RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.82 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
A.9%
B.10%
C.11%
D.12%
Answer: D.12%
Explanation: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.82
9.9 - 45x + 36x = 8.82
9x = 1.08
x = 0.12
The answer is D.
Question: If 2 < x < 7 and 8 << y < 9, then the lowest possible value for xy is
A.between 60 and 70
B.between 0 and 60
C.0
D.between 0 and -70
Answer: B.between 0 and 60
Explanation: If 2 < x < 7 and 8 << y < 9,
Say y = 8.9 (8<<y<9)
x = 6
So xy =53.4 which is less than 60.
Answer is B.
Question: Victor gets 92 % marks in examinations. If these are 460 marks, find the maximum marks.
A.334
B.500
C.376
D.288
Answer: B.500
Explanation: Let the maximum marks be m
Then 92 % of m = 460
⇒ 92/100 × m = 460
⇒ m = (460 × 100)/92
⇒ m = 46000/92
⇒ m = 500
Therefore, maximum marks in the examinations are 500.
Answer:B
Question: If y exceeds x by 25%, then x is less than y by?
A.20%
B.16 3/3%
C.16 2/3%
D.12 2/3%
Answer: A.20%
Explanation: X=100	y=125
125------25
100-------? => 20%
Answer:A
Question: From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?
A.1/10
B.4/9
C.1/2
D.3/5
Answer: D.3/5
Explanation: prob reqd= 1- probab of not having eq numbers
prob of not having eq no's is = prob of having 3 Boys and 1 girl or prob of having 3 girls and 1 boy
=(1* 3/15) +(3/15 * 1)=2/5
reqd prob= 1-2/5=3/5
Answer:D
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
A.2 2/3 days
B.2 8/3 days
C.2 23/3 days
D.8 2/3 days
Answer: A.2 2/3 days
Explanation: Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.
The number of days required = 8/3
= 2 2/3 days.
Answer: A
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
A.2%
B.25%
C.22%
D.29%
Answer: B.25%
Explanation: 800 --- 200
100 --- ? => 25%
Answer:B
Question: The product of all the prime numbers less than 18 is closest to which of the following powers of 10?
A.10^9
B.10^8
C.10^7
D.10^6
Answer: D.10^6
Explanation: OA: D
Question: The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
A.276
B.280
C.322
D.345
Answer: B.280
Explanation: Clearly, the numbers are (20 x 13) and (20 x 14).
Larger number = (20 x 14) = 280.
Answer: Option B
Question: Which of the following fractions Q, if written as a decimal, would have a 2 in the thousandths place ?
A. 3/11
B. 7/9
C. 1/8
D. 4/7
Answer: A. 3/11
Explanation: (A) Q=3/11 = 0.2727272727....
Answer: A
Question: Two family reunions are happening at the Park Avenue hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 70 people attend the Hall reunion, how many people attend both reunions
A. 2
B. 5
C. 10
D. 16
Answer: C. 10
Explanation: No of people in Oates reunion=40
No of people in Hall reunion=70
Attending both=x
All guests attend at least one.
Therefore, 100=40+70-(Both)
Both=10
Answer C
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
A.52:59
B.52:53
C.52:51
D.52:52
Answer: B.52:53
Explanation: Explanation:
Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer: B
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
A.650
B.656
C.756
D.760
Answer: C.756
Explanation: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 men ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 woman ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 men and 2 women ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=756
C)
Question: If 5 (A's capital) = 10 (B's capital) = 15 (C's capital). Then the ratio of their capitals is?
A.5:3:2
B.7:3:2
C.6:3:3
D.6:3:2
Answer: D.6:3:2
Explanation: 5A = 10B = 15 C
A:B:C = 1/5:1/10:1/15
= 6:3:2
Answer: D
Question: How many ways are there to arrange the letters in the word Teressa ?
A.1
B.1260
C.3780
D.7560
Answer: B.1260
Explanation: 7 total words, 2E, 2S
= 7! / 2 ! * 2! = 1260. Answer B
Question: 617+6.017+0.617+6.0017=?
