divelab/Sys2Bench huggingface dataset:
Question: Currently guavas cost 30 cents/pound. Due to a disease affecting the guava trees it is expected that next month guavas will cost 50% more than they do currently. How much are guavas expected to cost next month?
Options:
A)50 cents /pound
B)45 cents /pound
C)55 cents /pound
D)60 cents /pound
E)65 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 30 cents/pound + (50/100)(30 cents/pound)
= 30 cents/pound + 15 cents/pound
= 45 cents /pound
Answer : B
Answer: B
Question: There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
Options:
A)100
B)90
C)50
D)45 different pairs
E)25
Rationale: 1. first child out of 0 - 10 possibilities
2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10=90
3. exclude xy yx cases: 90/2=45
Second way
N=10C2=10!/(8!2!) =10*9/2=45
ANS:D
Answer: D
Question: 8.008/4.004
Options:
A)2
B)0.02
C)0.2
D)20
E)2
Rationale: Answer is 2, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/4004= 2
Answer A
Answer: A
Question: If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
Options:
A)4:3
B)4:0
C)4:5
D)4:7
E)4:2
Rationale: Explanation:
a1:a2 = 4:3
d1:d2 = 4:3
Answer: Option A
Answer: A
Question: A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 150
So, 2 ( L + B ) = 150
Or, L + B = 75
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 70
L = 70; B = 35
L + b = 105
(E) 80
L = 80; B = 40
L + b = 120
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B)
Answer: B
Question: Find the roots of quadratic equation: 3x2 - 7x - 6 = 0?
Options:
A)-6, 3
B)3, -2/3
C)-5, 2
D)-9, 2
E)None of these
Rationale: 3x2 - 9x + 2x - 6 = 0
3x(x - 3) + 2(x - 3) = 0
(x - 3)(3x + 2) = 0 => x = 3, -2/3
ANSWER:B
Answer: B
Question: While purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?
Options:
A)8 + 15/17
B)8 + 15/18
C)8 + 15/12
D)8 + 15/11
E)8 + 15/110
Rationale: Explanation:
Total sales tax paid = 7% of Rs, 400 + 9% of Rs. 6400
== Rs. (28 + 576) = Rs. 604.
Total cost of the items = Rs. (400 + 6400) = Rs. 6800.
Required percentage =% =%.
Answer: A) 8 + 15/17
Answer: A
Question: In a ground there are men and dogs. In all, there are 20 heads and 72 feet. How many men and how many horses are in the ground?
Options:
A)8 men and 14 dogs.
B)7 men and 14 dogs.
C)6 men and 14 digs.
D)5 men and 14 dogs.
E)4 men and 14 dogs.
Rationale: 6 men and 14 dogs.
Let M = men and D = dogs. We can come up with 2 equations.
M + D = 20
2M + 4D= 72
Solving the 2 equations will give 6 men and 14 dogs.
Answer C
Answer: C
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 8:30 am. They shall first cross each other at ?
Options:
A)7:15 am
B)7:30 am
C)8: 42 am
D)7:50 am
E)7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 8:30 + 12 mins = 8:42
Option C
Answer: C
Question: A 28 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)12
B)8
C)88
D)77
E)14
Rationale: 1: 2/5 = 5: 2
2/7 * 28 = 8
Answer: B
Answer: B
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1. 5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is
Options:
A)16 hours
B)18 hours
C)20 hours
D)24 hours
E)None
Rationale: Solution
Speed upsteram	= 7.5 kmph.
Speed downsteram	= 10.5 kmph.
Total time taken	=[10.5/7.5 + 105/10.5]hours
= 24 hours.
Answer D
Answer: D
Question: If m = ||n – 3| – 2|, for how many values of n is m = 6?
Options:
A)1
B)3
C)4
D)5
E)2
Rationale: m = ||n – 3| – 2| can be 4 only and only when n-3= +/-8. so there are 2 values of n
Answer : E
Answer: E
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed W ?
Options:
A) 6
B) 8
C) 10
D) 12
E) 16
Rationale: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this W we get x = 8.
B.
Answer: B
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 15% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Options:
A)70 lbs
B)40 lbs
C)30 lbs
D)50 lbs
E)63 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 15% profit
A+B = 100 pounds
(.07A + .15B)/(A+B) = .10
.07A + .15B = .1A + .1B
.05B = .03A
5B = 3A
5/3 = A/B
So, for every 5 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 63 pounds of A and 37 pounds of B.
option E
Answer: E
Question: The difference between two integers is 5. Their product is 500. Find the numbers.
