RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: How many two-digit numbers are there whose remainder when divided by 13 is 1, and whose remainder when divided by 6 is 5?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer D
Question: A boat can travel with a speed of 16 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 60 km downstream.
A.2 hours.
B.3 hours.
C.4 hours.
D.5 hours.
Answer: B.3 hours.
Explanation: Speed downstream = (16 + 4) km/hr = 20 km/hr.
Time taken to travel 60 km downstream = 60/20 = 3 hours.
Answer :B
Question: The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
A.22
B.30
C.99
D.38
Answer: B.30
Explanation: total age increased = (8 * 2) years = 16 years.
Sum of ages of two new men = (21 + 23 + 16) years = 60 years
Average age of two new men = (60/2) years = 30 years.
Answer: B
Question: Look at this series: XXIV, XX, __, XII, VIII, ... What number should fill the blank?
A.XV
B.XVI
C.XII
D.VII
Answer: B.XVI
Explanation: B
XVI
This is a simple subtraction series; each number is 4 less than the previous number.
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
A.197
B.219
C.120
D.165
Answer: C.120
Explanation: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x =120
Answer: C
Question: A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is?
A.65
B.67
C.87
D.85
Answer: D.85
Explanation: Let the number of wickets taken till the last match be x. Then,
(12.4x + 26)/(x + 5) = 12
= 12.4x + 26 = 12x + 60
= 0.4x = 34
= x = 340/4 =85
Answer: D
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.11 sec
B.30 sec
C.77 sec
D.14 sec
Answer: B.30 sec
Explanation: 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
Question: A woman has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.80
B.90
C.100
D.110
Answer: B.90
Explanation: Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
B)
Question: At a reception, one-third of the guests departed at a certain time. Later two-fifths of the guests departed. Even later two-thirds of the remaining guests departed. If six people were left, how many were originally present at the party?
A.28
B.37
C.20
D.45 people
Answer: D.45 people
Explanation: Explanation:
Let Original members be x
First One third guest departed i.e x/3
Remaining guests = x – (x/3) = 2x/3
Now from the remaining (2x/3) two-fifths departed = 2/5(2x/3) = 4x/15
i.e. Now remaining guests will be (2x/3 – 4x/15) = 2x/5
Now from remaining (2x/5) two-thirds departed = 2/3(2x/5) = 4x/15
Now remaining guests = (2x/5 – 4x/15) = 2x/15
Given 2x/15 = 6 ⇒ x = 45
Answer: D
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/3, 3/4, 1/5 respectively. Find the probability of success of at least two.
A.11/30
B.12/50
C.13/30
D.3/50
Answer: A.11/30
Explanation: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 3/4 x 4/5 + 3/4 x 1/5 x 2/3 + 1/3 x 1/5 x 1/4 + 1/3 x 3/4 x 1/5 = 11/30
ANSWER:A
Question: Find the value of 4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
A.800
B.3200
C.900
D.1600
Answer: B.3200
Explanation: Answer
4 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 4 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 4 x 4 x 4 x 50 = 3200
Correct Option: B
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
A.29:32
B.21:34
C.21:22
D.31:20
Answer: C.21:22
Explanation: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Question: (a-b)/(c/2)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the least possible value of the expression?
A.1/4`
B.2/4
C.4/2
D.1/2
Answer: B.2/4
Explanation: (a-b)/(c/2)
= 2(a-b)/c
The expression will have the least value when numerator 2(a-b) is the smallest.
= 2(2-1)/4
=2/4
Answer B
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
A.20
B.25
C.26
D.28
Answer: A.20
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Question: The HCF of two numbers is 40 and the other two factors of their LCM are 11 and 12. What is the largest number.
A.462
B.450
C.488
D.480
Answer: D.480
Explanation: Explanation:
HCF of the two numbers = 40
HCF will be always a factor of LCM
40 is factor of LCM
other two factors are 11 & 12
Then the numbers are (40 *11) and (40 x 12)
= 440 and 480
Answer: Option D
Question: The speed at which a man can row a boat in still water is 10 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 60 metres?
A.18 seconds
B.34 seconds
C.14 seconds
D.12 seconds
Answer: A.18 seconds
Explanation: Speed of the boat downstream = 10 + 2 = 12 kmph
= 12 * 5/18 = 10/3 m/s
Hence time taken to cover 60 m = 60*3/10
= 18 seconds.
