divelab/Sys2Bench huggingface dataset:
Question: A certain car can travel 56 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
Options:
A)52
B)65
C)78
D)91
E)104
Rationale: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters
Time = 5.7 hours
1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile
Speed (km/hour)= D/T = 56(km*) x 3.9 x 3.8 / 5.7
replace (km*) to miles ; multiply by 1/1.6 mile
Speed (miles/hour)= 56 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour
Ans :D
PS :i felt the factors were easy to cancel out ,so didn't require much rounding off
= 56 x 3.9 x 3.8 / 5.7 x 1.6
= 91
D
Answer: D
Question: Which of the following integers has the most number of divisors?
Options:
A)176
B)180
C)190
D)200
E)215
Rationale: 99 = 1*3*3*11
=> divisors of 99 are 1,3,11,9,33 and 99
101 = 1*101
divisors 182 are 1,2,7,13,14,26,91 and 182
176=is most no of divisors
ANSWER A
Answer: A
Question: A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained?
Options:
A)2878
B)8000
C)1000
D)2997
E)2701
Rationale: Along one edge, the number of small cubes that can be cut
= 100/5 = 20
Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 20 * 20 * 20 = 8000
Answer: B
Answer: B
Question: Local kennel has cats and dogs in the ratio of 6:8. If there are 10 fewer cats than dogs, how many dogs are in the kennel?
Options:
A)30
B)35
C)45
D)50
E)40
Rationale: Lets work with the data given to us. We know that there ratio of cats to dogs is 6:8 or
cats 6
dogs 8
we can write number of cats as 6x and number of dogs as 8x and we know that 8x-6x= 10(therefore 2x = 10 => x=5)
Then # of dogs = 8x5= 40
Answer is E
Answer: E
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/5
B)5/9
C)5/1
D)5/6
E)5/2
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C1/10C3
= 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Answer: D
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 13 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
Options:
A)20
B)78
C)59
D)90
E)100
Rationale: to choose the sample of 2 customers from 13. it can be done 13C2 possible ways.
So the answer is B. 78
Answer: B
Question: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: a= 5^15 - 625^3 => 5^15 - (5^4)^3 => 5^15 - 5^12 = 5^12(5^3 - 1) = 5^12*124
124 = 31*4
a/x is integer
For condition of 2<p<x only 5 and 31 satisfies this
Hence answer is C
Answer: C
Question: A positive integer n is called a “good” number if n3 + 7n − 133 = m3 for
some positive integer m. What is the sum of all “good” numbers?
Options:
A)24
B)25
C)29
D)30
E)0
Rationale: We consider the size of m relative to n. If m = n, then n is a good number if and only if
7n = 133. In this case, we get 19 is a good number. Now, suppose that m n + 1. Then
n3 + 7n − 133 = m3 (n + 1)3 = n3 + 3n2 + 3n + 1
so that 3n2 − 4n + 134 0. For positive integers n, it is easy to see that this is impossible. It
remains to consider m n − 1. For such m, we have
n3 + 7n − 133 = m3 (n − 1)3 = n3 − 3n2 + 3n − 1
which implies 3n2 + 4n − 132 0. It follows here that n 6. One checks that
63 + 7 · 6 − 133 = 53 and 53 + 7 · 5 − 133 = 33,
so 6 and 5 are good numbers. For n 4, we see that n3 +7n−133 < 0 and, hence, n3 +7n−133
cannot equalm3 for a positive integerm. Therefore, the sum of all good numbers is 19+6+5 = 30.
correct answer D
Answer: D
Question: Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ?
Options:
A)£ 9
B)£ 11
C)£ 13
D)£ 15
E)None of the these
Rationale: Explanation:
Let money with Ken = x. Then, money with Mac = x + £ 3.
Now, 3x = (x + x + £ 3) + £ 2 x = £ 5.
Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
Answer: C
Answer: C
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 15 nor by 20?
Options:
A)887
B)678
C)765
D)345
E)256
Rationale: In 1000 consecutive numbers, number of multiples of 15 = 1000/15 = 66 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 20 = 1000/20 = 50
Number of multiples of 15*20 i.e. 300 = 1000/300 = 3
Number of integers from 1 to 1000 that are divisible by neither 15 nor by 20 = 1000 - (66 + 50 - 3) {Using the concept of sets here) = 887
Answer is A
Answer: A
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 8% sugar. What percentage of the gallon is dye?