Options:
A)15, 20
B)20, 25
C)30, 25
D)21, 26
E)25, 27
Rationale: Explanation:
Let the integers be x and (x + 5). Then,
x(x + 5) = 500
x2 + 5x - 500 = 0
(x + 25)(x - 20) = 0
x = 20
So, the numbers are 20 and 25.
ANSWER IS B
Answer: B
Question: The sum of the first 60 positive even integers is 3,750. What is the sum of the odd integers from 101 to 200, inclusive?
Options:
A) 4,700
B) 7,500
C) 10,500
D) 15,000
E) 19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 60 positive even integers = 3750
sum of 1st 100 odd numbers = 5050 - 3750 = 1300
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......) = 6000 + 1300 =4700
A is the answer.
Answer: A
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?
Options:
A) 42
B) 84
C) 70
D) 98
E) 140
Rationale: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 12 mph then the maximum distance, in miles, that the cyclist could travel in 7 hours would be 7*12=84 miles.
Answer: B.
Answer: B
Question: If x ≠ 0 and x^3 - (2- x^3)/x^3 = y/x^2, then y =
Options:
A)-2-x
B)-2+x
C)-(x+2)
D)-2/x
E)1/x
Rationale: x^3 - (2- x^3)/x^3 = y/x^2
-2/x^3 = y/x^2
y = -2/x
Answer : D
Answer: D
Question: Three friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
Options:
A)5%
B)10%
C)20%
D)25%
E)33%
Rationale: Let x be the original price of one ticket.
The total original cost is 3x.
The new cost is 4y, where y is the discounted price of one ticket.
3x = 4y
y = 3x/4 =0.75x which is a discount of 25%.
The answer is D.
Answer: D
Question: A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 10 days.In how many days B alone can do the work?
Options:
A)5days
B)15 days
C)12 days
D)9 days
E)10 days
Rationale: Explanation:
A’s 5 day work = 5*1/15=1/3
Remaining work = 1-1/3=2/3
B completes 2/3 work in 6 days
B alone can do in x days
2/3*x=10
X=15 days
Answer: Option B
Answer: B
Question: If the sum of 5 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 5
Options:
A) I only
B) II only
C) III and II only
D) I and III
E) III only
Rationale: I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.
Therefore E is the answer.
Answer: E
Question: A company consists of 5 senior and 3 junior staff officers. If a committee is created with 1 senior and 2 junior staff officers, in how many ways can the committee be formed?
Options:
A) 15
B) 30
C) 45
D) 80
E) 200
Rationale: Choose 1 senior from 5 senior and choose 2 junior from 3 junior:
5C1 * 3C2 = 5 * 3 = 15
Ans: A
Answer: A
Question: The average of first ten prime numbers which are odd is?
Options:
A)15.9
B)15.5
C)15.2
D)15.8
E)13.2
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: D
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 10200, how much money did he borrow?
Options:
A)10000
B)80288
C)2668
D)2600
E)2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 10200
18x + 45x + 39x = (10200 * 100)
102x = 1020000 => x = 10000.
Answer:A
Answer: A
Question: By how much is three-fifth of 600 greater than four- seventh of 210 ?
Options:
A)320
B)240
C)420
D)None of these
E)Cannot be determined
Rationale: Solution
3/5 of 600 - 4/7 of 210 = 240.
Answer B
Answer: B
Question: If we have 8 people in a meeting, in how many ways they can sit around a table?
Options:
A)10*9!
B)9*8!
C)8*7!
D)7*6!
E)6*5!
Rationale: If there are "n" people sitting around a table, there are "(n-1)!" possible arrangements:
Here, n=8
(n-1)!=7!=7*6!
Ans:"D"
Answer: D
Question: The area of a square is equal to four times the area of a rectangle of dimensions 52 cm * 13 cm. What is the perimeter of the square?
Options:
A)200
B)208
C)210
D)220
E)228
Rationale: Area of the square = s * s = 4(52 * 13)
=> s = 52 cm
Perimeter of the square = 4 * 52 = 208 cm.
