divelab/Sys2Bench huggingface dataset:
Question: A, B and C started a shop by investing Rs. 10,000, Rs. 20,000 and Rs. 30,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 9,000, then the total profit was :
Options:
A)30,000
B)60,000
C)18,000
D)120,000
E)None
Rationale: Sol.
A : B : C = 10000 :20000 : 30000 = 1: 2 : 3. so, Câ€™s share : Total Profit = 3 : 6
Let the total profit be Rs. x. Then, 3/6 = 9000/x
x = 9000 * 6 / 3 = 18000.
Answer C
Answer: C
Question: problemsolvingproblemsolvingprob . . . . . . Find the 2015th term in the series?
Options:
A)23
B)26
C)13
D)76
E)18
Rationale: Sol.
Problemsolving = 14 letter word. So divide 2015 by 14 and find the remainder. Here remainder is 13. so 13th letter in problemsolving is 'n'
Answer:C
Answer: C
Question: If the area of circle is 1520 sq cm then its circumference?
Options:
A)221
B)138
C)166
D)116
E)112
Rationale: 22/7 r2 = 1520 => r = 22
2 * 22/7 * 22 = 138
Answer: B
Answer: B
Question: In how many ways can the letters of word EMULATION be arranged such that NO two vowels appear together?
Options:
A)9!
B)5!*4!
C)4!*5!
D)5!*4!*2!
E)6!*4!
Rationale: No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together.
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! ----> C is the correct answer.
Answer: C
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
Options:
A)65, 15
B)64, 16
C)62, 18
D)60, 20
E)61, 30
Rationale: Explanation:
x + y = 80
x – 4y = 5
x = 65 y = 15
ANSWER IS A
Answer: A
Question: How many prime numbers are between 78/14 and 55/4?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 78/14= 39/7 = 6-
55/4 = 14-
Prime numbers between 6 and 14 are 7, 11 and 13
- sign signifies that the number is marginally less .
Answer B
Answer: B
Question: 5 pears and 2 apples cost $16. 3 pears and 3 apples cost $15. How much does one apple cost?
Options:
A)3.5
B)3.25
C)3
D)2.5
E)2
Rationale: Let cost of 1 pear = x, let cost of 1 apple = y
5x + 2y = 16
y = (16 - 5x)/2
Again,
3x + 3y = 15
3x + 3((16 - 5x)/2) = 15
3x + 24 - 7.5x = 15
3x + 24 = 15 + 7.5x
9 = 4.5x
x = 2
Now plug this value into one of the initial equations:
5x + 2y = 16
5(2) + 2y = 16
10 + 2y = 16
2y = 6
y = 3
Answer: C
ANSWER:C
Answer: C
Question: Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?
Options:
A)2140
B)2520
C)2980
D)3260
E)3680
Rationale: The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is B.
Answer: B
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number L of imported lamps stocked at the store?
Options:
A)3
B)10
C)13
D)20
E)23
Rationale: We want to minimize not maximize the expression,.
L=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E
Answer: E
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses?
Options:
A)1/8
B)1/3
C)1/4
D)1/2
E)1
Rationale: P(THH) = 1/2*1/2*1/2=1/8
The answer is A.
Answer: A
Question: By selling 99 pens, a trader gains the cost of 9 pens. Find his gain percentage?
Options:
A)9 1/3%
B)9 7/3%
C)9 1/8%
D)9 1/3%
E)9 1/11%
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 9 pens
= Rs. 9
Profit% = 9/99 * 100
= 9 1/11%
Answer: E
Answer: E
Question: About the number of pairs which have 16 as their HCF and 121 as their LCM, the conclusion can be
Options:
A)only one such pair exists
B)only two such pairs exist
C)many such pairs exist
D)many such pairs exist
E)such pair did not exists
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: E
Answer: E
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 6)%. In terms of x, how many species of bacteria will the group be able to model?
Options:
A)(x)*(106 - x)
B)(x)(105 – x)
C)(100)(105 – x)
D)(100)(95 – x)
E)(x-5)/100
Rationale: Initial: (x/100)*10000 = 100x (bacterial species)
After reduce BY (x - 6)%, the percentage of bacterial species = 1 - (x - 6)% = 1 - (x - 6)/100 = (106 - x)/100
Note: Difference between reduce to[means: the remain] and reduce by[means: the remain = 1 -reduce by]
So, the number of bacterial species after reducing: 100x*(106 - x)/100 = (x)*(106 - x)
Ans is A.
