divelab/Sys2Bench huggingface dataset:
Question: A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
Options:
A)1/36
B)5/36
C)10/36
D)15/36
E)20/36
Rationale: First off, we want to find the probability of rolling a pair of any number. There are six
pairs and a total of 36 different ways to roll a pair of dices: 6/36 = 1/6.
Next, we want to account for the third die - it cannot be the same as the first two,
so it can be any of five numbers out of 6: 5/6.
Therefore probability is 5/6 x 1/6 = 5/36.
It is tempting here to think that we have solved the problem. But if we read carefully, the
question does not say that the first two dice have to be the same and the third die has
to be different.
the question says a gambler rolls 3 dice. So the first two do not have to be pairs.
As long as 2 of the 3 dice are pairs and the last die is a different number. To find the
number of way this can occur, we use combinations formula: 3!/2!1! = 3.
We multiply this to the numerator to give us 3 x 5/36 = 15/36.
ANSWER:D
Answer: D
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 5 days?
Options:
A)3
B)5
C)6
D)9
E)12
Rationale: Explanation: If six computers require 15 days to process the data, thats
a total of 90 computer-days the product of 6 and 15. If you change the number
of computers or the number of days, 90 will have to remain the product, whether
that means 90 days of one computer or one day with 90 computers.
In 5 days, the number of computers is:
5c = 90
c = 18
18 computers is 12 more than the 6 that it took to do the job in 15 days, so
the correct choice is (E).
Answer: E
Question: In a business, three friends X,Y and Z shared the profit in the ratio 5:7:8. X invested his amount for 14 months, Y for 8 months and Z for 7 months respectively. Find the ratio of their investments?
Options:
A)19:49:64
B)20:49:64
C)20:49:65
D)20:50:64
E)None
Rationale: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively Then, 14x : 8y : 7z = 5 : 7 : 8 Now, 14x/8y = 5/7 => y = (49/20)x 14x/7z = 5/8 => z = (16/5)x => x : y : z = x : (49/20)x : (16/5)x => x : y : z = 20 : 49 : 64
Answer B
Answer: B
Question: In Town X, 90 percent of the population are employed, and 20 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)66%
C)77%
D)88%
E)52%
Rationale: Total employed people 90%, out of which 20 are employed males, hence 70% are employed females.
(employed females)/(total employed people)=70/90=7/9=77%
Answer: C.
Answer: C
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Explanation:
63 + 83 + 103 = a3 => a = 12
A)
Answer: A
Question: Insert the missing number
3, -9, 27, -81, 243, (....)
Options:
A)0
B)-739
C)729
D)739
E)-729
Rationale: 3*-3=-9
-9*-3=27
27*-3=-81
-81*-3=243
243*-3=-729
ANSWER:E
Answer: E
Question: A certain mixture of nuts consists of 5 parts almonds to 1 parts walnuts, by weight. What is the number of pounds of almonds in 140 pounds of the mixture ?
Options:
A) 116
B) 84
C) 40
D) 28
E) 20
Rationale: Almonds : Walnuts = 5 : 1
Total mixture has 6 parts
In a 140 pound mixture, Almonds are 5/6 (total mixture)
= 5/6 * 140 = 116 pounds
Answer (A)
Answer: A
Question: In a can, there is a mixture of milk and water in the ratio 8 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5. Find the capacity of the can?
Options:
A)40
B)18.4
C)48
D)50
E)56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 8/13 (T - 8)
After adding milk, quantity of milk in the mixture = 12/17 T.
12T/17 - 8 = 8/13(T - 8)
20T = 1456 - 1088 => T = 18.4.
Answer:B
Answer: B
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C
Options:
A)Rs. 300
B)Rs. 400
C)Rs. 500
D)Rs. 600
E)None of these
Rationale: Explanation:
C's 1 day's work =
1/3−(1/6+1/8)
=(1/3−7/24)
=1/24
A:B:C=1/6:1/8:1/24
=4:3:1
C′sShare=1/8∗3200=400
Option B
Answer: B
Question: For how many integers n is 1^n+3 = (n+3)^1?