Answer: Option B
Answer: B
Question: Two employees X and Y are paid a total of Rs. 650 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)s.200.45
B)s.250.45
C)s.295.45
D)s.300.45
E)s.310.45
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 650
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 650
⇒ y[12/10 + 1] = 650
⇒ 22y/10 = 650
⇒ 22y = 6500
⇒ y = 6500/22 = Rs.295.45
C)
Answer: C
Question: On dividing 52 by a number, the quotient is 16 and the remainder is 4. Find the divisor?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: d = (D-R)/Q
= (52 - 4)/16
= 48/16 = 3
B)
Answer: B
Question: If s and t are positive integers such that s/t = 4.12, which of the following could be the remainder when s is divided by t ?
Options:
A)2
B)4
C)8
D)20
E)30
Rationale: The remainder is 0.12 or 12/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
30/Y=12/100
12Y=3000
Y=250
Answer: E.
Answer: E
Question: A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage
Options:
A)25% loss
B)25% gain
C)15% gain
D)15% loss
E)None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
B
Answer: B
Question: What is the next number: 3, 11, 83, __
Options:
A)631
B)731
C)831
D)849
E)901
Rationale: 3^0 + 2 = 3
3^2 + 2 = 11
3^4 + 2 = 83
3^6 + 2 = 731
The answer is B.
Answer: B
Question: A semicircle has a radius of 11. What is the approximate perimeter of the semicircle?
Options:
A)45
B)51
C)57
D)63
E)69
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*11 + 2*11 which is about 57.
The answer is C.
Answer: C
Question: The cubic f(x) = x3 - 7x - 6 has three distinct roots, a, b, and c. Compute 1/a + 1/b + 1/c .
Options:
A)-5/6
B)-6/6
C)-7/6
D)-8/6
E)-9/6
Rationale: 1/a+1/b+1/c=ab+bc+ca/abc
=-7/-6
=-7/6
correct answer C
Answer: C
Question: If x>=y and y>1 , what is the maximum value of log (base x) -(x/y) + log (base y)x^2/y?
Options:
A)-0.5
B)0
C)0.5
D)1
E)2
Rationale: log -(x/y) + log ( x^2)/y => - log x/y + 2log (x/y)
x y x y
By Formula (i) - log x/y = log y/x (ii) log y/x = log y - log x
x x x x x
log y - log x + 2{log x - log y }
x x y y
log y -1 + 2log x - 2 ==> log y + 2log x -3
x y x y
by Sub x &y as 2 by Question Condition---> Ans 1+2-3 = 0
ANSWER:B
Answer: B
Question: 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
Options:
A)233/3
B)233/8
C)233/1
D)233/2
E)263/3
Rationale: Required average = [(76 * 16) - (75 * 10)] / 6
= (1216 - 750)/6 = 466/3
= 233 /3.
Answer: A
Answer: A
Question: Cereal A is 9% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A) 2:9
B) 2:5
C) 1:6
D) 1:4
E) 1:3
Rationale: (9/100)A+(2/100)B = (4/100)(A+B)
5A =2B
=> A/B = 2/5
Answer is B.
Answer: B
Question: If a committee of 3 people is to be selected from among 9 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)420
B)540
C)550
D)672
E)720
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
18*16*14 / 6 = 672. Answer D.
Answer: D
Question: What will $3000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
Options:
A)$4316
B)$4632
C)$4864
D)$5184
E)$5548
Rationale: After one year: 1.2 * $3000
After two years: (1.2)^2 * $3000
After three years: (1.2)^3 * $3000 = $5184
The answer is D.
Answer: D
Question: A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is
Options:
A)31 years
B)32 years
C)33 years
D)34 years
E)35 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+40.
=> 2(x+6) = (x+40+6)
=> 2x+12 = x+46
=> x = 34 years
Answer: Option D
Answer: D
Question: Inland revenue paid $300 on its first 1000 watts of electricity and then $5000 on the next 10000 watts. By approximately what percent did the ratio of monies due to watts increase from the first $1000 watts to the next 10000 watts?
Options:
A)A) 80%
B)B) 6%
C)C) 60%
D)D) 20%
E)E) 40%
Rationale: First 1000 watts (3/10)
Next 10000 (5/10)
percentage increase is (difference/initial quantity)*100
(3/10)/(5/10 )* 100= 60%
Correct options is C
Answer: C
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price S per t-shirt that the vendor paid for these purchases?