A.6.2963
B.62.965
C.629.6357
D.6296.357
Answer: C.629.6357
Explanation: 617.00
6.017
0.617
6.0017
------------
629.6357
Answer is C
Question: The expression 10^13−120 is divisible by all of the following integers EXCEPT
A.2
B.13
C.4
D.8
Answer: B.13
Explanation: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (B) is correct. B
Question: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
A.55/228
B.55/228
C.55/221
D.55/212
Answer: C.55/221
Explanation: We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = \inline {\color{Black}26C_{2}} = = 325, n(B)= \inline {\color{Black}4C_{2}} = = 6 and n(A∩B) = \inline {\color{Black}2C_{2}} = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 80,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
A.2 : 3 : 4
B.3 : 2 : 4
C.6 : 2 : 1
D.6 : 4 : 7
Answer: D.6 : 4 : 7
Explanation: Sol.
A : B : C = (80000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =288 : 192 : 336 = 6: 4 : 7
Answer D
Question: . Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
A.540
B.300
C.890
D.750
Answer: A.540
Explanation: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
ANSWER A
Question: Evaluate : (2.39)(power 2) - (1.61) (power 2) / 2.39 - 1.61
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: Given Expression = a(power 2) - b(power 2) / a-b
= (a + b)(a - b) / (a-b)
= (a + b) = (2.39 + 1.61) = 4.
Answer is A.
Question: If x+|x|+y=4 and x+|y|-y=3 what is x+y=?
A.1
B.-1
C.3
D.5
Answer: C.3
Explanation: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =3
Hence answer should be C
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 757.48 = 443.095 + ?
A.870
B.790
C.680
D.770
Answer: C.680
Explanation: ? = 285 + 1895 – 755 – 745 or, ? = 680
Answer C
Question: If 522x is a 3 digit no. with as a digit x. If the no.is divisible by 6, What is the value of the digit x is?
A.1
B.6
C.4
D.7
Answer: B.6
Explanation: If a number is divisible by 6 , it must be divisible by both 2 and 3
In 522x, to this number be divisible by 2, the value of x must be even. So it can be 2,4 or 6 from given options
552x is divisible by 3, If sum of its digits is a multiple of 3.
5+5+2+x =12+x ,
If put x =2 , 12+2=14 not a multiple of 3
If put x =4 , 12+6=18 is a multiple of 3
If put x =6 , 12+2=14 not a multiple of 3
The value of x is 6.
B
Question: 4 points are marked on a straight line and another 5 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
A.91
B.105
C.196
D.2
Answer: D.2
Explanation: assuming that the top line can have either 2 points or 1 point...
4! / 1!3! - 4! / 2! 2! yields 2.
D
Question: 56, 63, 59, 11, 57, 6, 11
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
A.21
B.32
C.49
D.56
Answer: C.49
Explanation: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 6,11 ,11, 56, 57, 59,63
Median is very easy to tell - its 56. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 56? DE are already out.
Now, we have 21, 32 and 49 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 49. (Notice, if 21 is more than mean then 49 is also. If 32 is more than mean, 49 is also. )
Hence C it is!
Question: Based on this year's costs, a factory budgets P dollars for planing N new cars next year. If the average cost of building each car were to increase 50% from this year's cost, then the greatest number of cars that the factory could build next year using P dollars would be:
A.33% less than N
B.67% less than N
C.Equal to N
D.33% greater than N
Answer: A.33% less than N
Explanation: Correct answer is (A).
This year, the price of a car is price1=P/N.
If this price increases by 50% it becomes Price2=P/N*1.5
Then with P dollars, you can build P/Price2 cars i.e. P/(P/N*1.5) i.e. N/1.5 i.e. 0.67*N
Which is 33% less than N.
Question: A and B walk around a circular track. A and B walk at a speed of 4 rounds per hour and 5 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10.30 a.m.?
A.10
B.20
C.22
D.9
Answer: C.22
Explanation: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)
= 4 + 5 = 9 rounds per hour
=> They cross each other 9 times in 1 hour and 4 times in 1/2 hour
Time duration from 8 am to 10.30 am =2.5 hour
Hence they cross each other 22 times before 10.30 am
Answer : C
Question: The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 13 days, how large is the colony today?
A.512
B.1024
C.768
D.2048
Answer: B.1024
Explanation: 9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024
Ans:B
Question: In a certain pond, 35 fish were caught, tagged, and returned to the pond. A few days later, 35 fish were caught again, of which 2 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`s the approximate number of fish in the pond?
A.400
B.625
C.875
D.2500
Answer: C.875
Explanation: If x is total number of fish in the pond :
4 = 35/x * 100
=> x = 875
So answer is C
Question: What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it?
A.600
B.602
C.604
D.606
Answer: B.602
Explanation: The nth term is 2+3*(n-1).
