divelab/Sys2Bench huggingface dataset:
Question: The ages of Charlie and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:
Options:
A)15 years
B)16 years
C)135 years
D)21 years
E)18 years
Rationale: A
15 years
Charlie’s age = 3A and
Vaibhav’s age = 5A
{ (3A + 9)/(5A + 9) }=3/4
=> 4 (3A + 9) = 3 (5A + 9)
=> A = 3
Therefore, Vaibhav’s age = 15 years.
Answer: A
Question: A tank is 25 m long, 12 m wide and 6 m deep. What is the cost of plastering its walls and bottom at the rate of 75 paise per sq.m?
Options:
A)558
B)502
C)516
D)612
E)700
Rationale: TOTAL SURFACE S = 2LW + 2LH + 2WH
=(25 * 12) + (2 * 25 * 6 ) + ( 2 * 12 * 6 )
= 300 + 300 + 144
=744 M2
THEREFORE COST OF PLASTERING = 744 * 75 = 5800 PAISE = 558
ANSWER A
Answer: A
Question: Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?
Options:
A)56
B)44
C)26
D)48
E)49
Rationale: A
56
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
Answer: A
Question: If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a?
Options:
A)2
B)1
C)3
D)7
E)9
Rationale: (a5,608 + 584)/88 = a6,192/88
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
192/8 = 24 => So, we want divisible by 11.
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a619-2 => a61-7 => a5-4 => a1 => 11/11.
So a = 1.
Answer: B
Answer: B
Question: Determine the equation for the line parallel to r ≡ x + 2y − 2= 0 that passes through the point A = (1, 3).
Options:
A)x + 2y = 0
B)2y − 7= 0
C)x + 2y − 7= 0
D)x − 7= 0
E)x - 2y + 7= 0
Rationale: the equation for the line parallel to r ≡ x + 2y − 2= 0 is
x + 2y + K= 0
1 + 2• 3 + k = 0
k = −7
x + 2y − 7= 0
ANSWER C x + 2y − 7= 0
Answer: C
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th term in sequence S?
Options:
A)3(2^13)
B)9(2^15)
C)21(2^14)
D)9(2^14)
E)21(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3,
Answer : A
Answer: A
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Options:
A)19
B)28
C)30
D)37
E)35
Rationale: Explanation:
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x 120x = 40
x =	1/3
Number of floors covered by David in (1/3) min. = (1/3x 57	)=19.
So, their paths cross at (11 +19) i.e., 30th floor.
ANSWER IS C
Answer: C
Question: Q-2: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3?
Options:
A)9
B)10
C)11
D)12
E)14
Rationale: CONCEPT: A number will be divisible by 3 if sum of all the digits of the number is divisible by 3
Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition
If sum of Digits = 3, No. = 12, 21 --- 2 Cases
If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
If sum of Digits = 12, No. = 57, 75 --- 2 Cases
Total Cases = 2+4+6+2 = 14 cases
Answer: option E
Answer: E
Question: If 15 men can build a wall of forty two metres long in 5 days, what length of a similar wall can be built by 25 men in 4 days
Options:
A)48 metres
B)56 metres
C)60 metres
D)62 metres
E)None of these
Rationale: Explanation :
Solution: Let the required length be x metres.
More men, more length built (Direct proportion)
Less days, less length built (Direct proportion)
men 15 : 25
days 5 : 4
.'.(15*5*x) = (25*4*42)
x = 56 metres.
Answer : B
Answer: B
Question: A company makes a profit equal to 25% of its sales. The profit is shared equally among the 4 owners of the company. If the company generates sales of $5,000,000, how much money does each one of the owners get?
Options:
A)$ 112,500
B)$ 212,500
C)$ 312,500
D)$ 412,500
E)$ 512,500
Rationale: The profit made on sales of $5,000,000 is given by
25% * $5,000,000 = $ 1,250,000
The profit made by each one of the 4 owners is given by
$ 1,250,000 / 4 = $ 312,500
correct answer C
Answer: C
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 6 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
Options:
A)1/60
B)1/45
C)2/45
D)3/22
E)5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/22)*(6), which indeed is 6/22.
E
Answer: E
Question: Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white
Options:
A)1
B)2/3
C)1/3
D)4/3
E)5/3
Rationale: Explanation:
Total cases = 10 + 20 = 30
Favourable cases = 20
So probability = 20/30 = 2/3
Answer: Option B
Answer: B
Question: f n = 3^8 - 2^8, which of the following is not a factor of n?
