mathewhe/aqua_rat huggingface dataset:
Question: A trader sold an article on a certain price with 20% profit. If he sold double of previous selling price then find its profit %
(A) 140%
(B) 120%
(C) 100%
(D) 90%
(E) 80%
Rationale: let cost price = 100%
selling price = 120%
new s.p. = 240%
p% = 240-100 = 140%
Answer is A
Answer: (A) 140%
Question: Efrida and Frazer who live 12 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: It's a simple geometry problem. Look at the diagram below:
Answer: D.
Answer: (D) 10
Question: A contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose. After 120 days, he finds that only 240 meters of the tunnel is complete. How many more men should be employ in order to complete the work in time?
(A) 75 men
(B) 80 men
(C) 70 men
(D) 60 men
(E) 50 men
Rationale: In 120days, only 240m of the tunnel is constructed by 50 men.
The remaining 120days, 480m of the tunnel can be constructed by 120 men.
Additional number of men required = 120 - 50 = 70 men.
ANSWER:C
Answer: (C) 70 men
Question: If 9 - 4/X = 7 + 8/X, then X =
(A) 15
(B) 6
(C) 1
(D) 5
(E) 12
Rationale: We're given the equation 9 - 4/X = 7 + 8/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we have to multiple 2 of the numbers to give them that denominator...
9X - 4X/X = 7X + 8X/X
We can then eliminate that denominator, which gives us....
9X - 4 = 7X + 8
12 = 2X
Both 2X and 12 have a common denominator of 2, so we divide both sides by 2 for our final answer...
6 = X
B
Answer: (B) 6
Question: A person travelled from his house to office at 35km/hr and office to house at 65km/hr. Then find the average speed?
(A) 30km/hr
(B) 45.5km/hr
(C) 48km/hr
(D) 50.5km/hr
(E) 62km/hr
Rationale: Average speed = (2*35*65)/(35+65)= 45.5km/hrAnswer is B
Answer: (B) 45.5km/hr
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 18 seconds. The length of each train is:
(A) 25m
(B) 50m
(C) 72m
(D) 80m
(E) None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 18 secs the total distance traveled is 18x25/9 = 50 m.
Therefore the length of each train is = 50/2 = 25 m.
Answer A
Answer: (A) 25m
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 5 as remainder
(A) 1637
(B) 1456
(C) 1567
(D) 1678
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 5
5x = 1360
x = 272
Large number = 272+1365 = 1637
A
Answer: (A) 1637
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3000
(B) 4000.75
(C) 3587.5
(D) 3500
(E) 5020.75
Rationale: I = (8200 * 2.5 * 17.5)/100 = (8200 * 5 * 35)/(100 * 2 * 2) = Rs. 3587.50
ANSWER C
Answer: (C) 3587.5
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 15000
(B) 15002
(C) 26879
(D) 26992
(E) 12681
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x
= Rs. 1.08x = 18000 - 10/100(18000)
= 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A
Answer: (A) 15000
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 27
(B) 21
(C) 30
(D) 27
(E) 176
Rationale: 20 + 24 + 8 * 2
= 60/2
= 30
Answer:C
Answer: (C) 30
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $849,000 invested in preferred stocks, what is the total amount of money invested in the fund?
(A) $1,974,000
(B) $2,538,000
(C) $3,264,000
(D) $3,826,000
(E) $4,245,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 849---
Fund = 5 * 849---
Here, we can avoid the math and simply look at 5 * 9 -> 45. Only option E has 45 in it.
Answer (E).
Answer: (E) $4,245,000
Question: The average of first five multiples of 3 is?
(A) 6
(B) 8
(C) 9
(D) 5
(E) 7
Rationale: Average = 3(1 + 2 + 3 + 4 + 5)/5
= 45/5
= 9.
Answer:B
Answer: (B) 8
Question: A bowl of fruit contains 14 apples and 23 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples?
