mathewhe/aqua_rat huggingface dataset:
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1881, What is the value of n?
(A) 22
(B) 38
(C) 114
(D) 122
(E) 672
Rationale: Factorise 1881.. 3*11*57..
So n has to be a multiple of largest prime number,61..
So n=2*57=114..
Ans :C
Answer: (C) 114
Question: Find the value of (X) in the given equation ?
35% of 1500 + X = 45% of 4200 – 320
(A) ANSWER: 1049
(B) ANSWER: 1048
(C) ANSWER: 1041
(D) ANSWER: 1045
(E) ANSWER: 10412
Rationale: Explanation:
35% of 1500 + X = 45% of 4200 – 320
(35/100 * 1500) + X = (45/100 * 4200) – 320
525 + X = 1890 – 320
X = 1890 – 320 – 525
X = 1890 – 845
X = 1045
ANSWER:D
Answer: (D) ANSWER: 1045
Question: Mike started a business with Rs.45000. After 3 months John joined him with a capital of Rs. 60000. After another 6 months, Tom joined them with a capital of Rs.90000. At the end of the yr, they made a profit of Rs.20000. What would be Tom share in it?
(A) Rs. 2000
(B) Rs. 2500
(C) Rs. 3500
(D) Rs. 4000
(E) Rs. 5000
Rationale: Just take care of the months of investment, rest all will be simple.
Yogesh:Pranab:Atul = 45000*12:60000*9:90000*3 = 2:2:1
Atul's share = Rs. 20000 * (1/5) = Rs. 4000
(D)
Answer: (D) Rs. 4000
Question: Ram goes to market with a speed of 3km/h and comes back home with a speed of 2km/h. If he takes 5 hours in all, find the distance between home and market.
(A) 8 km
(B) 4 km
(C) 6 km
(D) 5 km
(E) 7 km
Rationale: Let the required distance be x km. Then time to go to the market =x/3 hrs. Time taken to go come back=x/2 hrs. Total time taken = (x/3+x/2) hrs. = 5x/6 Here 5x/6 =5, ie) x=6 Hence the distance between home and market = 6 km Answer :C
Answer: (C) 6 km
Question: A grocer has a sale of Rs. 5255, Rs. 5840, Rs. 5921, Rs. 6022 and Rs. 6499 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5500?
(A) 3463
(B) 4463
(C) 5463
(D) 4063
(E) 5063
Rationale: Total sale for 5 months = Rs. (5255 + 5840 + 5921 + 6022 + 6499) = Rs. 29537.
Required sale = Rs. [ (5500 x 6) - 29537 ]
= Rs. (33000 - 29537)
= Rs. 3463.
ANSWER:B
Answer: (B) 4463
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 9 sec
(B) 6 sec
(C) 8 sec
(D) 10 sec
(E) 11 sec
Rationale: T = 60/36 * 18/5 = 6 sec
ANSWER B
Answer: (B) 6 sec
Question: An athlete runs 200 meters race in 24sec. His speed is?
(A) 20km/hr
(B) 15km/hr
(C) 30km/hr
(D) 25km/hr
(E) 40km/hr
Rationale: speed = 200/24 = 25/3 m/sec
= 25/3 * 18/3 km/hr = 30km/hr
Answer is C
Answer: (C) 30km/hr
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 6 on the two dice?
(A) 5/9
(B) 5/12
(C) 7/12
(D) 11/18
(E) 19/36
Rationale: There are 36 possible outcomes for two dice.
The number of outcomes with an even number on the first die is 3*6=18.
The number of outcomes with a sum of 6 is 5.
We need to subtract the outcomes that have both an even number on the first die and a sum of 6 because we have counted those outcomes twice. This number of outcomes is 2.
The number of outcomes with either an even number on the first die or a sum of 6 is 18+5-2=21.
The probability is 21/36=7/12.
The answer is C.
Answer: (C) 7/12
Question: If 16% of 40% of a number is 6, then the number is
(A) 200
(B) 225
(C) 93.75
(D) 320
(E) None of these
Rationale: Explanation:
Let 16/100×40/100×a=6
a = 6×100×100/16×40=93.75
Correct Option: C
Answer: (C) 93.75
Question: How much 60% of 50 is greater than 40% of 30?