Options:
A)None of these
B)1
C)2
D)3
E)4
Rationale: If n=0
1^0+3= (0+3)^1
1^3 = 1 ; 3^1 =1 not ok
If n=1
1^1+3 =1 ; (1+3)^1=3^1=3 not OK
So, Answer : A
Answer: A
Question: one men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
Options:
A)4 days
B)5 days
C)6 days
D)7 days
E)8 days
Rationale: 1M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
35M + 105W = 84M +84M
21W = 49M
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
ANSWER:B
Answer: B
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)887
B)400
C)187
D)278
E)191
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages
1/6 : 1/8 : 1/24 = 4:3:1
C's share = 1/8 * 3200 = Rs. 400
Answer:B
Answer: B
Question: One woman and one man can build a wall together in one hour, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them two hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
Options:
A)5/7
B)6/7
C)10/7
D)12/7
E)22/7
Rationale: Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/1-->(1) , w + 2g = 1/1-->(2) and m + g =1/2-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/6,m=1/3 and w=2/3.
So, n = 1/(7/6) = 6/7
Option, B
Answer: B
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
Options:
A)12:8
B)8:16
C)9:16
D)8 :12
E)16:9
Rationale: Water:soap = 3:2
Soap:Salt=12:8
=> For 12 soap, salt = 8
=> For 2 Soap, salt = (8/12)*2 = 16/12=4/3
So, water:soap:salt = 3:2:4/3 = 9:6:4
After open container, water:soap:salt = 2.25:6:4
So, water:salt = 2.25:4 = 9:16
ANSWER:C
Answer: C
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Options:
A)Rs.932
B)Rs.132
C)Rs.108
D)Rs.109
E)Rs.131
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer: B
Answer: B
Question: A = {2,0, 1, -3, 6, -8}
B = {-1, 2, -4, 7,-6,20}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
Options:
A)1/4
B)1/3
C)5/12
D)4/9
E)1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/6*3/6 = 9/36;
P(negative, negative) = 2/6*3/6 = 6/36.
P = 9/36 + 6/36
= 15/36
= 5/12.
Answer: C.
Answer: C
Question: When a=x+(3/x) and b=x-(3/x), (2^a^2)/(2^b^2)=?
Options:
A)2
B)4
C)8
D)16
E)4096
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/x and a+b=2x, 2^(a-b)(a+b)=2^(6/x)(2x)=2^12=4096
Therefore, the answer is E
Answer: E
Question: A person travels equal distances with speeds of 5 km/hr, 6 km/hr and 7 km/hr and takes a total time of 47 minutes. The total distance is?
Options:
A)5 km
B)3 km
C)7 km
D)9 km
E)2 km
Rationale: Let the total distance be 3x km.
Then, x/5 + x/6 + x/7 = 27/53
27x/53 = 47/60 => x = 1.54
Total distance = 3 * 1.54 = 4.61 km.
Answer:A
Answer: A
Question: The arithmetic mean of set G is zero. If H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of G consisting of all those elements in G which are more than two but less than three standard deviations away from the arithmetic mean of G, what could be equal to the standard deviation of G?
Options:
A)0.54
B)0.77
C)0.82
D)0.97
E)1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S
H consists of all those elements in G that are more than 2 but less than 3 GDs away from the arithmetic mean of G
If an element is 1 GD away from the mean, we can write it as either m + GD or m - GD
Similarly, if an element is 2 GDs away from the mean, we can write it as either m + 2*GD or m - 2*GD
So, if these elements lie within 2 and 3GDs of mean, m=0
we can find which one of these values of GD satisfies each value within H
Only GD = 0.77 does
Answer : B
Answer: B
Question: A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:
Options:
A)430 Sq.m
B)425 Sq.m
C)450 Sq.m
D)475 Sq.m
E)350 Sq.m
Rationale: Distance covered in (9×1000)/(3600) × 12 = 30 m
Diagonal of squarre field = 30 m.
area of square field = 30(power)2/2
= 900/2 = 450 Sq.m
Answer is C.
Answer: C
Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
Options:
A)0
B)20
C)10
D)18
E)28
Rationale: Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.
Total number of candidates = 200.
Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.
We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.
ANSWER:C
Answer: C
Question: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.8. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
Options:
A)1/5
B)2/5
C)3/5
D)4/5
E)12/25
Rationale: p(m) =0.2
p(r) =0.2
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.2 =0.4
Corrected !!
Answer B
Answer: B
Question: Simplify: (i) 12.05*5.4+0.6
Options:
A)101.45
B)103.45
C)108.45
D)107.45
E)109.45
Rationale: Given exp. = 12.05*(5.4/0.6) = (12.05*9) = 108.45
Answer is C.
Answer: C
Question: How many different ways can 2 students be seated in a row of 6 desks, so that there is always at least one empty desk between the students?