(A) 3
(B) 6
(C) 14
(D) 17
(E) 20
Rationale: Number of apples = 14
number of oranges = 23
let number of oranges that must be removed so that 70% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 14+(23-x) = 37-x
14/(37-x) = 7/10
=>20 = 37-x
=>x= 17
Answer D
Answer: (D) 17
Question: The milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)
(A) 100
(B) 250
(C) 750
(D) 5437.5
(E) 5635.5
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 58*25*1/2=725 feet^3 of milk must be removed, which equals to 725*7.5=5437.5 gallons.
Answer: D.
Answer: (D) 5437.5
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice.
(A) 25
(B) 34
(C) 50
(D) 67
(E) 100
Rationale: A =25
1 oz concentrate + 3 oz ofwater = 4 oz jucie
300 oz concentrate +900 oz of waer = 1200 oz juice
no of cans==300/12=25
Ratio of juice to water ===> 1:3
total 200*6 ounces
12 ounce juice cans ==> 1200/12 == 100*1/4 (ratio of jiuce to total) == 25
Answer: (A) 25
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 70% profit?
(A) 220
(B) 1088
(C) 960
(D) 780
(E) 400
Rationale: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 170% of Rs. 640 = 170/100 * 640 = Rs. 1088.
B
Answer: (B) 1088
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 390 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 59
(C) 68
(D) 88
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 390
Breadth = 19.5 feet
Area to be fenced = 2B + L = 2 (19.5) + 20 = 59 feet answer : B
Answer: (B) 59
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,15
(A) 9700
(B) 9710
(C) 9720
(D) 9730
(E) 9740
Rationale: Explanation:
LCM of 27-18-12-15 is 540.
After dividing 9999 by 540 we get 279 remainder.
So answer will be 9999-279 = 9720
Option C
Answer: (C) 9720
Question: If x and y are integers and x=50y + 69, which of the following must be odd?
(A) xy
(B) x + y
(C) x + 2y
(D) 3x-1
(E) 3x+1
Rationale: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
C: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
Answer C
Answer: (C) x + 2y
Question: If A speaks the truth 30% of the times, B speaks the truth 40% of the times. What is the probability that at least one will tell the truth
(A) 0.58
(B) 0.9
(C) 1.9
(D) 2.2
(E) 2.3
Rationale: probability of A speaks truth p(A)=3/10;false=7/10
probability of B speaks truth p(B)=4/10;false=6/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(7/10)*(6/10)]=1-42/100=1-0.42=0.58
ANSWER:A
Answer: (A) 0.58
Question: If x + |x| + y = 7 and x + |y| - y =6 , then x + y =
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: If x + |x| + y = 7 and x + |y| - y =6 , then x + y =
can be done in 2.3 mins :
there are 4 cases to be tested :
1) x is -ve and y is -ve
substituting in the equation , we get x-x+y=7 and x-y-y=6 solve for x and y we get x=20 and y=7 , so x+y=27 REJECT
2)x is +ve and y is +ve
substitute in the equation, we ger x+x+y=7 and x+y-y=6 solve for x and y we get x=6 and y=-5 ,therefore x+y=1 not on list so REJECT
3) x is -ve and y is +ve
substitute , we get x-x=y=7 and x+y-y=6 solve fo x and y we get x=6 and y=7, x+y=13 not on list so REJECT
4) x is +ve and y is -ve
substitute , we get x+x=y=7 and x-y-y=6 solve for x and y , we get x=4 and y= -1 ,x+y=3 , ANSWER CHOICE ANSWER A
Answer: (A) 3
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
(A) 20
(B) 200
(C) 300
(D) 400
(E) 140
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5300
[4L - 40] = 5300 / 26.50 = 200
4L = 240
L = 240/4= 60 meters. Answer: B
Answer: (B) 200
Question: A bakery opened yesterday with its daily supply of 60 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  6
Rationale: answer is E ...6 dozens ....
half sold by noon --> 30 dozens (30 *12 =360)
remaining --> 30 dozens i.e 360 eggs...
