3
×
2
×
1
)
(
10
×
9
×
8
×
7
4
×
3
×
2
×
1
)
=
56
×
210
=11760
Option C
Answer: (C) 11760
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 63. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 7
(E) 4
Rationale: Let the number be x. Then,
3(2x + 9) = 63
2x = 12 => x = 6
ANSWER:B
Answer: (B) 6
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (6, -4). What is the slope of line m?
(A) -3
(B) -1
(C) -1/3
(D) 0
(E) 1
Rationale: The midpoint of (2,8) and (6,-4) is (4,2).
The slope of a line through (0,-2) and (4,2) is (2-(-2))/(4-0) = 4/4 = 1
The answer is E.
Answer: (E) 1
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even eleven-digit numbers are palindromes?
(A) 40
(B) 400
(C) 500
(D) 5,000
(E) 400,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.
The middle number in the eleven-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers , 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)
we thus have, 4 *10*10*10*10*10* = 400000. E
Answer: (E) 400,000
Question: What will come in place of the x in the following Number series? 15, 60, X, 960, 3840
(A) 280
(B) 960
(C) 820
(D) 800
(E) 980
Rationale: (B)
15 x 4 = 60, 60 x 4 = 240, 240 x 4 = 960, 960 x 4 = 3840.
Answer: (B) 960
Question: A single letter is selected at random from the word 'CARE'. The probability that it is a vowel is..??
(A) 2/11
(B) 3/11
(C) 4/11
(D) 2/4
(E) 1
Rationale: total vowels = 2, total number of letters = 4
so probability = 2/4
ANSWER:D
Answer: (D) 2/4
Question: When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to
(A) area
(B) circumference
(C) 4
(D) 2π
(E) None of these
Rationale: According to question, circumference of circle = Area of circle
or πd = π(d⁄2)2 [where d = diameter]
∴ d = 4
Answer C
Answer: (C) 4
Question: The least number by which 72 must be multiplied in order to produce a multiple of 112, is:
(A) 6
(B) 12
(C) 14
(D) 18
(E) 19
Rationale: Required number is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient= 14.
Therefore, required number= 14.
ANSWER:C
Answer: (C) 14
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) 3902
(B) 3928
(C) 3929
(D) 3900
(E) 39123
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Answer: (D) 3900
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?
(A) 235 miles.
(B) 245 miles.
(C) 255 miles.
(D) 265 miles.
(E) 275 miles.
Rationale: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 55 = 255 miles.
Answer C
Answer: (C) 255 miles.
Question: Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?
(A) $3039
(B) $3003
(C) $3002
(D) $3000
(E) $3004
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000
Answer:D
Answer: (D) $3000
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 88
(C) 66
(D) 55
(E) 22
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer:A
Answer: (A) 50
Question: In an aquarium there is 14 purple fish, 8 orange fish,12 pink fish, 3 golden fish. How many fish are there in an aquarium?
(A) 27
(B) 37
(C) 17
(D) 47
(E) 07
Rationale: 14+8+12+3=37. Answer is B
Answer: (B) 37
Question: If |20x-10| = 90, then find the product of the values of x?
(A) -45
(B) 50
(C) -62
(D) 35
(E) -20
Rationale: |20x-10| = 90
20x-10 = 90 or 20x-10 = -90
20x = 100 or 20x = -80
x = 5 or x = -4
product = -4*5 = -20
Answer is E
Answer: (E) -20
Question: A trader marks his books 30% more than the cost price. If he allows 20% discount, then find his gain or loss percent?
(A) 4% Gain
(B) 12% loss
(C) 4% loss
(D) No profit No loss
(E) None of these
Rationale: Let CP of an book = 100
MP of an book = 130
Discount 20 % on 130 = 26
SP of the book = 130 - 26 = 104
Gain = 4%
Answer : A
Answer: (A) 4% Gain
Question: The difference between simple and compound interest on Rs. 1400 for one year at 10% per annum reckoned half-yearly is?