Options:
A) 2
B) 3
C) 4
D)20
E) 12
Rationale: 10 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
10x2=20
D
Answer: D
Question: If a 3-member subcommittee is to be formed from a certain 5-member committee, how many different such subcommittee are possible?
Options:
A)6
B)10
C)20
D)108
E)216
Rationale: 1st member can be selected in 5 ways
2nd can be selected in 4 ways
3rd can be selected in 3 ways
So total ways : 60
But to avoid the similar scenarios 60/3!=10
ANS:B
Answer: B
Question: A train 400 m long passed a pole in 40 sec. How long will it take to pass a platform 600 m long?
Options:
A)28 sec
B)100 sec
C)85 sec
D)16 sec
E)15 sec
Rationale: Speed = 400/40 = 10 m/sec.
Required time = (400 + 600)/10
= 100 sec.
Answer:B
Answer: B
Question: In a certain parking lot, 2% of the cars are towed for parking illegally. However 90% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
Options:
A)10%
B)12%
C)16%
D)18%
E)20%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
2%*x = 10%*y
y/x = 1/5 = 20%
The answer is E.
Answer: E
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 34 percent of the total votes?
Options:
A)10%
B)12.5%
C)15%
D)17.5%
E)20%
Rationale: There were 80% of the votes remaining and he needed 14%/80% = 7/40 = 17.5%
The answer is D.
Answer: D
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n51?
Options:
A)100~1,000
B)1,000~10,000
C)10,000~100,000
D)100,000~1,000,000
E)1,000,000,000,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n51=2^50=(2^10)^5>(10^3)^5=10^15
Thus, the answer is E.
Answer: E
Question: An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 4 minutes, what part of the cistern will be emptied?
Options:
A)1/2
B)1/3
C)1/4
D)1/6
E)1/8
Rationale: 4/16 * 2/3 = 1/6
The answer is D.
Answer: D
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one ormore of the gang to his house?
Options:
A)234
B)255
C)260
D)265
E)278
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: B
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)7
C)6
D)5
E)2
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: A
Question: 4, 6, 12, 14, 28, 30, ?
Options:
A)20
B)40
C)no=60
D)80
E)100
Rationale: C
60
The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer: C
Question: At present, the ratio between the ages of Arun and Deepak is 4:2. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Options:
A)10 years
B)15 years
C)18 years
D)12 years
E)19 years
Rationale: Let the present ages of Arun and Deepak be 4x and 2x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 2x
= 10 years.
Answer:A
Answer: A
Question: The remainder when A=1+3+3^2+3^3+..........+3^200 is divided 13.
Options:
A)12
B)7
C)0
D)5
E)3
Rationale: A=1+3+3^2+3^3+..................+3^200
Is a Geometric progression having common ratio as '3' and number of terms as '201'.
Since Sum to n terms in GP = a(r^n-1)/(r-1)
where a=First term and r =common ration
Hence,
1*(3^201 -1 )/(3-1)
Rem of (3^201-1)/2 divided by 13
3^201 -1 /26
WKT, 3^3 = 27 = 26+1
{(26+1)^67 - 1}/26
{1-1}/26
=>0.C
Answer: C
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 80% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
Options:
A) 36%
B) 60%
C) 66%
D) 80%
E) 84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.8*0.8 = 0.64. So, the probability that he will be able to attend is 1 - 0.64 = 0.36.
Answer: A.
Answer: A
Question: If the sum of a number and its square is 132, what is the number?
Options:
A)15
B)11
C)28
D)91
E)none of these
Rationale: Let the number be x. Then,
x + x2 = 132
(x + 12)(x - 11) = 0
x = 11
ANSWER:B
Answer: B
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability K that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
Options:
A)(a) 4/10
B)(b) 4/9
C)(c) 1/2
D)(d) 6/10
E)(e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability K= 50/90 = 5/9
Correct answer E
Answer: E
Question: Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
Options:
A)21
B)20
C)19
D)16
E)15
Rationale: Marcella has 26 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 26 pairs of shoes minus the 5 'destroyed' pairs yields 21 pairs that still fulfill the requirements.
Answer: A
Answer: A
Question: Every day Daniel drives 60 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 60 miles at 4 miles/hour.
D = (R)(T)
60 = (4)(T)
60/4 = 15 = T
It takes 15 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (28 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
28 = (2)(T)
28/2 = 14 = T
It takes 14 hours for the second part
Total time to drive home on Monday = 4+14 = 18 hours
We're asked by what percent 18 hours is greater than 15 hours.