80% sold --> 80*360/100 =288 eggs
remaining 20 % --> 72 eggs (6 dozens ) --> answer
Answer: (E)  6
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,720, Deepak's share is:?
(A) s.8467
(B) s.8428
(C) s.8400
(D) s.8960
(E) s.8420
Rationale: Ratio of their shares
= 22500 : 35000
= 9:14
Deepak's share
= 14720 * 14/23
= Rs.8960.
Answer:D
Answer: (D) s.8960
Question: Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank
(A) 17 1/7 mins
(B) 20 mins
(C) 8 mins
(D) 9 mins
(E) none of these
Rationale: A = 20
B = 30
C = -40
LCM = 120
=> A = 6,TIMES
B = 4
C = -3
=> A+B-C
= 7
TIME TAKEN TO FILL THE TANK = 120/7 MINS = 17 1/7 MINS
ANSWER:A
Answer: (A) 17 1/7 mins
Question: A boy has 5 trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?
(A) 299
(B) 65
(C) 68
(D) 67
(E) 271
Rationale: The boy can select one trouser in 5 ways.
The boy can select one shirt in 13 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 13
= 65 ways.
Answer: B
Answer: (B) 65
Question: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following CANNOT be the difference of A and B ?
(A) 72
(B) 45
(C) 33
(D) 27
(E) 9
Rationale: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:
A = 10x + y
B = 10y + x
A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option C is not a multiple of 9.
Answer: C.
Answer: (C) 33
Question: A shopkeeper wants to make a minimum net profit of 5% on a pair of jeans she is selling, which she bought for $100. If originally, she was selling the pair at 20% gain, what is the largest discount she can allow?
(A) 12.5%
(B) 8%
(C) 8.3%
(D) 15%
(E) 4%
Rationale: A
If she bought the jeans at $100, she is currently selling them at (120/100)*100 = $120.
She wants to make a profit of 5%, which means she needs to sell them at (105/100)*100 = $105
The max discount she can allow is thus ((120-105)/120)*100 = 12.5%
Answer: (A) 12.5%
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
(A) 27 grams
(B) 28 grams
(C) 29 grams
(D) 31 grams
(E) 32 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 28 grams
28/7 = 4
C. 29 grams
29/7 = 4.142.......
D. 31 grams
31/7 = 4.428.....
E. 32 grams
32/7 = 4.571....
Hence our answer will be (B)
Answer: (B) 28 grams
Question: A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
(A) 12km
(B) 16 km
(C) 20 km
(D) 24 km
(E) None of these
Rationale: Explanation :
Let distance be D
10 = D/4 + D/6
Answer – D
Answer: (D) 24 km
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 182 cms. What was the ratio of men to women?
(A)  5:2
(B)  5:1
(C)  4:3
(D)  4:1
(E)  3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 182cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 182M)/(W+M) = 180
170W + 182M = 180W + 180M
2M = 10W
M = 5W
M/W = 5/1
The ratio of men to women is 5 to 1.
B
Answer: (B)  5:1
Question: Three distinct single-digit numbers. A,B,C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or 0 and -x if x is -ve), then the number of different possible values of abs(A+B+C) is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A,B,C may be
(1,2,4) & (4,2,1)
(1,3,9) & (9,3,1)
(2,4,8) & (8,4,2)
(4,6,9) & (9,6,4)
find abs(A+B+C) for these 8 GPs
7,13,15,19
So,we get 4 different values
ANSWER:D
Answer: (D) 4
Question: Round off 9824.119 to the nearest thousand, hundred, ten and one.Represent the result with q,r,s,t, respectively.Which of the following statements is correct?
(A) q<s<t<r
(B) s<r<t<q
(C) r<s<q<t
(D) r<q<t<s
(E) r<s<t<q
Rationale: 9824.119..