(A) 18
(B) 55
(C) 33
(D) 22
(E) 11
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Answer: (A) 18
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 22% vinegar, dressing P comprises what percentage of the new dressing?
(A) 35%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.22
0.2x = 0.12
x = 0.6 = 60%
The answer is D.
Answer: (D) 60%
Question: For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If p is the smallest prime factor of h(100) +2(100)+1, then p is?
(A) between 1 and 20
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) 1
Rationale: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 100. So h(100)+2(100)+1 will have 1 in the units digit so smallest prime factor is 1.
Answer: E
Answer: (E) 1
Question: A computer factory produces 4200 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
(A) 2.25
(B) 3.125.
(C) 4.5
(D) 5.225
(E) 6.25
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 4200/( 28*24*2) = 3.125
Answer B
Answer: (B) 3.125.
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is?
.
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: 72 x 1 = 72
72 x 2 = 144
14^4=12^2
Largest possible which can divide 12 is 12
Answer = B
Answer: (B) 12
Question: In a mixture of 13 litres, the ratio of milk and water is 3 : 2. If 3 liters of this mixture is replaced by 3 liters of milk, then what will be the ratio of milk and water in the newly formed mixture?
(A) 9 : 1
(B) 9 : 2
(C) 9 : 7
(D) 9 : 4
(E) 9 : 3
Rationale: Given: Total quantity of mixture = 13 liters
3 litres of mixture is removed from the container – So, let's forget this altogether!
Now, you are left with only 10 litres of mixture in 3:2 ratio.
Milk in 10 litres mix = 10 x	3	= 6 litres
(2 + 3)
Water in 10 litres mix = 10 x	2	= 4 litres
(2 + 3)
We add 3 litres milk to this.
So, milk in new mix is = 6 liters + 3 litres = 9 litres
Water= 4 litres
Ratio of milk : water = 9 : 4
Correct option: D
Answer: (D) 9 : 4
Question: A circular mat with diameter 7 inches is placed on a square tabletop, each of whose sides is 10 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 2/6
(B) 3/9
(C) 1/6
(D) 3/2
(E) 1/7
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (22/7)(7)(7)
Area of the Table = (10)(10)
So the quick way to estimate is looking at the fraction like this:154/100 nearest to 3/2
Answer: D
Answer: (D) 3/2
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/115
(B) 2/115
(C) 1/216
(D) 1/213
(E) 1/215
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and further to $400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 12%
(B) 12.5%
(C) 6.67%
(D) 6.25%
(E) 8.33%
Rationale: Answer
Initial amount invested = $ X
Amount at the end of year 3 = $ 300
Amount at the end of year 8 (another 5 years) = $ 400
Therefore, the interest earned for the 5 year period between the 3rd year and 8th year = $400 - $300 = $100
As the simple interest earned for a period of 5 years is $ 100, interest earned per year = $20.
Therefore, interest earned for 3 years = 3 * 20 = $ 60.
Hence, initial amount invested X = Amount after 3 years - interest for 3 years
= 300 - 60 = $ 240.
Rate of interest = (interest per year/principal)*100 = 20/240*100 = 8.33%
choice is (E)
Answer: (E) 8.33%
Question: The cost of 4 bananas and 4 oranges is $36. The cost of 2 bananas and 5 oranges is $33. What is the cost of 1 orange?
(A) 2
(B) 5
(C) 4
(D) 6
(E) 5.5
Rationale: Let the cost of 1 banana = x, let the cost of 1 orange = y
4x + 4y = 36
x = (36 - 4y)/4
x = 9 - y
Again,
2x + 5y = 33
2(9 - y) + 5y = 33
18 - 2y + 5y = 33
3y = 15
y = 5
Answer: B
Answer: (B) 5
Question: A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 8 rows or 6 rows or 4 rows, then no tree will be left. Find the least number of trees required
(A) 22
(B) 60
(C) 24
(D) 76
(E) 21
Rationale: Explanation:
The least number of trees that are required = LCM(8,6,4) = 24.
Answer: C
Answer: (C) 24
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 565. What is the sum of the last 5 integers in the sequence?
(A)  585
(B)  580
(C)  575
(D)  590
(E)  565
Rationale: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+565=590
D
Answer: (D)  590
Question: (ab)x−2=(ba)x−7. What is the value of x ?