The 201st term is 2 + 3(200) = 602
The answer is B.
Question: For all integers a and b, a%b = (a + b)(a - b). If 6%x = 11, then which of the following could be a value of x?
A.-5
B.-3
C.2
D.3
Answer: A.-5
Explanation: 6%x = (6+x)(6-x)
36-x^2 = 11
x^2 = 25
x=-5,5
Ans: A
Question: If two projectiles are launched at the same moment from 1182 km apart and travel directly towards each other at 460 km per hour and 525 km per hour respectively, how many minutes will it take for them to meet?
A.68
B.72
C.76
D.80
Answer: B.72
Explanation: The projectiles travel a total of 985 km per hour.
The time to meet is 1182/985=1.2 hours = 72 minutes
The answer is B.
Question: In how many different ways can the letters of the word "CLAIM" be rearrangement?
A.100
B.120
C.140
D.150
Answer: B.120
Explanation: The total number of arrangements is
5P5 = 5! = 120
B)
Question: The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 then find the perimeter of the rectangle.
A.77 cm
B.88 cm
C.64 cm
D.11 cm
Answer: C.64 cm
Explanation: Let Breadth = x cm,
then, Length = 3x cm
x2+(3x)2=(810−−√)2=>10x2=640=>x=8
x2+(3x)2=(810)2=>10x2=640=>x=8
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm
Answer:C
Question: The average (arithmetic mean) monthly income of four workers is $2,600. After one worker’s income increases by 20 percent the new average income is $2,800. What was the original income of the worker whose monthly income increased?
A.$4,000
B.$4,500
C.$4,100
D.$4,300
Answer: A.$4,000
Explanation: Increase in total income was 200*4=$800, we know that this increase was 20% (1/5th) of the workers original income, thus his/her original income was 800*5=$4,000.
Answer: A
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.11 1/2 min
B.11 1/4 min
C.11 2/4 min
D.11 1/5 min
Answer: B.11 1/4 min
Explanation: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 2, 4, 7, and 10
A.16
B.15
C.18
D.19
Answer: B.15
Explanation: A. 13 (can be weighed by keeping weights of 10, 2 and 4 )
B. 15 (cannot be weighed)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 19(can be weighed by keeping weights of 10, 2 and 7 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
B
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.118 km
B.162 km
C.1767 km
D.1887 km
Answer: B.162 km
Explanation: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
A.27
B.76
C.82
D.80
Answer: D.80
Explanation: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240
= 80
Answer:D
Question: Jack splits his bucket of apples into 5 groups of equal size, but has 2 left over. The next day, he repeats the process with a bucket that contains exactly 3 times as many apples as the day before. How many does he have left over this time?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Set x = to number of apples in his basket, and y to be the number of apples per group.
x = 5*y +2.
3x = 15*y+6
3x = 3*5*y + 6
3x = 5(3(y+1))+1
Remainder is then 1, so option B.
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 9 m x 6 m x 22.5 cm?
A.6400
B.6410
C.6440
D.7200
Answer: D.7200
Explanation: Number of bricks = Volume of Wall/Volume of Bricks
=900x600x22.5/25x11.25x6= = 7200
answer :D
Question: The price of sugar is increased by 8%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
A.(800/108) %
B.(107/100) %
C.(100/107)%
D.(7/100)%
Answer: A.(800/108) %
Explanation: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $108.
We want the spendings to remain at $100.
(New consumption)*108 = 100 --> (New consumption) = 100/108 kg.
Percent decrease = Change/Original *100 = (1 - 100/108)/1*100 = 800/108%.
Answer: A.
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
A.$146.6
B.$120
C.$180
D.$220
Answer: A.$146.6
Explanation: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.15E ==> 11A =220 +11.5E -------(2)
Substituting (1) in (2):
13E = 220+11.5E ==>1.5E= 220 or E =440/3 =146.6
A
Question: Eleven books consisting of 2 financial management, 4 marketing management and 5 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
A.1/1455
B.1/1355
C.1/2255
D.1/1155
Answer: D.1/1155
Explanation: Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer
D
Question: P and Q invested in a business. The profit earned was divided in the ratio 3 : 5. If P invested Rs 12000, the amount invested by Q is
A.30000
B.50000
C.40000
D.20000
Answer: A.30000
Explanation: Let the amount invested by Q = q
12000:q=3:5
⇒12000×5=3q
⇒q=(12000×5)/3=30000
Answer is A
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
A.1 hour
B.2 hour
C.3 hour
D.4 hour
Answer: A.1 hour
Explanation: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Option A
Question: What is the value of (P + Q)/(P - Q) if P/Q is 6?