Options:
A)5
B)65
C)13
D)97
E)35
Rationale: = (3^4 -2^4) (3^4+2^4)
number is not divisible by 35
=97*13*5
E
Answer: E
Question: If k^3 is divisible by 60, what is the least possible value of integer k?
Options:
A)12
B)30
C)60
D)90
E)120
Rationale: 60 = 2^2*3*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Answer: B
Question: Denominator of a number is 4 less than the numerator. If 6 is added to the numerator, it becomes 3 times the denominator. Find the denominator.
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Let the Numerator be X and Denominator be Y. Then
=>X=Y+4 and 6+X=3*Y
=>6+Y+4=3*Y
=>2Y=10=>Y=5
Option C
Answer: C
Question: If 0.2 of a number is equal to 0.08 of another number, the ratio of the numbers is :
Options:
A)2 :3
B)3 :4
C)2 : 5
D)20 : 3
E)30:7
Rationale: 0.2A = 0.08B
-> A/B = 0.08/0.20 = 8/20 = 2/5
:. A : B = 2 : 5
ANSWER:C
Answer: C
Question: A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of Rs.40, then how many shirts, cash costing Rs.32, he should purchase ?
Options:
A)6
B)5
C)10
D)7
E)8
Rationale: Explanation:
Suppose the number of shirts = x.
Then, rebate = [25/100×32x]=8x
8x=40 or x = 5.
Correct Option : B
Answer: B
Question: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
Options:
A)18
B)21
C)38
D)40
E)57
Rationale: 5/6*P have horseshoes, so P is a multiple of 6.
2/3*5/6*P = 5/9*P are Icelandic ponies with horseshoes, so P is a multiple of 9.
The minimum value of P is 18. Then H = P+4 = 22.
The minimum number of horses and ponies is 40.
The answer is D.
Answer: D
Question: Henry sold an item for Rs.7200/- and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of 20%?
Options:
A)10600
B)10800
C)11000
D)11200
E)11400
Rationale: Explanation:
20% loss means SP = 80% of CP
:. CP = Rs.7200x100/80 = Rs.9000.
The SP for a gain of 20% = 9000+20% of 9000 = 9000+1800 =Rs10800.
Answer: Option B
Answer: B
Question: Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 45% took a marketing class last semester, and 45% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
A)60%
B)50%
C)25%
D)15%
E)10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 20 + 45 - {both} + 45
{both} = 10%.
The answer is E.
Answer: E
Question: Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1000
B)B)1055
C)C)1065
D)D)1075
E)E)1095
Rationale: Cost of 8 kg grapes = 75 × 8 = 600.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 600 + 495 = 1095.
E)
Answer: E
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 10p, in terms of p?
Options:
A)10p
B)2p
C)5p
D)7p
E)p^2
Rationale: Y=30p
other number is 10p
then GCF(30p,10P)=10P; A is the correct answer
Answer: A
Question: Everyone shakes hands with everyone else in a room. Total number of handshakes is 120. Number of persons=?
Options:
A)a.14
B)b.12
C)c.11
D)d.15
E)e.16
Rationale: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2
So n(n-1)/2 = 120 OR n(n-1)=240 OR n=16
Answer is (E)
Answer: E
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3168, how much was it in the beginning?
Options:
A)A)3800
B)B)4200
C)C)4400
D)D)4500
E)E)4600
Rationale: X * (90/100) * (80/100) = 3168
X = 4400
ANSWER:C
Answer: C
Question: A dealer originally bought 90 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
Options:
A)q/60
B)3q/2
C)145q
D)q/90
E)145/q
Rationale: The cost of each battery was q/90.
Each battery was sold for 1.5q/90 = 3q/180 = q/60.
The answer is A.
Answer: A
Question: The first term in a sequence is 1 and the second term is 10. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 29th term in the sequence?
Options:
A)3.5
B)5.5
C)10
D)10.5
E)29
Rationale: The third term is 5.5 since this is the average of 1 and 10.
Then the next terms will all be 5.5 since the average stays at 5.5
The answer is B.
Answer: B
Question: Billy makes $124 more than Kimberly in a week. Wynona makes 3 times as much as Billy and Kimberly put together in a week, which totals $2,436. How much would Billy, Kimberly, and Wynona make together in a month?