Options:
A) 6
B) 6.4
C) 7.5
D) 8
E) 24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/8
=> 4/5 = x/8 => x = 4*8/5 = 6.4
Answer is B
Answer: B
Question: Little John had $10.10. He spent $3.25 on sweets and gave to his two friends $2.20 each. How much money was left?
Options:
A)$2.45
B)$2.54
C)$2.35
D)$2.48
E)$2.49
Rationale: John spent and gave to his two friends a total of
3.25 + 2.20 + 2.20 = $7.65
Money left
10.10 - 7.65 = $2.45
Answer :A
Answer: A
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9-sided polygon)?
Options:
A)1/2
B)1/3
C)1/4
D)1/6
E)1/9
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/6 = 1/3.
The answer is B.
Answer: B
Question: A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio.
Options:
A)35:44
B)34:44
C)22:44
D)20:40
E)50:45
Rationale: In case of stock1, if he invest Rs.105, he will get a dividend of Rs.12 (assume face value = 100)
In case of stock2, if he invest Rs.88, he will get a dividend of Rs.8 (assume face value = 100)
ie, if he invest Rs.(88*12)/8, he will get a dividend of Rs.12
Required ratio = 105 : (88 × 12)/8 = 105 : (11 × 12) = 35 : (11 × 4) = 35 : 44
Answer is A.
Answer: A
Question: A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 45% of which are not silver, what percentage of total number of cars are silver?
Options:
A)30%
B)35%
C)40%
D)45%
E)50%
Rationale: The number of silver cars is 0.15*40 + 0.45*80 = 42
The percentage of cars which are silver is 42/120 = 35%
The answer is B.
Answer: B
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Options:
A)384
B)288
C)277
D)299
E)212
Rationale: Average mark scored by all the three boys
= [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer: A
Answer: A
Question: A set of numbers has the property that for any number t in the set, t + 5 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 4
III. 5
Options:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
Rationale: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be -1+5=4, as 4 is in the set so must be 4+5=9, as 9 is in the set so must be 9+5=14 and so on.
Answer: B.
Answer: B
Question: A scooter costs 30,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
Options:
A)10,000
B)12,500
C)12,800
D)12,000
E)15,360
Rationale: After first year, the value of the scooter = 24,000
After second year, the value of scooter = 19,200
After third year, the value of scooter = 15,360
Answer E
Answer: E
Question: When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
Options:
A)40
B)65
C)73
D)60
E)80
Rationale: D
60
Let the number be
2 + 1/2[1/3(a/5)] = a/15
=> 2 = a/30 => a = 60
Answer: D
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for 95 cents, and Zachary buys a pencil and an eraser for 55 cents. How many cents would it cost to buy three pencils, three notebooks, and three erasers? (Assume that there is no volume discount.)
Options:
A)305
B)325
C)345
D)365
E)385
Rationale: pencil + notebook = 80
notebook + eraser = 95
pencil + eraser = 55
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 230 cents
The cost to buy 3 of each would be (3/2)(230) = 345
The answer is C.
Answer: C
Question: Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?
Options:
A)50
B)70
C)140
D)190
E)210
Rationale: Tc : Tea caffeine
Td : Tea No caffeine
Cc : Coffee Caffeine
Cd : Coffee No Caffeine
As per question, Tc + Td + Cc + Cd = 460 -- (1)
Also, Tc + Cc = 270 -- (2)
Td = 2 * Tc -- (3)
Cc + Cd = 250 -- (4)
Now, substituting (4) in (1), we will have Tc + Td + 250 = 460
or Tc + Td = 210. -- (5)
Substitute (3) in (5), we will get Tc = 70. Substitute Tc in (2), we will get Cc = 200
Now substitute Cc in (4), we will get Cd = 50. hence, A
Answer: A
Question: At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is sixty percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
Options:
A)1.5j + 10
B)3j + 20
C)4.5j + 30
D)5.5j + 30
E)8.6j + 52
Rationale: Ans E
Given
Price of Jeans = J
Price of shoes = 20+3J
Price of Sweater = 1.6(20+3J)
Total Price of all three items = J+20+3J+1.6(20+3J) = 52+8.6J
Answer: E
Question: In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
Options:
A)240,000
B)300,000
C)168,000
D)36,000
E)24,000
Rationale: Explanatory Answer
Let the percentage of the total votes secured by Party D be x%
Then the percentage of total votes secured by Party R = (x - 12)%
As there are only two parties contesting in the election, the sum total of the votes secured by the two parties should total up to 100%
i.e., x + x - 12 = 100
2x - 12 = 100
or 2x = 112 or x = 56%.
