divelab/Sys2Bench huggingface dataset:
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)22
B)66
C)48
D)77
E)21
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Answer: C
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
Options:
A)A)5322
B)B)5330
C)C)6300
D)D)5340
E)E)5342
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300.
C
Answer: C
Question: Which of the following is equal to (x+1)!/x!
Options:
A)x-1
B)1+(1/x)
C)x+1
D)1
E)x
Rationale: (x + 1)! = (x + 1) * x!
(x + 1)!/x! = x + 1
Answer: C
Answer: C
Question: There are 47 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
A)39
B)40
C)51
D)58
E)63
Rationale: {Total} = {M} + {N} - {Both}
{Total} = 47 + 28 - 12 = 63.
Answer: E.
Answer: E
Question: which of the following will not give an integer on taking square root?
Options:
A)64
B)529
C)441
D)484
E)450
Rationale: square root(64)=8
square root(529)=23
square root(441)=21
square root(484)=22
square root(450) is not an integer
so the answer is E
Answer: E
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
Options:
A)700
B)710
C)720
D)800
E)820
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C)
Answer: C
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 140 kilometers?
Options:
A)4.5
B)5.5
C)6.5
D)7.5
E)3.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 140 kilometers?
140 ÷ 40 = 3.5 × 1 gallon = 3.5 gallons
correct answer E
Answer: E
Question: Charlie's lawn service fills up all their gas cans every Friday at Zeb's store. They have to get enough gas for 10 lawn mowers and 10 weed-eaters. The weed-eaters use 5 liters of gas each. The mowers us 60% more than the weedeaters.
Zeb charges .75 cents service per item. Fuel is .40 cents per liter. How much will it cost to fill all mowers and weed-eaters?
Options:
A)$77
B)$60
C)$67
D)$62
E)$55
Rationale: Lots of calculations.
.75*20 + 10*.40*5+ 5*(8/5)*10*.40
Answer=$67
The correct option is C
Answer: C
Question: A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?
Options:
A)40
B)30
C)20
D)50
E)60
Rationale: Suppose x bottles can fill the tin completely
Then4/5x-3/4x=6-4
X/20=2
X=40
Therefore required no of bottles =40
Answer is A.
Answer: A
Question: A goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds.What is the length of the goods train?
Options:
A)230 m
B)250 m
C)260 m
D)270 m
E)240 m
Rationale: s=270+x/t
72*5/18=270+x/26
x=250
ANSWER:B
Answer: B
Question: The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ?
Options:
A)25
B)18
C)16
D)15
E)14
Rationale: let S.P. of X books = Rs 100 = C.P. of 20 books
Therefore, C.P. of one book = Rs 5
Profit = 25 %
Therefore, S.P of one book = 6.25
S.P of X articles = 6.25 X
6.25 X = 100 => X = 16
ANSWER:C
Answer: C
Question: he average of 10 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)0
B)1
C)10
D)9
E)8
Rationale: Average of 10 numbers = 0.
Sum of 10 numbers (0 x 10) = 0.
It is quite possible that 9 of these numbers may be positive and if their sum is a the 10th number is (-a).
Answer: Option D
Answer: D
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)378
B)277
C)375
D)287
E)279
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: C
Question: Consider two statements
Statement 1 => If X is an integer and X=2p+1 where p is not an integer.
Statement 2 => If Y is an integer and Y=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of X and Y respectively
Options:
A)Odd,Even
B)Odd,Odd
C)Even,Odd
D)Even,Even
E)Cannot be determined
Rationale: x = integer
x = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even x would odd
if n odd x would be even
Similarly other
answer will be E
Answer: E
Question: Martin has a business washing cars. Last year he washed 20 cars a
week. This year, he wants to increase his business to 1,200 cars a year.
How many cars will he have to wash each month on average?
Options:
A)200 cars
B)500 cars
C)300 cars
D)100 cars
E)400 cars
Rationale: The last year part is extra information. 1200÷12 (months in a year)= 100
He will have to wash 100 cars each month.
correct answer D
Answer: D
Question: A train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds. Its length is?
Options:
A)275
B)287.5
C)288
D)233.5
E)245.6
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 23 => y = x/23
x + 125 / 33 = x / 23
x = 287.5 m.
Answer:B
Answer: B
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.2, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
Options:
A)$16.60
B)$20.75
C)$22.50
D)$42.75
E)$45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .2 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .2 = 16.60 $
Answer A
Answer: A
Question: What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5?
Options:
A)1
B)3
C)2
D)4
E)5
Rationale: Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 1*4*3= will give units digit as 2
So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2.