Answer: A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 80 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
A. 16
B. 48
C. 20
D. 24
Answer: B. 48
Explanation: Time taken = Total Distance / Relative Speed
Total Distance = 80 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 80 / 10 = 8 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 8 = 48 kms... Answer - B
Question: What is the greatest number which divides 29, 32, 38 and leaves same remainder in each case?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: Explanation:
HCF of differences between given numbers is the required answer
32 - 29 = 3
38 - 32 = 6
38 - 29 = 9
HCF of 3, 6, 9 is 3
Answer: Option B
Question: How many positive integers will divide evenly into 420?
A.8
B.12
C.16
D.18
Answer: B.12
Explanation: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 12
Option CB
Question: A student chose a number, multiplied it by 3, then subtracted 138 from the result and got 102. What was the number he chose?
A.80
B.120
C.130
D.140
Answer: A.80
Explanation: Solution:
Let xx be the number he chose, then
3⋅x−138=102
3x=240
x=80
Answer A
Question: Ajay spends 25 per cent of his salary on house rent, 5 percent on food, 10 percent travel, 10 percent on clothes and the remaining amount of Rs.20000 is saved. What is Ajayâ€™s income?
A.Rs.40000
B.Rs.80500
C.Rs.60700
D.Rs.70500
Answer: A.Rs.40000
Explanation: Explanation:
Savings = Income â€“ expenditure
100 â€“ (25+5+10+10) = 50%
50% of income = Rs.20000
:. Income = 20000 x 100/50 = Rs. 40000.
Answer: Option A
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
A.5 : 2
B.7 : 3
C.9 : 2
D.13 : 4
Answer: B.7 : 3
Explanation: Let the present ages of father and son be x and y years respectively.
Then (x-10) = 3 (y-10) or
3y-x = 20 ------ (1)
and (x+10) = 2 (y+10) or
x-2y = 10 ----- (2)
(1) + (2) -> y = 30
Substituting y = 30 in equation (1) we get x = 70
Ratio of their ages = 70 : 30 or 7:3
ANSWER:B
Question: A vendor sold two things at same cost of 15 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
A.0.65 loss
B.0.75 loss
C.0.80 loss
D.0.55 loss
Answer: B.0.75 loss
Explanation: CP when profit of 25% = 12
CP when loss of 20% = 18.75
Total CP = 30.75
Total SP = 30.00
Total loss = 0.75
ANSWER:B
Question: If 3 pounds of dried apricots that cost x dollars per pound are mixed with 4 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
A.(3x + 4y)/5
B.(3x + 4y)/(x + y)
C.(3x + 4y)/(xy)
D.5(3x + 4y)
Answer: A.(3x + 4y)/5
Explanation: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 3x;
Cost of prunes = 4y;
Cost per pound = (3x + 4y)/5;
Ans is (A).
Question: What will be the cost of building a fence around a rectangular plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 50?
A.A)Rs.3944
B.B)Rs.3948
C.C)Rs.3519.5
D.D)Rs.3949
Answer: C.C)Rs.3519.5
Explanation: Let the side of the rectangle plot be a ft.
a*b = 289 =>1.7 b*b = 289
b = 13.03
a = 22.17
Length of the fence = Perimeter of the plot = 2(a+b) = 70.39 ft.
Cost of building the fence = 70.39 * 50 = Rs.3519.5
Answer: C
Question: What is the last number in a sequence of 5 consecutive integers, given that their sum is 335?
A.69
B.70
C.68
D.66
Answer: A.69
Explanation: The median is: 335/5 = 67. Middle position.
Middle position is also: 5/2 = 2.5, rounded up: 3rd position
3rd position is: 5-3 = 2 positions away from the last position
67 + 2 = 69
Answer: A
Question: If two numbers are in the ratio 5:2. If 10 is added to both of the numbers then the ratio becomes 5:4 then find the smallest number?
A.2
B.3
C.4
D.6
Answer: A.2
Explanation: 5:2
5x + 10 : 2x + 10 = 5 : 4
5[2x + 10] = 4[5x + 10]
10x + 50 = 20x + 40
20x - 10x = 50 - 40
x = 1
Then the second number is = 2X
2x = 2
Option A
Question: Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
A.8820
B.8828
C.8628
D.8891
Answer: C.8628
Explanation: Amount = [8000 * (1 + 5/100)2]
= 8000 * 21/20 * 21/20
= Rs.8820
Answer: C
Question: The difference between simple and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is?