(A) 1.5
(B) 4.5
(C) 7.5
(D) 9.5
(E) 8.7
Rationale: Explanation:
(a/b)x−2=(b/a)x−7⇒(a/b)x−2=(a/b)−(x−7)⇒x−2=−(x−7)⇒x−2=−x+7⇒x−2=−x+7⇒2x=9⇒x=92=4.5
Option B
Answer: (B) 4.5
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 65.50, his capital is?
(A) 24,602
(B) 26,200
(C) 24,600
(D) 24,628
(E) 24,6012
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 65.50
32x - 31x = 6550 * 4
x = 26,200.
Answer: B
Answer: (B) 26,200
Question: The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-9), how many units is P from the y-axis?
(A) 18
(B) 12
(C) 9
(D) 4.5
(E) 3
Rationale: The x-axis is 9 units from the point P.
Thus the y-axis is 18 units from the point P.
The answer is A.
Answer: (A) 18
Question: If the price of 100 toys is 2500, then what will the price of 50 toys ?
(A) 144
(B) 1250
(C) 117
(D) 287
(E) 112
Rationale: One toy price = 2500/100 = 25
50 toy price = 50 * 25 = 1250
Answer : B
Answer: (B) 1250
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 120 more than A :
(A) 2348
(B) 3480
(C) 2767
(D) 1998
(E) 2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 120
Total earning = \inline \frac{58xy}{100} = 3480
Answer: B) Rs.3480
Answer: (B) 3480
Question: In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old?
(A) 7/8
(B) 14/15
(C) 29/30
(D) 44/45
(E) 131/135
Rationale: The number of people younger than 70 years old is 2700-900 = 1800
The number of females older than 70 years old is 0.6*1200 = 720
The number of people who are either female or younger than 70 is 1800+720 = 2520.
P(a person is younger than 70 or male) = 2520/2700 = 14/15
The answer is B.
Answer: (B) 14/15
Question: On a sum of money, the S.I. for 2 years is $600, while the C.I. is $615, the rate of interest being the same in both the cases. The rate of interest is?
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: Difference in C.I. and S.I for 2 years = $615 - $600 = $15
S.I for one year = $300
S.I. on $300 for 1 year = $15
Rate = (100 * 15)/(300) = 5%
The answer is B.
Answer: (B) 5%
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
ANSWER:B
Answer: (B) 4
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 22
(B) 37
(C) 48
(D) 266
(E) 121
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Answer: (C) 48
Question: The sum of the first 80 positive even integers is 6480. What is the sum of the first 80 odd integers?
(A) 6200
(B) 6300
(C) 6400
(D) 6500
(E) 6600
Rationale: Sum of first n even numbers = n(n+1) =6480
Sum of first n odd numbers = n^2 = 80*80 = 6400 (here n=80)
Answer : C
Answer: (C) 6400
Question: The food in a camp lasts for 20 men for 40 days. If ten more men join, how many days will the food last?
(A) 40 days
(B) 20 days
(C) 30 days
(D) 50 days
(E) 45 days
Rationale: one man can consume the same food in 20*40 = 800 days.
10 more men join, the total number of men = 20
The number of days the food will last = 800/20 = 40 days.
ANSWER:A
Answer: (A) 40 days
Question: A trouser in bazaar was marked down 40% the first week and another 10% the next week. What percent of the regular price was the final cost of the trouser after the two markdowns?
(A) 30%
(B) 36%
(C) 40%
(D) 50%
(E) 54%
Rationale: If the price of the trouser is 100, and it is marked down by 40% and then by 10% or charged 60% of the price first and 90% of the price of reduced price, the final price is :-
100*60*90/10000= 54
54% is the final price of old price.