Options:
A)$12,992
B)$9,744
C)$29,232
D)$11,232
E)None of the above
Rationale: b-k=124
3(b+k)=2,436 or b+k=812
Solving the 2 equations you get B=$468 and K=$344
So 4(468+344+2436)=$12,992
Correct Answer: A
Answer: A
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Options:
A)13√4
B)13√2
C)23√2
D)12√4
E)13√9
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: B
Answer: B
Question: If a number between 10 and 60 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
Options:
A)31/41
B)1041
C)14/41
D)27/41
E)16/51
Rationale: If tens digi is 6 ---> ones digit : 0
If tens digi is 5 ---> ones digit : 0, 1, 2, 3, 4
If tens digi is 4 ---> ones digit : 0, 1, 2, 3
If tens digi is 3 ---> ones digit : 0, 1, 2
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 60-10+1=51.
So the probability is 16/51.
The answer is (E).
Answer: E
Question: The average age of A and B is 50 years. If C were to replace A, the average would be 50 and if C were to replace B, the average would be 40. What are the age of A, B and C?
Options:
A)100,100, 80
B)50, 50, 40
C)40, 60, 40
D)50, 60, 40
E)None of the above
Rationale: Given A + B = 100â€¦(i)
C + B = 100â€¦ (ii)
A + C = 80â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C = 140â€¦(iv)
from (i) and (iv), we get
C = 40years
âˆ´ B = 60 years and A = 40 years
Answer C
Answer: C
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
Options:
A)17/140
B)29/180
C)26/143
D)1/5
E)39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 7*2 = 14 hours;
In 1 hour 15 journeymen can finish 1/14 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job.
Answer: A
Answer: A
Question: If x^4 > x^5 > x^3, which of the following could be the value of x?
Options:
A)-3
B)-2
C)-2/3
D)2/3
E)3
Rationale: Let's break this question down into two parts. I: x4>x5x4>x5 and II: x5>x3x5>x3
Consider Part I:
x4>x5x4>x5
For this to be true, either xx is negative or it is a fraction less than 1
Consider Part II:
x5>x3x5>x3
If xx is negative, then for this to be true, xx has to be greater than -1.
If xx is a fraction less than 1, then for this part to be true, xx must also be negative.
In either case, xx can be represented by the inequality 0>x>−10>x>−1.
The only option that satisfies this condition is C (-2/3)
ANSWER:C
Answer: C
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
Options:
A)1/7
B)1 by 6
C)2/3
D)2/5
E)3/5
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Answer: B
Question: What is the sum of all the numbers between 1 and 16, inclusive?
Options:
A)190
B)200
C)185
D)166
E)213
Rationale: All you have to do is add 1+2+3+4...+14+15+16, which is 190.
Final Answer:
A
Answer: A
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 34, 26, 36, 33 and 35 ?
Options:
A)33
B)28
C)27
D)24
E)23
Rationale: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 34, 26, 36, 33 and 35
24, 26, 30, 33, 34, 35, 36, 42...
numbers less than median are 24, 26, 30, 33..
the median of these numbers = center of 26 and 30 = 28
B
Answer: B
Question: If Re.250 amounts to Rs.400 over a period of 5 years. What is the rate of simple interest?
Options:
A)11%
B)12%
C)13%
D)10%
E)14%
Rationale: 150 = (250*5*R)/100
R = 12%
Answer:B
Answer: B
Question: For the given equation x9+5x8−x3+7x+2=0,x9+5x8−x3+7x+2=0, how many maximum real roots are possible?
Options:
A)3
B)7
C)4
D)0
E)1
Rationale: f(x) = x9+5x8−x3+7x+2=0x9+5x8−x3+7x+2=0
In f(x), there are 2 changes of sign. So, there are two positive roots.
f(-x) = - x9+5x8−x3+7x+2=0x9+5x8−x3+7x+2=0
In f(-x), there are 3 changes of sign. So, there are three negative roots.
So, in all there are 5 real roots possible (2 positive and 3 negative) and as degree of the given equation is 9, there are total 9 roots. So, remaining 4 roots will be imaginary.
Answer:C
Answer: C
Question: The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.
Options:
A)5:25
B)4:25
C)3:15
D)7:15
E)6:15
Rationale: Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2
= 4x2: 25x2
= 4 : 25.
ANSWER B 4:25
Answer: B
Question: In how many ways R can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
Options:
A)1. 10!/(2! * 3!)
B)2. 10!/(8! * 7!)
C)3. 5!/(3! * 2!)
D)4. (5!)^3/(3! * 2!)
E)5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways.R
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: D
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $8.40?
Options:
A)426
B)430
C)443
D)530
E)486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 8.4$, we can buy as many as 5 packs of 100 (5 x 1.5$ = 7.5$). We then have 0.9 $ left. so we buy 30 individual envelopes. If we add up the numbers, we get 500+30=530 envelopes. Answer D
Answer: D
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $1.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $1.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:
$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)
If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.