A.2
B.3
C.4
D.6
Answer: B.3
Explanation: Explanation:
S.I. = (1200 * 10 * 1)/100 = Rs. 120
C.I. = [1200 * (1 + 5/100)2 - 1200] = Rs. 123 Difference = (123 - 120) = Rs. 3.
Answer:B
Question: 15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours?
A.360
B.480
C.720
D.960
Answer: D.960
Explanation: D
15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour.
5 grams sugar cubes will take less time to move.
Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour.
More ants, more sugar cubes they can move.
20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour
Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams.
Question: If w/x = 5/7 and w/y = 4/7, then (x + y)/y =
A.1/2
B.7/3
C.6/7
D.1/5
Answer: B.7/3
Explanation: Ratio 1:
7w = 5x
Ratio 2:
7w = 4y
5x = 4y
x= 4y/3
(x+y)/y = ((4y/3)+y)/y = y(4/3 +1)/y = 7/3
Answer is B
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 kg. the weight of the new student is ?
A.10.6 kg
B.10.8 kg
C.11 kg
D.14.9 kg
Answer: C.11 kg
Explanation: Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.8 - 19 x 15) kg
= 11 kg.
Correct Option: C
Question: How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the ones digit and the hundered digit are switched?
A.3
B.19
C.22
D.30
Answer: D.30
Explanation: Answer is 30
No of digits between 310 and 400 (exclusive) = 400-310-1 = 89
No Intergers divisble by 3 =~ 89/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and ones digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and ones digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : D
Question: A crate measures 2 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=2 for the surface 8*12 face.
Volume = 8pi
Answer A
Question: If 4<(7-x)/2, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A.II only
B.III only
C.I and II only
D.II and III only
Answer: B.III only
Explanation: 12<7-x
x<-5
x+5<0
1.5<x...not possible
2.True.....Check for values x=-6,-7,-8....... etc
3.True.. Since x+5<0 -(x+5) will always be positive
Hence, Ans is B..
Question: If 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
A.41
B.42
C.36
D.44
Answer: C.36
Explanation: n(n-1)/2 =9*8/2
=36
ANSWER:C
Question: If a and b are positive integers and (2^a)^b = 2^2, what is the value of 2^a*2^b?
A.8
B.4
C.16
D.32
Answer: A.8
Explanation: 2^ab =2^2 therefore ab=2 either a=1or2 or b=2 or 1
therefore 2^a* 2^b = 2^(a+b)= 2^3 =8
A
Question: Dan's age after 20 years will be 7 times his age 4 years ago. What is the present age of Dan?
A.6
B.8
C.10
D.12
Answer: B.8
Explanation: Let Dan's present age be x.
x+20 = 7(x-4)
6x = 48
x = 8
The answer is B.
Question: Marge has Q candies, where Q is an integer such that 20 < Q< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder Q= 2
C
Question: Find the compound ratio of (2:3), (5:3) and (2:5) is
A.1:2
B.2:3
C.3:4
D.4:9
Answer: D.4:9
Explanation: Required ratio = 2/3 * 5/3 * 2/5 = 4/9 = 4:9
Answer is D
Question: The average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
A.75 kg
B.65 kg
C.55 kg
D.89 kg
Answer: D.89 kg
Explanation: Total weight increased = (8 x 3) kg = 24 kg.
Weight of new person = (65 + 24) kg = 89 kg.
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
A.120 metres
B.250 metres
C.324 metres
D.150 metres
Answer: B.250 metres
Explanation: Speed=60 x5/18m/sec=50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50/3	x 15m = 250 m.
ANSWER:B
Question: A right triangle AEC has to be constructed in the xy-plane so that the right angle is at A and AE is parallel to x axis. The coordinates of A, E and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
A.63
B.336
C.567
D.3024
Answer: D.3024
Explanation: All the cordinates are integer hence,
possible AE values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 5 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
A. 400
B. 500
C. 1,250
D. 2,500
Answer: B. 500
Explanation: total fish = x
percentage of second catch = (5/50)*100 = 10%
so, x * 10% = 50
x = 500 ans B.
Question: If 12 men or 20 women can do a piece of work in 81 days, then in how many days can 9 men and 12 women together do the work?
A.10 days
B.30 days
C.20 days
D.60 days
Answer: D.60 days
Explanation: D
60 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 81 days. So, 27 women can do it in (20 * 81) /27 = 60 days.
Question: There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
A.15
B.30
C.120
D.240
Answer: C.120
Explanation: Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C.