Answer: A
Question: In Township K each property is taxed at 8 percent of its assessed value. If the assessed value of a property in Township K is increased from $18,000 to $28,000, by how much will the property tax increase?
Options:
A) $320
B) $800
C) $320
D) $600
E) $850
Rationale: Increase in house value = $28,000 - $18,000 =$10000
So, tax increase = 8% of$10000=$800
Answer: B
Answer: B
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 24. What is the rate of interest per annum?
Options:
A)8
B)2
C)9
D)4
E)6
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 104
15000[(1 + R/100)2 - 1 - 2R/100] = 24
15000[(100 + R)2 - 10000 - 200R]/10000 = 24
R2 = (24 * 2)/3 = 16 => R = 4
Rate = 4%
Answer: Option D
Answer: D
Question: A sum of Rs. 2691 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)1629
B)1656
C)1277
D)6298
E)1279
Rationale: (x*8*3)/100 = ((2691 - x)*3*5)/100
24x/100 = 40365/100 - 15x/100
39x = 40365 => x = 1035
Second sum = 2691 â€“ 1035 = 1656
Answer:B
Answer: B
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)876
B)268
C)269
D)600
E)278
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer:D
Answer: D
Question: There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be?
Options:
A)4.46
B)4.39
C)4.42
D)4.49
E)4.33
Rationale: (sum of the 4 times)/4 = 4.5
sum of the 4 times = 18
new sum = 18+4.3 = 22.3
new average = 22.3/5 = 4.46
ans: A
Answer: A
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 20 inches and Jordan's rectangle is 6 inches long, how wide is Jordan's rectangle, in inches?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Area of first rectangle is 15*20=300 hence area of second would be 6x=300x
x=50
answer is D
Answer: D
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)2.9 hrs
B)8.9 hrs
C)9.3 hrs
D)7.2 hrs
E)8.6 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/7)
= 3/28
The cistern will be filled in 28/3 hrs i.e., 9.3 hrs.
Answer:C
Answer: C
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)6 kmph
B)9 kmph
C)8 kmph
D)10 kmph
E)1 kmph
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: C
Question: On his drive to work, Leo listens to one of three radio stations A, B or W. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to W. If W is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Options:
A)0.027
B)0.09
C)0.417
D)0.657
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to W and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: D
Question: is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
Options:
A)13 days
B)10 days
C)16 days
D)11 days
E)18 days
Rationale: B
10 days
A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: B
Question: What will be the vulgar fraction of 0.70
Options:
A)3/5
B)7/10
C)3/2
D)3/7
E)3/8
Rationale: Explanation:
0.70 = 70/100 = 7/10
Option B
Answer: B
Question: 220, 218, 214, 208, 200, 190, ?
Options:
A)120
B)140
C)147
D)178
E)189
Rationale: 220
220 - 2 = 218
218 - 4 = 214
214 - 6 = 208
208 - 8 = 200
200 - 10 = 190
190 - 12 = 178
Answer is D
Answer: D
Question: If the President and Vice President must sit next to each other in a row with 6 other members of the Board, how many different seating arrangements are possible?
Options:
A)120
B)240
C)300
D)10080
E)720
Rationale: We need to take President and VP as one unit. Therefore we have 7 people to arrange=7! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=7!*2!=10080 ways
Answer D
Answer: D
Question: Of the science books in a certain supply room, 50 are on botany, 62 are on zoology, 83 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
Options:
A)321
B)159
C)166
D)285
E)324
Rationale: First, you can take all 50 Botany books, all 62 zoology books and all 50 geology books because you're sure to never pick 80 of them.
There are still 83 on physics and 110 on chemistry
The worst case could be that we pick 79 physics and 79 chemistry. So that the next book picked will necessary complete 80 books picked, either in physics or chemistry.
Minimum number of books picked to reach 80 in the same science should be : 50 + 62 + 50 + 79 +79 + 1 = 321
A
Answer: A
Question: The present worth of Rs.169 due in 2 years at 4% per annum compound interest is
Options:
A)Rs 155.25
B)Rs 156.25
C)Rs 157.25
D)Rs 158.25
E)None of these
Rationale: Explanation:
In this type of question we apply formula
Amount=P /(1+R/100)n
Amount=169 /(1+4/100)2
Amount=169∗25∗25/26∗26
Amount=156.25
Option B
Answer: B
Question: For prime numbers x and y, x^3*y^5=z^4. How many positive factors does positive integer z have?