(A) 8.25
(B) 3.5
(C) 9.0
(D) 3.15
(E) 2.0
Rationale: S.I. = (1400 * 10 * 1)/100 = Rs. 140
C.I. = [1400 * (1 + 5/100)2 - 1400]
= Rs. 143.5 Difference = (143.5 - 140)
= Rs.3.50
Answer:B
Answer: (B) 3.5
Question: If xy > 0, 1/x + 1/y = 4, and 1/xy = 6, then (x+y)/2 = ?
(A) 1/25
(B) 1/6
(C) 1/5
(D) 1/3
(E) 6
Rationale: (1/X+1/Y)=4 canbe solved as {(x+y)/xy}=6. Substituting for 1/xy=6, we get
x+y=4/6
==> (x+y)/2= 4/(6*2)=1/3.
D
Answer: (D) 1/3
Question: If S is the sum of reciprocals of a list of consecutive integers from 55 to 64, inclusive, S is approximately equal to
(A) 0.16
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
Rationale: We need to find the approximate value of 1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64. Now, the sum of these 10 terms will be very close to 10 times 1/60, which is 0.016*10=0.16.
Answer: A.
Answer: (A) 0.16
Question: The percentage profit earned by selling an article for Rs. 1620 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 3000
(B) 1812.5
(C) 2000
(D) 5600
(E) 3400
Rationale: C.P. be Rs. x.
Then, (1620 - x)/x * 100 = (x - 1280)/x * 100
1620 - x = x - 1280
2x = 2900 => x = 1450
Required S.P. = 125 % of Rs. 1450 = 125/100 * 1450 = Rs. 1812.5.
ANSWER B
Answer: (B) 1812.5
Question: Complete the series
13, 9, 5, 1, -3,-7 , -11...
(A) -4
(B) 0
(C) 3
(D) -2
(E) -15
Rationale: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option E) -15
Answer: (E) -15
Question: How many different ways can 2 students be seated in a row of 5 desks, so that there is always at least one empty desk between the students?
(A)  2
(B)  3
(C)  4
(D)  6
(E)  12
Rationale: 6 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
6x2=12
E
Answer: (E)  12
Question: Positive Integer A gives the remainder of 20 when divided by another positive Integer B. If A/B = 47.50, what is the value of B?
(A) 96
(B) 75
(C) 40
(D) 25
(E) 12
Rationale: .50 of B = Remainder
.50 of B = 20
B = (20 *100) / 50 = 40.
C
Answer: (C) 40
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 19
(B) 17
(C) 10
(D) 18
(E) 16
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.Answer: C
Answer: (C) 10
Question: In a workshop there are 5 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) A)168.
(B) B)80.
(C) C)100.
(D) D)48.
(E) E)16.
Rationale: ways to select one shelf = 2
ways to select one bed = 5
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 2*5*10 = 100
Answer : C
Answer: (C) C)100.
Question: There is a 20% chance Sandy will visit China this year, while there is a 60% chance that she will visit Malaysia this year. What is the probability that Sandy will visit either China or Malaysia this year, but NOT both?
(A) 40%
(B) 48%
(C) 56%
(D) 64%
(E) 72%
Rationale: P(China and not Malaysia) = 0.2*0.4 = 0.08
P(Malaysia and not China) = 0.6*0.8 = 0.48
Total probability = 0.08 + 0.48 = 0.56 = 56%
The answer is C.
Answer: (C) 56%
Question: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:
(A) 9%
(B) 26%
(C) 50%
(D) 80%
(E) 34%
Rationale: C
C.P. of each pen be Re. 1.
Then, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.
Gain % = 4/8 * 100 = 50%
Answer: (C) 50%
Question: In how many ways can a team of 4 persons be formed out of a total of 8 persons such that two particular persons should be included in each team?
(A) 15
(B) 20
(C) 18
(D) 22
(E) 30
Rationale: Two particular persons should be included in each team. Therefore we have to select remaining 4-2=2 persons from 8-2=6 persons.