If Party D got 56% of the votes, then Party got (56 - 12) = 44% of the total votes.
44% of the total votes = 132,000
i.e., 44/100*T = 132,000
=> T = 132000*100/44 = 300,000 votes.
The margin by which Party R lost the election = 12% of the total votes
= 12% of 300,000 = 36,000.
The correct choice is (D)
Answer: D
Question: Each of the following numbers has a remainder of 4 when divided by 6 except:
Options:
A)4
B)16
C)64
D)26
E)46
Rationale: It's D
26 = 6*4+2
Answer: D
Question: A man spends 10% of his income in house rent, 20% of the rest on his childrenâ€™s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
Options:
A)3600
B)4500
C)5000
D)2000
E)2500
Rationale: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
ANSWER A
Answer: A
Question: In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
Options:
A)13
B)15
C)12
D)7
E)9
Rationale: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.
Now, according to the question,
nC2 = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n^2-n = 210;
Or, n^2-n-210 = 0;
Or, n = 15, -14;
But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.
Ans: B
Answer: B
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)12 years
B)15 years
C)11years
D)22years
E)20 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Ans- D
Answer: D
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)A)3820
B)B)930
C)C)9309
D)D)3900
E)E)5625
Rationale: Explanation:
Area = (l + b – d) d
(80 + 60 – 15)15 => 1875 m2
1875 * 3 = Rs.5625
Answer: Option E
Answer: E
Question: If Sand is coded as Brick, Brick as House, House as Temple, Temple as Palace then where do you worship?
Options:
A)Palace
B)Temple
C)Brick
D)House
E)none
Rationale: palace because temple is coded as palace
ANSWER:A
Answer: A
Question: Today X is twice as old as Y and Y is 3 years younger than Z. If X, Y, and Z are all alive 4 years from today, which of the following must be true on that day. I. X is twice as old as Y II. Y is 3 years younger than Z III. X is older than Z
Options:
A)I
B)II
C)I,II & III
D)III
E)II, III
Rationale: Say Z age is 10
Y age is 7
X age is 14
After 4 years
Z age is 14
Y age is 11
X age is 28
i.e ) after 4 years
Y is 3 years younger than Z
X is twice as old as Y
X is older than Z
Answer : C
Answer: C
Question: If a farmer wants to plough a farm field on time, he must plough 260 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Options:
A)312
B)490
C)720
D)435
E)679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 260â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
260x=85(x+2)+40
175x=210
x=1.2
So the farmer planned to have the work done in 6 days, and the area of the farm field is 260(1.2)=312 hectares
correct answer A
Answer: A
Question: Find the last digit of (1021^3921)+(3081^3921)
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: last digit of 1st expression is 1 and second expression is also 1
as, 1 raised to any power will be 1 itself
so, 1+1 = 2
so the last digit will be 2
ANSWER:C
Answer: C
Question: Three pipes A, B and C can fill a tank in 4 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 5 hours. How many hours will take C alone to fill the tank?
Options:
A)10/3
B)15/4
C)20/3
D)25/4
E)35/6
Rationale: The rate of A+B+C is 1/4 of the tank per hour.
After 2 hours, the tank is half full.
The rate of A+B is 1/2 * 1/5 = 1/10 of a tank per hour.
The rate of C is 1/4 - 1/10 = 3/20
C can fill the tank in 20/3 hours.
The answer is C.
Answer: C
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
Options:
A)207
B)530
C)648
D)600
E)700
Rationale: No of shares = 4455/8.25 = 540
face value = 540*10 = 5400
annual income = 12/100*5400 = 648
ANSWER C
Answer: C
Question: Given that 0 < a < b < c < d, which of the following the largest ?
Options:
A)(c+d) / (a+b)
B)(a+d) / (b+c)
C)(b+c) / (a+d)
D)(b+d) / (a+c)
E)None
Rationale: Explanation :
For the fraction to be largest, denominator should be minimum and numerator should be maximium.
Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.
Hence 1.) (c+d) / (a+b)
Answer : A
Answer: A
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)Rs. 2000
B)Rs. 2200
C)Rs. 2300
D)Rs. 2400
E)Rs. 2500
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
D
Answer: D
Question: In a Fish tank there are 8 fishes are there. In how many possibilities to choose 6 fishes from the tank?
Options:
A)20
B)21
C)28
D)8
E)30
Rationale: The possible way to select 6 fishes out of 10 fishes in the tank is 8C6.