Question: An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …, 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion when read upside down — for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?
A.80
B.78
C.71
D.69
Answer: C.71
Explanation: Explanation :
We need to figure out which all numbers cause a confusion when reversed : 0, 1, 6, 8, 9.
1st digit cannot be 0. So, 9 combinations are possible for the 1st digit.
2 digits are distinct. So, 2nd digit cannot be 1st digit.
Hence, again 9 combinations possible for 2nd digit. So, totally, 9 * 9 = 81 numbers are possible.
Since 1st digit is not 0, we can neglect confusions caused by 0, as, if a number with 2nd digit 0 is reversed, it will have its 1st digit as 0, and that is not possible, and hence no confusion. i.e. If we reverse 60, we get 09, but since 0 is not the 1st digit, the agency knows 09 is wrong, and hence it causes no confusion.
The remaining numbers are 1,6,8,9.
Numbers starting with 1: 16, 18, 19 cause confusion.
Numbers starting with 6: 61, 68, 69 cause confusion.
Numbers starting with 8: 81, 86, 89 cause confusion.
Numbers starting with 9: 91, 96, 98 cause confusion.
Now if you think again 69 and 96 does not cause confusion when read upside down. 69 when read upside down is 69, and 96 when read upside down is 96! So, only 10 numbers out of 81 cause confusion.
Hence, there are 71 numbers.
Answer : C
Question: If (x - 1)^2 = 324, which of the following could be the value of x - 4?
A.16
B.14
C.-19
D.-21
Answer: D.-21
Explanation: (x - 1)^2 = 324
(x - 1) = 18 or -18
x = 19 or -17
x - 4 = 15 or -21
The answer is D.
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 55% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
A.7
B.25
C.35
D.45
Answer: A.7
Explanation: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 55% = 99 responded as satisfied, So remaining Satisfied are 120 - 99 = 21
so 21 is what percentage of 300 - 7%
So the answer should be A
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 5 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
A.2y
B.4y
C.23/5y
D.6y
Answer: C.23/5y
Explanation: Anthony performed for 14 days meansw Cindy performed for(14-5)=9 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/9
Solving we get, x=23/5y
Now Anthony's Advance is x=23.5y .So answer should be C.
Question: The product of two numbers is 2028 and their HCF is 13. What are the number of such pairs?
A.1
B.2
C.5
D.23
Answer: B.2
Explanation: Let the numbers be 13x and 13y ( HCF of the numbers = 13)
13x × 13y = 2028
xy = 12
co-primes with product 12 are (1, 12) and (3, 4) ( we need to take only
co-primes with product 12. If we take two numbers with product 12, but not co-prime,
the HCF will not remain as 13)
Hence the numbers with HCF 13 and product 2028
= (13 × 1, 13 × 12) and (13 × 3, 13 × 4)
= (13, 156) and (39, 52)
So, there are 2 pairs of numbers with HCF 13 and product 2028
Answer is B
Question: Vishal has 7 pairs of shoes; each pair is a different color. If Vishal randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
A.2/15
B.1/15
C.1/13
D.1/10
Answer: C.1/13
Explanation: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1
Probability of selecting the next shoe (out of 13 available) having the same color = 1/13 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
C is the correct answer.
Question: Find the area of a parallelogram with base 20 cm and height 16 cm?
A.198 cm2
B.320 cm2
C.279 cm2
D.128 cm2
Answer: B.320 cm2
Explanation: Area of a parallelogram
= base * height
= 20 * 16 = 320 cm2
Answer:B
Question: five points lie on the circumference of a ellipse. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
A.4
B.15
C.6
D.5
Answer: D.5
Explanation: Number of triangles can be formed out of 6 points= 5C3=10
Number of quadrilaterals can be formed out of 6 points= 5C4=5
10-5=5.
Answer=D
Question: How many five letter combinations can be formed using the letters of the word CARTS?
A.12
B.20
C.60
D.120
Answer: D.120
Explanation: The number of letters in the given word is four.
The number of five letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 * 1= 120.
Answer: D
Question: If Carol invested Rs. 2955 at 84 to obtain an income of Rs. 180, calculate the dividend from Carol's stock.
A.6.9
B.4.4
C.5.1
D.4
Answer: C.5.1
Explanation: By investing Rs.2955, income = Rs.180
By investing Rs.84, income = 180Ã—84/2955=5.1
ie, dividend = 5.1%
Answer is C.