A.4/3
B.2/3
C.2/6
D.7/5
Answer: D.7/5
Explanation: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (6 + 1)/(6 - 1)
= 7/5
ANSWER:D
Question: Two brothers took the GMAT exam, the higher score is R and the lower one is S. If the difference between the two scores is equal to their average, what is the value of S/R ?
A.3
B.2
C.1/2
D.1/3
Answer: D.1/3
Explanation: Answer is D : 1/3
R - S = (R + S)/2
Solving for S/R = 1/3
D
Question: If x and y are integers and x + y = 8, which of the following must be true?
A.x and y are consecutive integers.
B.Both x and y are even.
C.If x > 0, then y < 0.
D.If x < 0, then y > 0.
Answer: D.If x < 0, then y > 0.
Explanation: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option D is right could you explain
Question: if 4y = 12x + 20,4x + 2y = 20 ,what is the value of y?
A.8.5
B.6
C.7
D.8
Answer: D.8
Explanation: solution:
I---> y = 3x + 5
sub in II
4x + 2(3x + 5) = 20
10x = 10
x = 1
sub x=1 in other equation
4y = 12(1) + 20
y = 8
answer is D
Question: The radius of a wheel is 20 cm. What is the distance covered by the wheel in making 500 resolutions?
A.708 m
B.704 m
C.314.3 m
D.714 m
Answer: C.314.3 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 20 = 31428.5 cm
= 314.3 m
Answer:C
Question: Half of 4 percent written as decimal is
A.0.02
B.0.5
C.0.05
D.0.005
Answer: A.0.02
Explanation: Explanation:
It will be 1/2(4%) = 1/2(4/100) = 4/200 = 0.02
Answer: Option A
Question: The pages of a report are numbered consecutively from 1 to 6. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =
A.4
B.5
C.6
D.3
Answer: A.4
Explanation: sum of the first few numbers =1+2+3+4 =10
sum of the last few = 5 +6 =11 page no.4 answer .A
Question: Kelvin earns $60 a week from his job. His income increased and now makes $70 a week. What is the percent increase?
A.16.66%
B.20%
C.22.5%
D.23%
Answer: A.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
A
Question: Suraj has a certain average of runs for 16 innings. In the 17th innings he scores 112 runs thereby increasing his average by 6 runs. What is his average after the 17th innings?
A.18
B.25
C.16
D.72
Answer: C.16
Explanation: To improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings.
Thus, the average after the 17th innings
= 112 - 96 = 16.
ANSWER:C
Question: In a group of ducks and cows, the total number of legs are 8 more than twice the no. of heads. Find the total no.of buffaloes.
A.5
B.4
C.6
D.3
Answer: B.4
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 8
=> 2x = 8 => x = 4
B
Question: Agnes has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
A. 32
B. 30
C. 29
D. 28
Answer: A. 32
Explanation: 5v + 10y = 460
v > y
Pick an easy number to work with.
suppose v=30.
Then you have 150.
You need another 310 and that means you need y=31 which is greater than v.
Therefore, v > 30.
The only answer choice where v > 30 is if v = 32.
A is the answer.
Question: If a positive integer n is divisible by both 3 and 5, then n must also be divisible by which of the following?
I. 15
II. 8
III. 45
A.None
B.I only
C.II only
D.I and II
Answer: B.I only
Explanation: A multiple of 3 and 5 is also a multiple of 15, but not necessarily a multiple of 8 or 45.
The answer is B.
Question: 6 highschool boys gather at the gym for a game of mini-volleyball. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?
A.27
B.51
C.90
D.45
Answer: D.45
Explanation: Arrange the 6 boys in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (D)
You get 6!/(2! * 2! * 2!) * 2!
Answer : D
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.1000
B.1055
C.1065
D.1075
Answer: B.1055
Explanation: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
B)
Question: Find the total number of prime factors in the expression (4)11 x (7)5 x (11)2.
A.22
B.29
C.19
D.5
Answer: B.29
Explanation: (4)11x (7)5 x (11)2 = (2 x 2)11 x (7)5 x (11)2 = 211 x 211 x75x 112
= 222 x 75 x112
Total number of prime factors = (22 + 5 + 2)
= 29.
ANSWER B 29