Options:
A)$12.20
B)$12.50
C)$12.55
D)$12.70
E)$13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average S= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: A
Question: A boat travels 80 km downstream in 8 hours and 48 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
Options:
A)7 km/hr, 3 km/hr
B)5 km/hr, 4 km/hr
C)1 km/hr, 6 km/hr
D)2 km/hr, 1 km/hr
E)4 km/hr, 1 km/hr
Rationale: Downstream speed=80km/8hrs
=10kmph
upstream speed=48km/12hrs
=4kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(10+4)/2kmph
=7kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(10-4)/2kmph
=3kmph
ans is 7km/hr,3km/hr
ANSWER:A
Answer: A
Question: Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?
Options:
A)0.8 inches
B)1.1 inches
C)1.6 inches
D)2.0 inches
E)2.5 inches
Rationale: Total Area = 8 * 8 * pi
Radius = 64 pi
Surface = .75 * 64 * pi = 48 pi
Radius of surface = 4 sqrt (3) ~ 6.8
Radius width = 8 - 6.8 = 1.2
Answer: B
Answer: B
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 34 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Options:
A)17 litres
B)22.67 litres
C)11 litres
D)07 litres
E)38.67 litres
Rationale: 262.85(34)+3,104.35x = 1,399.45(34 + x)
Solve the equation.
262.85(34)+3,104.35x = 1,399.45(34 + x)
8936.9+ 3,104.35x = 47,581.3 + 1,399.45x
8936.9 + 1,704.9x = 47,581.3
1,704.9x = 38,644.40
x ≈ 22.67
Answer is B.
Answer: B
Question: There is a 30% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?
Options:
A)25.0%
B)37.5%
C)50.0%
D)62.5%
E)75%
Rationale: P(Chile and not Madagascar) = 0.3*0.5 = 0.15
P(Madagascar and not Chile) = 0.5*0.7 = 0.35
Total probability = 0.15 + 0.35 = 0.5 = 50%
The answer is C.
Answer: C
Question: 9 3/4 + 7 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)7 817/1020
E)None of them
Rationale: Given sum=9+3/4+7+2/17-(9+1/15)
=(9+7-9)+(3/4+2/17-1/15)
=7+(765+120-68/1020
=7 817/1020
Answer is D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/28
B)2/129
C)2/21
D)2/20
E)2/25
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (Â³Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: C
Question: 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: To find the number of vans, we divide 123 by 8.
123 * 8 = 15 and remainder = 3
So 15 vans are needed to transport 15 * 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.
correct answer B
Answer: B
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)7 months
B)10 months
C)9 months
D)11 months
E)8 months
Rationale: 7*5: 5*x = 7:10
x = 10
ANSWER:B
Answer: B
Question: Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?
Options:
A)probability is 1/27
B)16/81
C)8/27
D)19/27
E)26/27
Rationale: Let the probability of an archer hitting a target be xx. Then the probability of two hitting the target will be P=x∗x=49P=x∗x=49 - -> x=23x=23, so the probability of an archer missing the target will be P=1−23=13P=1−23=13.
The probability of all three men missing the target will be P=(13)3=127P=(13)3=127.
Answer: A.
Answer: A
Question: When average age of 21 members are 0, how many members greater than 0?
Options:
A)17
B)20
C)21
D)24
E)25
Rationale: Average of 21 numbers = 0.
Sum of 21 numbers (0 x 21) = 0.
It is quite possible that 20 of these numbers may be positive and if their sum is a then 21st number is (-a)
Answer is 20 (B)
Answer: B
Question: An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?
Options:
A)3000
B)2000
C)4000
D)2500
E)3500
Rationale: Explanatory Answer
This question is a word problem in linear equations. The problem is solved by framing two linear equations from the information given in the question and solving them.
Let 's' be the number of small slices and 'b' the number of large slices sold on that night.
Therefore, s + b = 5000 ... eqn (1)
Each small slice was sold for Rs.150.
Therefore, 's' small slices would have fetched Rs.150s.
Each large slice was sold for Rs.250.
Therefore, 'b' large slices would have fetched Rs.250b.
Total value of sale = 150s + 250b = 10,50,000 (note the left hand side is in Rupees and hence we have to convert right hand also to Rupees from Lakhs of Rupees)
Or 150s + 250b = 10,50,000 ... eqn (2)
Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)
Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000
Or b = 3000
We know that s + b = 5000
So, s = 5000 - b = 5000 - 3000 = 2000.
2000 small slices were sold.
Answer B
Answer: B