8C6=8!/2!*6!=8*7*6!/6!*2*1
8C6=28
There are 28 ways to select a 6 fishes from the tank.
Answer: C
Question: John and Peter are among the nine players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?
Options:
A)3/10
B)4/11
C)5/12
D)6/13
E)7/15
Rationale: The total possible ways of selecting a 6-member team is 9C6 = 84
The possible ways which include John and Peter is 7C4 = 35
The probability of choosing both John and Peter is 35/84 = 5/12
The answer is C.
Answer: C
Question: A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
A)2
B)8
C)9
D)11
E)15
Rationale: 220 + 43 = 263/17 = 8 (Remainder)
B
Answer: B
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options:
A)2520
B)2376
C)3235
D)3569
E)6323
Rationale: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m2
Answer:A
Answer: A
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 84 km downstream
Options:
A)1 hour 40 min
B)2 hour 40 min
C)1 hour 20 min
D)1 hour 30 min
E)1 hour 50 min
Rationale: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 84 km
Time taken =distance/speed
=84/52
= 1.66 hours
= 1 hour 40 min.
ANSWER:A
Answer: A
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour ?
Options:
A)8 minutes
B)10 minutes
C)12 minutes
D)14 minutes
E)16 minutes
Rationale: Explanation:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54) hour
= (1/6)*60 minutes
= 10 minutes
Option B
Answer: B
Question: I bought two books; for Rs.450. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)337
B)262.5
C)299.5
D)266.5
E)299
Rationale: x*(85/100) = (450 - x)119/100
x = 262.5
Answer: B
Answer: B
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)6.24 km
B)6 km
C)5.76 km
D)5.66 km
E)7 km
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
ANSWER:C
Answer: C
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 7 on the two dice?
Options:
A)7/12
B)5/12
C)11/36
D)7/36
E)5/36
Rationale: There are 36 possible outcomes for two dice.
The number of outcomes with an even number on the first die is 3*6=18.
The number of outcomes with a sum of 7 is 6.
We need to subtract the outcomes that have both an even number on the first die and a sum of 7 because we have counted those outcomes twice. This number of outcomes is 3.
The number of outcomes with either an even number on the first die or a sum of 7 is 18+6-3=21.
The probability is 21/36=7/12.
The answer is A.
Answer: A
Question: Submarine P and Submarine Q are equipped with sonar devices that can operate within a 5,000 yard range. Submarine P remains in place while Submarine Q moves 4,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West
Options:
A)I only
B)I and III only
C)II only
D)III only
E)I,II only
Rationale: It's evident if we make a diagram for the Movement of Q respect to P.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : B
Answer: B
Question: The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?
Options:
A)20 sq. ft
B)27 sq. ft
C)37 sq. ft
D)47 sq. ft
E)57 sq. ft
Rationale: Other side	=
15 2	- 9 2
2	2
ft
=
225	-	81
4	4
ft
=
144
4
ft
=	6 ft.
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
B)
Answer: B
Question: A card is drawn from a pack of 52 cards. The probability of getting a face card?
Options:
A)2/15
B)2/13
C)1/15
D)4/13
E)5/7
Rationale: Clearly in the 52 cards out of which there are 16 face cards.
probability of getting a face card = 16/52 = 4/13
correct option is D
Answer: D
Question: A cube of edge 6 cm is cut into cubes each of edge 3 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
Options:
A)1:4
B)1:25
C)1:52
D)1:522
E)None
Rationale: Sol.
Required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1/4= 1:4.
Answer A
Answer: A
Question: If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is
Options:
A)3:4
B)2:3
C)4:3
D)1:3
E)1:5
Rationale: total profit =1000
ratio=400/600
=2:3
ANSWER:B
Answer: B
Question: 385, 462, 572, 396, 427, 671, 264
Options:
A)385
B)427
C)671
D)264
E)None of these
Rationale: Solution
In each number except 427,the middle digit is the sum of the other two. Answer B
Answer: B
Question: Obra drove 200π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
Options:
A)6.67%
B)12.5%
C)41.66%
D)25%
E)33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 200π/480π =41.66%
Hence, answer is C.
Answer: C
Question: Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6 , then the resultant number contains same all digits, different places
Options:
A)143857
B)142857
C)144857
D)142853
E)142854
Rationale: Correct Answer : B
142857 * 1= 142857
142857 * 2= 285714
142857 * 3= 428571
142857 * 4= 571428
142857 * 5= 714285
142857 * 6= 857142
Answer: B