You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)
Answer is A.
Answer: A
Question: A can finish a piece of work in 4 days. B can do it in 8 days. They work together for two days and then A goes away. In how many days will B finish the work?
Options:
A)4
B)5
C)6
D)2
E)8
Rationale: 2/4 + (2 + x)/8 = 1 => x = 2 days
Answer: D
Answer: D
Question: If each term in the sum a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12 => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
ANSWER:C
Answer: C
Question: Two trains start from the same station at the same time and travel in opposite directions. One
train travels at an average rate of 40 mph, the other at 65 mph. In how many hours will they be
315 miles apart?
Options:
A)1 hour
B)2 hours
C)3 hours
D)4 hours
E)5 hours
Rationale: First we’ll make the d=rt chart. But we won’t fill in the d.
d = r x t
Train 1 40 x
Train 2 65 x
The reason we have an x in the time column is because they left at the same time and will be 315
at the same time. In other words, their times are equal.
Now, the big question. Are there distances equal? Since they do not meet the criteria in a TYPE
A problem, the answer is no. That means the sum of the distances must be equal to a number.
D1 + D2 = #
40x + 65 = 315
105x = 315
x = 3 It will take three hours.
correct answer C
Answer: C
Question: At a party, there were five times as many females as males and six times as many adults as children. Which of the following could be the number of people at the party?
Options:
A)384
B)258
C)216
D)120
E)77
Rationale: Five times as many females as males --> F = 5M.
Three times as many adults as children --> (F + M) = 6C.
The number of people at the party = F + M + C = 6C + C = 7C.
The number of people at the party must be a multiple of 7. The only answer choice which is a multiple of 7 is E.
Answer: E.
Answer: E
Question: The average of first ten prime numbers:
Options:
A)5.6
B)11.2
C)12.9
D)6.3
E)7.4
Rationale: Explanation:
The first ten prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Average = 129/10 = 12.9
Answer: Option C
Answer: C
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 12 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
Options:
A)2,000
B)5,000
C)10,000
D)30,000
E)52,000
Rationale: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
12 broken glass will be from 30000 bulbs
Answer is D
Answer: D
Question: The local carpenter made a beautiful table for my father. He told him that the type of wood which he used costs G dollars per kg, and that the table only weight F kilograms. If the carpenter worked for D hours on the table and makes E dollars per hour, how much profit will my father make when he sells the table for V dollars?
Options:
A)V-GF-DE
B)V+GE-DF
C)V-(GF-DE)
D)G(V-DE)+F
E)(FG+DE)+V
Rationale: The wood will cost= GF dollars
The carpenter will be payed an amount= DE dollars
Hence, the cost price= GF+DE dollars
The selling price= V dollars
And the profit= V-(GF+DE)
The answer is A
Answer: A
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
Options:
A)1 hr
B)7 hr
C)9 hr
D)4 hr
E)9 hr
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
Answer: A
Answer: A
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ?
Options:
A)21.
B)28.
C)5.
D)49.
E)52.
Rationale: Delta x will give us the dimension of one side of the parallelogram = 5-4= 1 unit
Delta y will give us the dimension of the other side of parallelogram = 9-4=5 unit
Area of parallelogram = 1*5 = 5
ANSWER IS C
Answer: C
Question: For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
Options:
A)18.1
B)21.1
C)36.5
D)42.2
E)84.4
Rationale: Let x and z be the smallest and largest of the original set, respectively.
z - x = 84.4
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1
The answer is B.
Answer: B
Question: A discount of 10 percent on an order of goods followed by a discount of 30 percent amounts to
Options:
A)the same as one 45 percent discount
B)the same as one 40 percent discount
C)the same as one 37 percent discount
D)the same as one 30 percent discount
E)the same as one 25 percent discount
Rationale: 0.9*0.7*x=0.63x from initial value, meaning 0.37 or 37% discount
C
Answer: C
Question: The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a.?
Options:
A)Rs. 20.25
B)Rs. 22.50
C)Rs. 25
D)Rs. 42.75
E)None
Rationale: Solution
S.I. = Rs. 202.50, R = 4.5% ,T = 1 year.
principal = Rs. (100x202.50/4.5x1)= Rs. 4500.
Now,P = Rs. 4500,R = 5% ,T = 1 year.
S.I. = Rs.(4500x5x1/1000 = Rs. 225.
∴ Difference in interest = Rs. (225 - 202.50)= Rs. 22.50.
Answer B
Answer: B