Option C
Answer: C
Question: In a public show 75 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
Options:
A)100
B)110
C)120
D)140
E)150
Rationale: 75 % of 600
= 75/100 × 600
= 450
Therefore, the number of vacant seats = 600 - 450 = 150.
Answer:E
Answer: E
Question: In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
Options:
A)60/ 120
B)15 / 120
C)30 / 120
D)80 / 120
E)40/ 120
Rationale: Number of people whose age is less than 20 is given by
120 - 90 = 30
Probability P that a person selected at random from the group is less than 20 is gieven by
30 / 120 = 0.25
correct answer C
Answer: C
Question: 0.99999+0.11112=?
Options:
A)1
B)1.0001
C)1.0021
D)1.111
E)1.11111
Rationale: 0.99999 + 0.11112
= 0.99999 + 0.11111 + 0.00001
= (0.99999 + 0.00001) + 0.11111
= 1 + 0.11111
= 1.11111
E
Answer: E
Question: Find the one which does not belong to that group?
Options:
A)16
B)36
C)77
D)64
E)4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 77.
Answer:C
Answer: C
Question: If one positive integer is greater than another positive integer by 4, and the difference of their cubes is 316, what is their sum?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
The two numbers are 3 and 7.
The answer is C.
Answer: C
Question: A car X takes 3 hours more than a bus Y in covering 40 km. If the car triples its speed it takes 1 hour less than bus. What is the speed of the car?
Options:
A)6 km/hr
B)6.25 km/hr
C)6.67 km/hr
D)7 km/hr
E)None of these
Rationale: Explanation :
Let the car's speed be x km/hr.
=> 40/x-40/(3x)=4
=> 80/3x=4
=> 12x=80
=> x=6.67 km/hr
Answer : C
Answer: C
Question: A can finish a piece of work in 4 days. B can do it in 12 days. They work together for two days and then A goes away. In how many days will B finish the work?
Options:
A)6 days
B)5 days
C)7 days
D)4 days
E)3 days
Rationale: 2/4 + (2 + x)/12= 1 => x =6 days
Answer: A
Answer: A
Question: If k is the greatest positive integer such that 4^k is a divisor of 32! then k =
Options:
A)3
B)4
C)5
D)6
E)10
Rationale: 32/4=8
32/16=2
8+2 =10=k
Answer:E
Answer: E
Question: A local bank that has 9 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 9 codes?
Options:
A)9 codes 3 integers
B)4
C)5
D)6
E)7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Total = 9 Codes.. Answer: A
Answer: A
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be
Options:
A)7
B)9
C)12
D)14
E)15
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
A)
Answer: A
Question: If the number 5 * 2 is divisible by 6, then * = ?
Options:
A)8
B)6
C)2
D)1
E)5
Rationale: C
2
6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
Answer: C
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)160
B)175
C)180
D)195
E)166
Rationale: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
=160 x 2.40 + x x 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer: B
Answer: B
Question: How many litres of pure acid are there in 8 litres of a 20% solution?
Options:
A)2 litres
B)1.4 litres
C)1 litres
D)1.6 litres
E)None of these
Rationale: Explanation :
Quantity of pure acid = 8 × (20/100) = 1.6
Answer : Option D
Answer: D
Question: The radius of a cylinder is 8 m, height 14 m. The volume of the cylinder is:
Options:
A)2816
B)5500
C)3300
D)1100
E)4400
Rationale: Cylinder volume = Ï€r(power2)h
= 22/7 Ã— 8 Ã— 8 Ã— 14
= 2816 m(power3)
Answer is A.
Answer: A
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)11
B)77
C)12
D)99
E)887
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: C
Question: If n is an integer and n^4 is divisible by 20, which of the following could be the remainder when n is divided by 20?
Options:
A)5
B)10
C)12
D)16
E)18
Rationale: option 1
Remainder 5 means 20+5=25
n^4= 25^4= 25*25*25*25/20 is not an integer
option 2
Remainder 10 means 20+10=30
n^4= 30*30*30*30/20 is an integer means n^4 is divisible by 20 if we take n=10
so B is correct
Answer: B
Question: The profit earned after selling an article for Rs.675 is twice the loss incurred after selling the article for Rs.435. What is the cost price of the article?
Options:
A)Rs.450
B)Rs.595
C)Rs.400
D)Rs.395
E)None of these
Rationale: Explanation:
Let ‘x’ be the CP of the article.
i.e. Rs.675-x = 2(x-435)
675-x = 2x-870
675+870 = 3x, therefore, x=1545/3 =Rs.515
Answer: Option E
Answer: E
Question: At what rate percent per annum will the simple interest on a sum of money be 7/5 of the amount in 10 years?