Options:
A)One
B)Two
C)Three
D)Four
E)Five
Rationale: Solution: given x^3*y^5=z^4; here if x and y are two different prime numbers then z = x^3/4 * y^5/4
in this case z can not be and integer.
now to make z = (x^3*y^5)^1/4 an integer it is required to have x=y then equation will become z=x^2 or z=y^2
hence total positive factors will be 3.	ANSWER:C
Answer: C
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
Options:
A)20%
B)40%
C)50%
D)80%
E)30%
Rationale: C
50%
L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: C
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options:
A)10 days
B)11 days
C)15 days
D)20 days
E)None of these
Rationale: B's 1 day's work=(1/12-1/20)=2/60=1/30
Now, (A+B)'s 1 day's work=(1/20+1/60)=4/60=1/15
So, A and B together will complete the work in 15 days.
Correct Option: C
Answer: C
Question: Mike has forty-five cents. If mike gives away two nickles and a dime, how much money does he have left?
Options:
A)10 cents
B)16 cents
C)35 cents
D)25 cents
E)40 cents
Rationale: Nickle = 5 cents
Dime = 10 cents
45-(2)5-10 = 25
D.25 cents
Answer: D
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
Options:
A)Rs. 113.5
B)Rs. 119.7
C)Rs. 124.75
D)Rs. 130.75
E)Rs. 134.45
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: C
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 60, what is his shoe size?
Options:
A)25
B)60
C)35
D)40
E)50
Rationale: Solution -
Given that, G = 2B and Life expectancy(L) = 60
L=2SB/G -> 60 = 2SB/2B --> S=60.
ANS B
Answer: B
Question: A car gets 60 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 170 kilometers?
Options:
A)3.5 gallons
B)2.37 gallons
C)5.7 gallons
D)4.25 gallons
E)2.83 gallons
Rationale: Each 60 kilometers, 1 gallon is needed. We need to know how many 60 kilometers are there in 170 kilometers?
60 Ã· 170 = 2.83 Ã— 1 gallon = 2.83 gallons
correct answer is E) 2.83 gallons
Answer: E
Question: Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank?
Options:
A)70
B)71
C)80
D)90
E)96
Rationale: A
Answer: A
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 33 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 litres
C)11 litres
D)07 litres
E)38 litres
Rationale: 262.85(33)+3,104.35x = 1,399.45(33 + x)
Solve the equation.
262.85(33)+3,104.35x = 1,399.45(33 + x)
8,674.05 + 3,104.35x = 46181.85 + 1,369.45x
8,674.05 + 1,704.9x = 46181.85
1,704.9x = 37,507.8
x = 22
Answer is B.
Answer: B
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.11 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1276
B)1200
C)2832
D)1299
E)1320
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 11 = 1320
Answer: Option E
Answer: E
Question: 189. The inside dimensions of a rectangular wooden box
are 12 inches by 14 inches by 16 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
Options:
A) 3
B) 4
C) 5
D) 6
E) 7
Rationale: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 16x14width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 14, so the radius will be 7.
E
Answer: E
Question: If a fair coin is tossed six times, what is the probability of getting exactly five heads in a row?
Options:
A)1/64
B)1/32
C)1/16
D)3/64
E)3/32
Rationale: P(HHHHHT) = 1/64
P(THHHHH) = 1/64
The sum of these probabilities is 2/64 = 1/32
The answer is B.
Answer: B
Question: If an integer r is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that r(r + 1)(r + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: for r Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Answer: D
Question: there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
Options:
A)15.42
B)37.25
C)12.54
D)32.37
E)23.47
Rationale: Sol: total weight of(36+44) students=(36*40+44*35)kg =2980kg.
Therefore weight of the total class=(2980/80)kg =37.25kg.
Ans: B
Answer: B
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm2. Find the lengths of all sides.
Options:
A)10 and 3
B)7 and 10
C)10 and 7
D)3 and 10
E)10 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 18 cm2 more than the first area. Therefore
A1+18=A2
x(x−3)+18=(x+1)(x−2)
x2−3x+18=x2+x−2x−2
2x=20
x=10. So, the sides of the rectangle are 10 cm and (10−3)=7 cm long.
So answer is C.
Answer: C
Question: Ella leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Ella's house. The distance between their homes is 42 kilometers, Ella's walking speed is 5 km/h, and Ed's walking speed is 3 km/h. How many kilometers will Ella walk before she meets Ed?
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: Ella walks 10 km in the first two hours so there are 32 km remaining.
When Ed starts walking, they complete a total of 8 km per hour.