Hence, required number of ways= 6C2 = 15
Answer is A
Answer: (A) 15
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
(A) 2 hrs
(B) 6 hrs
(C) 7 hrs
(D) 8 hrs
(E) 9 hrs
Rationale: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.
Answer:C
Answer: (C) 7 hrs
Question: Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 25/49, what is the probability that the next one she draws will be pink?
(A) 1/49
(B) 2/7
(C) 3/7
(D) 16/49
(E) 40/49
Rationale: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 25/49 = (5/7) * (5/7)
Therefore probability that the next one she draws is pink = 2/7
Option (B)
Answer: (B) 2/7
Question: If 3log(4*5^2) = x, find x
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 3(log2^2*5^2)=x
3log(5*2)^2=x
3*2log(5*2)=x
6log10=x
log10 base 10=1
so
6*1=x
x=6
ANSWER:B
Answer: (B) 6
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
(A) 1050
(B) 1060
(C) 1020
(D) 1048
(E) 1078
Rationale: 600- - 84
90
6 510
1--12
85---1020
ANSWER C
Answer: (C) 1020
Question: The entry in the following sequence is determined by the rule if 1 is entry in the sequence the next three entries are n-1, entries are
(A) 0,1,2
(B) 0,-1,1
(C) 0,1,2
(D) 2,3,4
(E) 0,1,0
Rationale: at the starting point we have entry it just 1
now at the time of first entry we have n-1=1-1= 0
now we have two entries that is 1(default) , 0(first entry)
now at the time of second entry we have n-1=2-1=1
so we have 0,1 and now at the time of third entry
n-1=3-1=2;
so
0,1,2
ANSWER:C
Answer: (C) 0,1,2
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
(A) 1/9
(B) 10/243
(C) 1/27
(D) 10/271
(E) 1/1000000
Rationale: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 10/(9*9*3+9*3) = 1/27.
Answer: C.
Answer: (C) 1/27
Question: three partners A, B, C start a business. Twice A’s capital is equal to thrice B’s capital and B’s capital is four times C’s capital. Out of a total profit of Rs. 16,500 at the end of the year, B’ share is:
(A) 2,000
(B) 4,000
(C) 5,000
(D) 6,000
(E) None
Rationale: Sol.
Let C = x. Then, B = 4x and 2A = 3 * 4x = 12x or A = 6x.
∴ A : B : C = 6x : 4x : x = 6 : 4 : 1.
So, B’s capital = Rs. [16500 * 4/11] = Rs. 6000.
Answer D
Answer: (D) 6,000
Question: Sachin is younger than Rahul by 14 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 48
(B) 24.8
(C) 24.21
(D) 24.88
(E) 49
Rationale: Explanation:
If Rahul age is x, then Sachin age is x - 14,
so,
9x - 126 = 7x
2x = 126
x = 63
So Sachin age is 63 - 14 = 49
Answer: E) 49
Answer: (E) 49
Question: By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 5% on the marked price. His gain percent during the sale is?
(A) 6%
(B) 2%
(C) 8%
(D) 3%
(E) 4%
Rationale: Marked price = Rs. 300
C.P. = 100/120 * 300 = Rs. 250
Sale price = 95% of Rs. 300 = Rs. 285
Required gain % = 15/250 * 100 =6%.
Answer: A
Answer: (A) 6%
Question: John builds a square with a side of 12 cm from some wire. If from the same wire, he builds a rectangle with a width of 6 cm, what will be the length of the rectangle?
(A) 18 cm
(B) 19 cm
(C) 20 cm
(D) 21 cm
(E) None
Rationale: Solution:
If the side of the square is 12 cm, then its perimetre will be 48 cm. We build the rectangle from the same wire, so it will have the same perimetre. Its width is 6 cm, so its length will be (48-12) ÷ 2 = 36 ÷ 2 = 18 cm
Answer A
Answer: (A) 18 cm