Options:
A)4%
B)7%
C)9%
D)3%
E)14%
Rationale: Let sum = x. Then, S.I. = 7x/5, Time
= 10 years.
Rate = (100 * 7x) / (x * 5 * 10)
= 14%
Answer: E
Answer: E
Question: A race course is 400 m long. A and B run a race and A wins by 5m. B and C run over the same course and B win by 4m. C and D run over it and D wins by 16m. If A and D run over it, then who would win and by how much?
Options:
A)D by 7.2 m
B)A by 7.2 m
C)A by 8.4 m
D)D by 8.4 m
E)None of these
Rationale: Explanation :
If A covers 400m, B covers 395 mIf B covers 400m, C covers 396 mIf D covers 400m, C covers 384 mNow if B covers 395 m, then C will cover(396/400)×395=391.05 mIf C covers 391.05 m, then D will cover(400/384)×391.05=407.24If A and D run over 400 m, then D win by 7.2 m (approx.)
Answer : A
Answer: A
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
Options:
A)25
B)37
C)54
D)65
E)75
Rationale: when divided 2,3,4 leaves remainder 1 and leaves remainder 0 while dividing 5
ANSWER:A
Answer: A
Question: If A : B= 2 : 4 and B : C = 6 : 8, then A : B : C is:
Options:
A)11:2:3
B)22:44:66
C)12:24:32
D)6:9:12
E)4:8:10
Rationale: A:B=2:4, B:C=6:8, A:B:C=2Ã—6:6Ã—4:4Ã—8
â‡’ 12:24:32
Answer: C.
Answer: C
Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%. then what was the cost of the tax free items?
Options:
A)Rs.15
B)Rs.15.70
C)Rs.19.70
D)Rs.20
E)None
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 6% of x	= 30/100
x ‹=› (30/100×100/6)
= 5.
Cost of tax free items	= Rs.[25 - (5 + 0.30)]
= Rs. 19.70
Answer C
Answer: C
Question: If 75 percent of a class answered the first question on a certain test correctly, 45 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A) 40%
B)(8) 20%
C) 30%
D) 50%
E) 65%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 45% - {Both} + 20% --> {Both} = 40%.
Answer: A
Answer: A
Question: There has been successive increases of 25% and then 15% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
Options:
A)30%
B)50%
C)66.66%
D)15%
E)75%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.15*1.25*P = x*P
y = x / (1.15*1.25) which is about 0.7x which is a decrease of about 30%.
The answer is A.
Answer: A
Question: A batch of cookies was divided amomg 3 tins: 2/3 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/5 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin
Options:
A)21/31
B)9/4
C)5/9
D)7/5
E)9/7
Rationale: This will help reduce the number of variables you have to deal with:
G + B = 2/3
R = 1/3
B = 1/5
We can solve for G which is 7/10
What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?
So..
X*(G+R)=G
X*(7/10 + 1/3) = 7/10
X = 21/31
ANSWER: A
Answer: A
Question: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son
Options:
A)34,11
B)35,10
C)36,9
D)40,5
E)None of these
Rationale: Explanation:
Let sons age = x years. Then fathers age = (45 - x)years.
(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9
Their ages are 36 years and 9 years.
Option C
Answer: C
Question: Find 96 ×× 98
Options:
A)92/8
B)92/12
C)92/13
D)92/10
E)92/11
Rationale: Here both numbers are less than 100. So they are deficient of - 4 and - 2 compared with 100. So
Answer:	A
Answer: A
Question: a man owns 1/3 of market reserch beauro buzness,and sells 3/5 of his shares for 15000rs,what is the value of buzness?
Options:
A)55000
B)75000
C)65000
D)190000
E)250000
Rationale: If value of business=x
Total sell (2x/3)(3/4)=15000
->x=75000
ANSWER:B
Answer: B
Question: (x to power 1/3) - (x to power 1/9)=60
We have to find out the value of x ??
Options:
A)4^9
B)4^8
C)4^7
D)4^6
E)4^5
Rationale: let x^(1/9) =y
y^3-y =60
y(y^2-1) = 60
y=4
x^(1/9)= 4
x = 4^9
ANSWER:A
Answer: A
Question: A company recently conducted a survey and found that 20,000 of its customers live in rural areas. If the number of customers who live in urban areas is 100 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
Options:
A)40,000
B)45,000
C)50,000
D)55,000
E)60,000
Rationale: The number of customers in urban areas is 20,000+1*20,000=40,000.