E is the answer
Answer: (E) 54%
Question: Evaluate 4.3*4.3*4.3+1/4.3*4.3-4.3+1
(A) 14.3
(B) 52.3
(C) 5.3
(D) 42.3
(E) 32.3
Rationale: Given Expression = a3+b3 /a2-ab+b2 =(a+b)
= (4.3+1)= 5.3
ANSWER:C
Answer: (C) 5.3
Question: Find the odd man out. 9, 16, 36, 121, 169, 225, 361, 400, 440
(A) 169
(B) 225
(C) 361
(D) 440
(E) 400
Rationale: Explanation :
Each of the given numbers except 440 is a perfect square
Answer : Option D
Answer: (D) 440
Question: The compounded ratio of (2 : 3), (6: 11) and (11 :2) is
(A) 2:0
(B) 2:1
(C) 2:9
(D) 2:2
(E) 2:5
Rationale: Answer: B) 2:1
Answer: (B) 2:1
Question: A worker is paid x rupees for painting every 6 metres of a wall and y rupees for painting every extra metre. During one week, he painted 6 metres on Monday, 7 metres on Tuesday, 8 metres on Wednesday, 9 metres on Thursday and 10 metres on Friday. What is his average daily earning rupees for the five day week?
(A) x + (8/5)y
(B) x+2y
(C) 10x + (8/5)y
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + y)
On Wednesday, the payment = Rs (x + 2y)
On Thursday, the payment = Rs (x + 3y)
On Friday, the payment = Rs (x + 4y)
Average daily earning during the five-day week = (5x + 10y)/5
= x +2y
Answer :B
Answer: (B) x+2y
Question: A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
(A) 20 days
(B) 10 days
(C) 30 days
(D) 40 days
(E) 50 days
Rationale: A
20 days
Time taken by A to finish the work = XY/(Y-X)
10 x 20 / (20-10)
200/10
20 days
Answer: (A) 20 days
Question: An odd integer between 600 and 800 is divisible by 7 and also divisible by 9. What is the sum
of its digits?
(A) 7
(B) 12
(C) 18
(D) 21
(E) 27
Rationale: The integer is a multiple of 63. There are three such multiples between 600 and 800. They are
630, 693, and 756. Only 693 is odd.
correct answer C
Answer: (C) 18
Question: If k is a positive integer, which of the following must be divisible by 26?
(A)  (k – 4)(k)(k + 3)(k + 7)
(B)  (k – 4)(k – 2)(k + 3)(k + 5)
(C)  (k – 2)(k + 3)(k + 5)(k + 6)
(D)  (k + 1)(k + 3)(k + 5)(k + 7)
(E)  (k – 3)(k + 1)(k + 4)(k + 6)
Rationale: 24=8*3.
Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.
Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.
So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.
Answer:D.
Answer: (D)  (k + 1)(k + 3)(k + 5)(k + 7)
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
(A) 50.5 kg
(B) 56.5 kg
(C) 60.9 kg
(D) 66.5 kg
(E) 75.5 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: (D) 66.5 kg
Question: 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 9 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(A) 30
(B) 20
(C) 19
(D) 29
(E) 39
Rationale: Let 1Man does 1unit/hr of work
15M in 21 days of 8hrs will do (15*21*8) units
3W = 2M
1W=(2/3)units/hr
21W with 9hrs a day will take (15*21*8)/(21*9*(2/3)) days
=> 20 Days
ANSWER:B
Answer: (B) 20
Question: In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1140
(B) 1160
(C) 1180
(D) 1200
(E) 1040
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 70 * 12 = 840.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 840 + 200 = 1040.
E)
Answer: (E) 1040
Question: Average of five numbers is 8, and the sum of three of the numbers is 21, what is the average of the other 2 numbers?
(A) 9.1
(B) 5.2
(C) 9.5
(D) 7.8
(E) 5.6
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=8a+b+c=21(21+d+e)/5=821+d+e=40d+e=19average=19/2=9.5Ans C
Answer: (C) 9.5
Question: We had $1400 left after spending 30% of the money that we took for shopping. How much money did we start with?
(A) $2000
(B) $2100
(C) $2200
(D) $2300
(E) $2400
Rationale: Let x be the amount of money we started with.
0.7x = 1400
x = 2000
The answer is A.
Answer: (A) $2000
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Menâ€™s wages are?