Nearest thousand 10000..q
Nearest hundred 9800..r
Nearest ten 9820..s
Nearest one 9824..t
r<s<t<q
The correct option is E
Answer: (E) r<s<t<q
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 10
(B) 18
(C) 63
(D) 36
(E) 72
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
ANSWER:D
Answer: (D) 36
Question: Evaluate: 30 - 12÷3×2 =
(A) 11
(B) 22
(C) 33
(D) 44
(E) 55
Rationale: According to order of operations, 12÷3×2 (division and multiplication) is done first from left to right
12÷3×2 = 4 × 2 = 8
Hence
30 - 12÷3×2 = 30 - 8 = 22
correct answer is B) 22
Answer: (B) 22
Question: A train running at the speed of 72 km/hr crosses a pole in 8 seconds. Find the length of the train.
(A) 150 meter
(B) 145 meter
(C) 160 meter
(D) 135 meter
(E) None of these
Rationale: Explanation:
Speed = 72*(5/18) m/sec = 20 m/sec
Length of Train(Distance) = Speed * Time
=20*8=160 meter
Option C
Answer: (C) 160 meter
Question: Last September the sales total for a certain car dealership was 400% greater than the average monthly sales total for the other 11 months. The sales total for September was approximately what percent of the year´s sales?
(A) 15 %
(B) 27%
(C) 31%
(D) 42%
(E) 75%
Rationale: 11 moth avg = x
11 month total = 11x
sept = 400% of x + x = 5x
sept/total = =5x/(11x+5x) = =31%
ANSWER:C
Answer: (C) 31%
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 360 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 600
(B) 620
(C) 500
(D) 520
(E) 720
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 360) = 2 + 2(extra)
=> 2x - 720 = x => x = 720.
ANSWER:E
Answer: (E) 720
Question: The supplementary of an angle is thrice its complimentary. Find the angle.
(A) 60
(B) 45
(C) 90
(D) 180
(E) 120
Rationale: let angle=x;
by question--
180-x=3(90-x)
x=45
ANSWER:B
Answer: (B) 45
Question: The average weight of 25 girls increases by 1 kg when a new girl comes in place of one of them weighing 55 kg. What might be the weight of the new girl?
(A) 85 kg
(B) 90 kg
(C) 83 kg
(D) 80 kg
(E) 82 kg
Rationale: Total weight increased = 25 x 1 kg = 25 kg.
Weight of new person = 55 + 25 kg =80 kg
Answer : D
Answer: (D) 80 kg
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was:
(A) A)14
(B) B)17
(C) C)56
(D) D)89
(E) E)34
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22.
Son's age 5 years back (22 - 5) = 17 years.
Answer:B
Answer: (B) B)17
Question: L = {3, 4, 5, 5, 6, 7}
M = {2, 2, 2, 8, 8, 8}
N = {15, 15, 15, 15, 15, 15}
Rank those three sets from least standard deviation to greatest standard deviation.
(A) L, M, N
(B) M, L, N
(C) M, N, L
(D) RANKING=N, L, M
(E) N, M,
Rationale: Square of Standard deviation is sum of squares of deviation from the mean divided by the number of terms.
If deviation from the mean is higher for the same number of elements, standard deviation will be higher.
L = {3, 4, 5, 5, 6, 7}
Mean is 5 and deviation of 2 elements from mean is 0, of 2 elements is 1 and of 2 elements is 2.
M = {2, 2, 2, 8, 8, 8}
Mean is 5 and deviation of all elements from the mean is 3. So SD here will be higher than SD of L.
N = {15, 15, 15, 15, 15, 15}
Mean is 15 here and all elements have 0 deviation from mean so SD = 0 here. This is the minimum possible SD.