The answer is A.
Answer: A
Question: The vertex of a rectangle are (1, 0), (5, 0), (1, 1) and (5, 1) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
Options:
A)1/2
B)2
C)1/6
D)3
E)1/4
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 0.5). The slope of a line passing through (0,0) and (3, 0.5) is 0.5/3 = 1/6.
The answer is C.
Answer: C
Question: If a and b are different values and a – b = 2(√a - √b), then in terms of b, a equals:
Options:
A)√b
B)b
C)b - 4√b + 4
D)b + 2√b + 1
E)b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 2(√a - √b) -----> ( √a + √b) ( √a - √b) = 2(√a - √b ) -------> √a + √b = 2, so
√a = 2 - √b, square both sides and solve. Answer is C.
Answer: C
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $6 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)$28
B)$82
C)$110
D)$138
E)$196
Rationale: by the question, the equation would be 150 p - 86*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 196. Answer E for me.
Answer: E
Question: Out of the three numbers A, B and C, A exceeds B by 20 and C exceeds A by 55. If the sum of all the numbers is 230, What is the difference between the largest and the smallest number?
Options:
A)87
B)65
C)75
D)19
E)11
Rationale: Explanation:
We have , A = B + 20 & C = A + 55 = B + 75
Thus, (B + 20) + (B) + (B + 75) = 230
B = 45
Thus, A = 65 & C = 120. Hence, (C) – (B) = 120 – 45 = 75
Short-Cut Method : Since C is larger than A by 55 and A is larger than B by 20, we get, the Required difference = 55 + 20 = 75 (without calculating the actual values of A, B and C).
ANSWER:C
Answer: C
Question: In a board game, a stack of 44 cards, 6 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
Options:
A)3/22
B)1/11
C)1/9
D)1/7
E)1/5
Rationale: After 2 cards have been selected, there are 42 cards remaining.
P(third card has a picture of fruit) = 6/42 = 1/7
The answer is D.
Answer: D
Question: The speed of a car increases by 2kms after every one hour. If the distance travelled in the first one hour was 35kms, what was the total distance travelled in 12 hours?
Options:
A)456kms
B)482kms
C)552kms
D)556kms
E)None of these
Rationale: Total distance travelled in 12 hours = (35+37+39+...upto 12 terms).
This is an A.P. with first term, a=35, number of terms, n=12, common difference d=2
Required distance = 12/2(2*35+(12-1)*2)=6(70+22)=552km.
Correct Option: C
Answer: C
Question: In an examination, 300 students appeared. Out of these students; 25 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
Options:
A)63
B)37
C)54
D)99
E)01
Rationale: The number of students with first division = 25 % of 300 = 25/100 × 300 = 8400/100 = 75
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (75 + 162) = 63
Answer:A
Answer: A
Question: It is known that no more than 9 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
Options:
A)35
B)105
C)420
D)210
E)2520
Rationale: The question states that there are no more than 9 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5, 6, 7, 8 or 9 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 9).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6, 7,8,9), i.e., 2520.
Answer (E)
Answer: E
Question: The arithmetic mean of the set S = {7, K, 6, 12, M, 7} is 8. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
Options:
A)6
B)6.5
C)7
D)7.5
E)8
Rationale: The sum of the numbers is 6*8 = 48
K+M = 48 - 12 - 7 - 7 - 6 = 16
Since K ≠ M, K and M do not equal 8.
Thus one of the two numbers is 7 or less and one is 9 or more.
Then middle two numbers in the set are 7 and 7.
The median is 7.
The answer is C.
Answer: C
Question: Find large number 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 15 as remainder
Options:
A)1236
B)1346
C)1657
D)1874
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: John has taken four (6) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
Options:
A)87
B)90
C)92
D)94
E)102
Rationale: 87-82=5*6=30 points
2*87=174
174+30=204 points to be scored in the 2 tests.
Avg of 2 tests = 204/2=102
Answer: E
Traditional Method:
Total scored till now 82*6=492
Total score to avg 87 in 8 tests = 87*8=696
Total to be scored on 2 tests = 696-492=204
Avg on 2 tests = 204/2 = 102
Answer E
Answer: E
Question: A caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $250.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
Options:
A)$0.60
B)$0.80
C)$1.00
D)$1.20
E)$1.40
Rationale: Let price of a sundae = S
Price of ice cream bar = .6 $
125 * .6 + 125*S = 250
=> 125*S = 175
=> S = 1.4
Answer E
Answer: E