(A) Rs.6
(B) Rs.6.5
(C) Rs.8
(D) Rs.5
(E) Rs.2
Rationale: Answer: Option A
5M = xW = 8b
5M + xW + 8b ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: (A) Rs.6
Question: If A : B = 4 : 9 and B : C = 5 : 9 then A : B : C is :
(A) 20 : 35 : 63
(B) 35 : 36 : 63
(C) 30 : 35 : 65
(D) 20 :45: 81
(E) None of these
Rationale: Expl : A : B = 4 : 9
B : C = 5 :9 = 5*9/5 : 9 *9/5 = 9 : 81/5
A : B : C = 4 : 9 : 81/5 = 20 : 45 : 81
Answer: D
Answer: (D) 20 :45: 81
Question: Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls.
(A) 35.7%
(B) 25.7%
(C) 15.7%
(D) 55.7%
(E) 45.7%
Rationale: Let the cost price of 1 balls be Rs 1
Cost of 14 balls= Rs 14
Selling price of 14 balls = 9
Gain/loss = 14 - 9 = 5
%=5/14âˆ—100= 35.7
Answer: A
Answer: (A) 35.7%
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 11/21
(C) 2/7
(D) 5/7
(E) 13/21
Rationale: 5c2/7c2=10/21
ANSWER:A
Answer: (A) 10/21
Question: The average marks of a class of 26 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.2
(B) 59.5
(C) 52.8
(D) 52.5
(E) 53.1
Rationale: Sum of the marks for the class of 26 students = 26 * 40 = 1040
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 76 students =
1040 + 3000 = 4040
Average marks of all the students = 4040/76
= 53.15
Answer:E
Answer: (E) 53.1
Question: If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 =
(A)  1
(B)  7/2
(C)  17/5
(D)  18/5
(E)  4
Rationale: 2*(m+2m = 5) equals 2m+4n=10
2m+4n=10
- 2m + n= 7
= 3n=3
Therefore n = 1
Plug and solve...
2m + 1 = 7
2m=6
m=3
(6+1)/2= 7/2
B
Answer: (B)  7/2
Question: If an object travels 80 feet in 4 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 7.25
(B) 9.47
(C) 11.58
(D) 13.64
(E) 15.92
Rationale: 80 feet/4 seconds = 20 feet/second
(20 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 13.64 miles/hour (approximately)
The answer is D.
Answer: (D) 13.64
Question: A box contains 35 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first hundred natural numbers. What is the chance that it is a multiple of either 11 or 15?
(A) 5/20
(B) 3/20
(C) 7/20
(D) 11/20
(E) 9/20
Rationale: The probability that the number is a multiple of 11 is 9/100. (Since 11*9 = 99).
Similarly the probability that the number is a multiple of 15 is 6/100. {Since 15*6 =
90).
Neither 11 nor 15 has common multiple from 1 to 100. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 11 or 15 is (9+6)/100 = 3/20.
ANSWER:B
Answer: (B) 3/20
Question: A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
(A) A)100
(B) B)102
(C) C)108
(D) D)110
(E) E)120
Rationale: The girl can select one jeans in 10 ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 10 * 12 = 120 ways.
E
Answer: (E) E)120
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is
(A) 4 hours
(B) 4 hours 30 minutes
(C) 4 hours 45 minutes
(D) 5 hours
(E) None of these
Rationale: Explanation:
Time taken in walking both ways = 7 hours 45 minutes --------(i)
Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)
By equation (ii)*2 -(i), we have
Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45
Answer: C
Answer: (C) 4 hours 45 minutes
Question: If x^2+(1/x^2)=9, x^4+(1/x^4)=?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 79
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=9^2-2=79.
Thus, the answer is E.
Answer: (E) 79
Question: There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: total persons=100
no.peoplehaving phone=70
no.people having car=75
no.people having house=80
no.people got marriage=85
people got married,having car,house,phone=70
ANSWER:C
Answer: (C) 70
Question: A person purchased a TV set for Rs. 15000 and a DVD player for Rs. 6000. He sold both the items together for Rs. 31500. What percentage of profit did he make?
(A) 48%
(B) 50%
(C) 40%
(D) 45%
(E) 20%
Rationale: The total CP = Rs. 15000 + Rs. 6000
= Rs. 21000 and SP
= Rs. 31500
Profit(%)
= (31500 - 21000)/21000 * 100
= 50%
Answer: B
Answer: (B) 50%
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 56
(B) 50
(C) 72
(D) 27
(E) 25
Rationale: Speed of the train relative to man = (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45
==> x = 50 km/hr.
Answer: B
Answer: (B) 50