Answer N, L, M
Answer (D)
Answer: (D) RANKING=N, L, M
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4years
(B) 8years
(C) 10years
(D) 12years
(E) None of these
Rationale: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer: A
Answer: (A) 4years
Question: The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
(A) 4
(B) 8
(C) 16
(D) 18
(E) None of these
Rationale: Explanation:
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
ANSWER IS B
Answer: (B) 8
Question: Find the area of a parallelogram with base 20 cm and height 10 cm?
(A) 287 cm2
(B) 887 cm2
(C) 200 cm2
(D) 250 cm2
(E) 668 cm2
Rationale: Area of a parallelogram = base * height
= 20 * 10
= 200 cm2
Answer: C
Answer: (C) 200 cm2
Question: The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:
(A) 30º
(B) 45º
(C) 60º
(D) 90º
(E) 80º
Rationale: shadow of the tree is √3 times the height of the tree.
shadow of a tree will be = √3x.
tan θ = AB/AC = x/√3x.
tan θ =1/√3.
tan θ = tan 1/√3.
tan θ = tan30°.
θ = 30° ANSWER : A
Answer: (A) 30º
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2.2 m
(B) 2.4 m
(C) 3 m
(D) 3.4 m
(E) 3.6 m
Rationale: Area of the park = (60 x 40) m2= 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2= 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
ANSWER : C
Answer: (C) 3 m
Question: One night 10 percent of the female officers on a police force were on duty. If 200 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 90
(B) 180
(C) 270
(D) 500
(E) 1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 200
Number of female officers on duty on that night = 200/2 = 100
(10/100)*F =100
=>F = 1000
Answer E
Answer: (E) 1,000
Question: If a refrigerator contains 12 cans such that there are 7 blue cans and 5 red cans. In how many ways can we remove 8 cans so that at least 1 blue can and 1 red can remains in the refrigerator.
(A) 452
(B) 453
(C) 454
(D) 455
(E) 456
Rationale: The possible cases of (b,r) draws are (6,2) (5,3) (4,4)
6 2---->7c6*5c2--->7*10=70
5 3---->7c5*5c3--->21*10=210
4 4---->7c4*5c4--->35*5=175
70+210+175=455
ANSWER:D
Answer: (D) 455
Question: The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Write equation in N as follows
N + 1/N = 78/15
Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
correct answer is E) 5
Answer: (E) 5
Question: 60% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 70
(B) 97
(C) 80
(D) 90
(E) 76
Rationale: Given, 60% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 60% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/60 = 40
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (40 + 120)/2 = 80.
Answer:C
Answer: (C) 80
Question: A standard Veggiematik machine can chop 25 carrots in 5 minutes. How many carrots can 5 standard Veggiematik machines chop in 5 minutes?
(A) 45
(B) 75
(C) 110
(D) 125
(E) 150
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 25 Carrots - 5 minutes,
1 standard Veggiematik machine - 5 Carrots - 1 minute,
Now
5 standard Veggiematik machine - ? Carrots - 5 minutes,
Hence = 5X5X5 =125 Carrots
Answer D
Answer: (D) 125
Question: amir has 3 desert every sunday...he stocked up 10 different chocolates and 12 diff icecreams,given that he never has same combination and doesn't 3 chocolates nor 3 icecreams,how many sundays it requires for his stock to be over?
(A) 1045
(B) 1200
(C) 2400
(D) 7200
(E) 3600
Rationale: he either can have 2 chocolates and 1 icecream or 1 chocolate and 2 icecream.
so the solution would be.
10C2*12C1 + 10C1*12C2 = 1200
ANSWER:B
Answer: (B) 1200
Question: In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
(A) 25
(B) 36
(C) 53
(D) 55
(E) 60
Rationale: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
C
Answer: (C) 53
Question: Find the average of first 27 natural numbers.
(A) 14
(B) 14.2
(C) 15.2
(D) 15.8
(E) 28
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 27 natural numbers = (27 x 28)/2 = 378
Therefore, required average of = 378/27 = 14
ANSWER: A
Answer: (A) 14