18/15 = 1.2, so it is 20% greater.
B
Answer: B
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 65% play football, how many play both?
Options:
A)120
B)150
C)240
D)180
E)160
Rationale: n(A) = 75*600/100 = 450
n(B) = 65*600/100 = 390
n(AUB) = 600
n(AnB) = 450+390-600 = 240
Answer is C
Answer: C
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6800?
Options:
A)s. 4991
B)s. 5991
C)s. 6001
D)s. 6791
E)s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(6800*6)-34009]
= Rs.(40800-34009)
= Rs.6791.
ANSWER:D
Answer: D
Question: Which of the following fractions has a decimal equivalent that is a terminating decimal?
Options:
A)10/189
B)15/196
C)16/225
D)25/144
E)39/128
Rationale: a) 10/189
denominator sum of digits is 18 so its divisible by 3 eliminate
b) 15/196
This has a prime factor of 7 when do the prime factorization of the denominator.. Eliminate
c) 16/225
denominator sum of digits is 9 so its divisible by 3 eliminate
d) 25/144
denominator sum of digits is 9 so its divisible by 3 eliminate
e) 39/128 Correct answer
ANSWER:E
Answer: E
Question: Sophia finished 2/3 of a book. She calculated that she finished 30 more pages than she has yet to read. How long is her book?
Options:
A)A)90
B)B)150
C)C)130
D)D)190
E)E)210
Rationale: Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has x−2/3*x=1/3*x pages left.
2/3*x−1/3*x=30
1/3*x=30
x=90
So the book is 90 pages long.
Answer is A.
Answer: A
Question: A train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)52
C)26
D)21
E)14
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 510 + 140 = 650 m
Required time = 650 * 2/25 = 52 sec
Answer:B
Answer: B
Question: What is the next number of the following sequence
12, 36, 80, 150,.... ?
Options:
A)252
B)262
C)272
D)282
E)292
Rationale: 12=2^3+2^2
36=3^3+3^2
80=4^3+4^2
150=5^3+5^2
=>6^3+6^2=216+36=252
ANSWER:A
Answer: A
Question: What is the sum of the greatest common factor and the lowest common multiple of 36 and 56?
Options:
A)512
B)508
C)451
D)516
E)451
Rationale: Prime factorization of 36 = 2 x 2 x 3 x 3
Prime factorization of 56 = 2 x 2 x 2 x 7
GCF = 4
LCM = 504
Sum = 508
Ans: B
Answer: B
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Options:
A)40
B)80
C)120
D)200
E)130
Rationale: Explanation:
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40. Answer: A
Answer: A
Question: Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7
meter 65 cm
Options:
A)45cm
B)255cm
C)244cm
D)55cm
E)None of these
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1575 cm, 1125cm, 765cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms
is 255.
Answer: Option A
Answer: A
Question: The average of 2,7,6 and x is 5 and the average of 18,1,6,x and y is 10. What is the value of y?
Options:
A)10
B)20
C)15
D)25
E)30
Rationale: We have : (2+7+6+x) /4 = 5
15+x = 20
x = 5
(18+1+6+x+y)/5 = 10
25+5+y = 50
y = 20
Answer is B
Answer: B
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. what is the age of the youngest child ?
Options:
A)4
B)8
C)10
D)None of these
E)Cannot be determined
Rationale: Explanation:
Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12.
We know that the sum of their ages is 50 .
so, x+(x+3)+(x+6)+(x+9)+(x+12) = 50
inline Rightarrow x= 4
inline therefore The youngest child is 4 years old. Answer: C
Answer: C
Question: A can do work in 9 days, B can do work in 18 days. In how many days they will complete the work together.
Options:
A)8 days
B)7 days
C)6 days
D)5 days
E)4 days
Rationale: Bigger no=18, Ratio=9:18=1:2
No of days = 18/(1 + 2)
= 6 days
ANSWER:C
Answer: C
Question: The largest five digit number which is a perfect cube, is:
Options:
A)85184
B)91125
C)97336
D)96806
E)99999
Rationale: Explanation:
46*46*46 = 97336
Answer: C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)150 meter
B)170 meter
C)156 meter
D)168 meter
E)154 meter
Rationale: Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 9
= 150 meter
Answer:A
Answer: A
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11% per annum then the gain of B in a period of 3 years is?
Options:
A)110
B)106
C)105
D)107
E)109
Rationale: (3500*1*3)/100 => 105
Answer: C
Answer: C