They will meet four hours after Ed starts walking.
Since Ella walks for 6 hours, she walks 30 km.
The answer is C.
Answer: C
Question: John bought 9.25m of cloth for $407. Find the cost price per metre.
Options:
A)46
B)47
C)58
D)44
E)54
Rationale: Cloth bought by John = 9.25 m
Cost of 9.25 m = $407
Cost per metre = 407 ÷ 9.25
The cost of the cloth per metre = $ 44
Answers: D
Answer: D
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 11 unsaleable mangoes in the crate then how msny mango are there in the crate?
Options:
A)100 mangoes
B)110 mangoes
C)120 mangoes
D)130 mangoes
E)125 mangoes
Rationale: 110 mangoes
ANSWER:B
Answer: B
Question: four children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
Options:
A)560
B)720
C)1440
D)4320
E)4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 560.
A is the right answer.
Answer: A
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Options:
A)10
B)11
C)12
D)15
E)19
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: C
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $6840. What is the average monthly balance maintained by John in his
account during the year?
Options:
A)2840
B)5680
C)6840
D)7540
E)34200
Rationale: Soln:-
Bank balance is doubled with accumulation of interest to 6840..
this means INTEREST is 6840/2=3420 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 34200..
ANSWER:E
Answer: E
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1680, then what is the smallest possible value of n?
Options:
A)4
B)6
C)7
D)10
E)12
Rationale: 3360=2^4*3*5*7
2^4 means that n must be at least 6. That is, We need 2, 4, and 6.
However, we also need 7, so n must be at least 7.
The answer is C.
Answer: C
Question: The average of first 16 even numbers is?
Options:
A)19
B)18
C)16
D)11
E)17
Rationale: Sum of 16 even numbers = 16 * 17 = 272
Average = 272/16 = 17
Answer:E
Answer: E
Question: The number of students in the three sections of a class are in the ratio 2:3:4. The average marks scored in each of these sections is in the ratio 4:3:1. By what percent is the average mark of the second section more than the class average?
Options:
A)23.27%
B)28.57%
C)32.38%
D)36.74%
E)38.74%
Rationale: Let the number of students be 2x, 3x, 4x.
Let the average marks be 4y,3y,y.
Average mark of class = ( 8xy+9xy+4xy)/(2x+3x+4x)
=21xy/9x=7y/3
Percentage difference = ( 3y - 7y/3)/7y/3 *100
= 28.57%
ANSWER:B
Answer: B
Question: If a*b=2a-3b+ab,then3*5+5*3 is equal to
Options:
A)22
B)24
C)26
D)28
E)30
Rationale: 3*5+5*3= (2x3-3x5+3x5)+(2x5-3x3+5x3)
=22
ANSWER A 22
Answer: A
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Options:
A)299
B)277
C)298
D)600
E)271
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D
Answer: D
Question: The average of a non zero number and its square is 5 times the number. The number is
Options:
A)9
B)17
C)29
D)295
E)None
Rationale: Sol.
Let the number be x. Then,
x + x2 / 2 = 5x
‹=› x2 – 9x = 0
‹=› x (x - 9) = 0
‹=› x = 0 or x = 9.
So, the number is 9.
Answer A
Answer: A
Question: If the mean of numbers 38, x, 70, 88 and 110 is 69, what is the mean of 50, 72, 97, 125,147 and x?
Options:
A)73.5
B)77.86
C)86.67
D)66.69
E)70.56
Rationale: Mean = (Sum of all no. in series)/(no. in series)
M1 = 69 = (X+38+70+88+110)/(5)
69 x 5 = 290 + X
X = 39
Therefore mean of 2nd series
M2 = (X+50+62+97+125+147)/6
M2 = 86.67
Answer = C
Answer: C
Question: What is the ratio whose terms differ by 40 and the measure of which is 2⁄7
Options:
A)16 : 56
B)14 : 56
C)15 : 56
D)16 : 72
E)None of these
Rationale: Let the ratio be x: (x + 40).Then,
x/(x+40)=2/7 ⇒ 2x + 80 ⇒ x = 16.
∴ Required ratio = 16 : 56.
Answer A
Answer: A
Question: Find the greatest number which leaves the same remainder when it divides 21, 57 and 105.
Options:
A)18
B)8
C)12
D)16
E)None of these
Rationale: 105 - 57 = 48
57 - 21 = 36
105 - 21 = 84
The H.C.F of 36, 48 and 84 is 12.
ANSWER:C
Answer: C