divelab/Sys2Bench huggingface dataset:
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 26, by how much does the temperature in degrees Celsius (C) increase?
Options:
A)9
B)14.44
C)47
D)48 3/5
E)59
Rationale: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+26=58 --> C=5/9*26=14.44.
Increase = 14.44 degrees.
Answer: B.
Answer: B
Question: The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
Options:
A) 4
B) 2
C) 2
D) 10
E) 12
Rationale: r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8.
Answer A
Answer: A
Question: When 100 is divided by positive integer x, the remainder is 3. What is the remainder when 197 is divided by x?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: if100/x leaves a reminder 3 then (100-3) i.e. 97 is divisible by x
So (100+97)/x leaves a reminder rem(100/x)+rem(97/x)=> 3+0=3
Answer :B
Answer: B
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
Options:
A)50
B)60
C)80
D)100
E)120
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.8x(1/2) = 50
=> x =50
Thus proved...option A.
Answer: A
Question: A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)200
B)220
C)240
D)250
E)270
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 38 = 15
x + 300 = 570
x = 270 m.
Answer: Option E
Answer: E
Question: What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?
Options:
A) 95
B) 99
C) 26
D) 73
E) None of the Above
Rationale: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -13
Thus 2xy +5 = x^2 + y^2 - 13
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 99
Thus the answer is B
Answer: B
Question: The length of the room is 4m and width is 5m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter?
Options:
A)1000
B)2000
C)4000
D)3000
E)6000
Rationale: l=4m w=5m
area of the floor = 4 x 5 = 20 sq m
cost of paving = 200 x 20= Rs. 4000
Answer: C
Answer: C
Question: Nina has exactly enough money to purchase 5 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
Options:
A)$16.7
B)$24
C)$30
D)$36
E)$40
Rationale: A its is.
Let price = X
(x-1.25)8 = 5X
X= 10/3
hence total money = 5*10/3= 16.7
Answer: A
Question: At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?
Options:
A)70
B)120
C)100
D)90
E)110
Rationale: let the total number of boys and girls at the beginning of the year be 3x and 4x respectively.
now 10 boys and 20 girls are transferred to another school. thus no. of boys and girls students left in the school X are 3x-10 and 4x-20 respectively. the ratio of these boys and girls students = 4/5
thus we have (3x-10)/(4x-20) = 4/5
15x-50= 16x-80
x=30
thus total no. of boys at the beginning of the year =4(30)= 120
Answer is option B
Answer: B
Question: If |m+n|=|m-n|, then m*n must be equal to:
Options:
A)-3
B)0
C)-2
D)-4
E)-5
Rationale: Solution 1: Distance perspective
|m-n| = |m+n| ==> The distance of m and n is equal to the distance of m and -n.
<=======(-n)=======0=======(n)======>
Only 0 is the value that has a distance equal to n and -n.
Solution 2:
|m-n| = |m+n| (square both)
m^2 -2mn + n^2 = m^2 + 2mn + n^2
4mn = 0
mn = 0
Answer: B
Answer: B
Question: City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)56
B)57.5
C)58.9
D)61.4
E)62
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: B
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?
Options:
A)1,008
B)1,296
C)1,512
D)2,016
E)2,268
Rationale: We want A, B, and C to be before F, G and H.
Let's deal with this constraint first: consider A, B, and C as one unit {ABC} and F, G and H also as one unit {FGH}. According to the condition we need them to be arranged as {ABC}{FGH}. A, B, and C, within their unit can be arranged in 3! ways, similarly F, G and H , within their unit can also be arranged in 3! ways.
So, we have a line with 6 people XXXXXX. D can take any place in the line so D has 7 options: *X*X*X*X*X*X*.
Now, we have a line with 7 people and E can take any place there, so E has 8 options: *X*X*X*X*X*X*X*.
Total = 3!*3!*7*8 = 2,016.
Answer: D.
Answer: D
Question: In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 1, then what is the increase in the number of pandas?
Options:
A) 2
B) 4
C) 5
D) 10
E) 3
Rationale: One short cut to solve the problem is
c:p = 1:3
c increased to 2
=> 1:3 = 2:x
=> x = 6
=>p increased by 3
E is the answer
Answer: E
Question: In eight years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?
Options:
A)1–5
B)1.5–5
C)11–15
D)16–20
E)21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+8 = 4(a+8)
Twenty years ago, David was twice as old as Ellen --> d-16 = 2(e-16)
David is seven years older than Ellen --> d = e + 7
e+7-16 = 2e-32
e-9= 2e-32
e = 23
d = 30
38 = 4a + 32
a = 1.5
Answer: B
Answer: B
Question: If x+y=2z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
Options:
A) 2z+1
B) 3z
C) 5z
D) z
E) 3z/2
Rationale: Pick any number like X=12, Y=10 and Z= 11 so that X+Y=2Z, now then the arithmetic mean will be (12+10+11)/3=11. Now, just look at the answers and put the value of Z there.
(A) 2.11+1=23, no.
(B) 3.11=33,no
(C) 5.11=55, no
(D) 11, it can be the answer, lets check us the other options
(E) (3.2)/2=3, no
so the answer will be D..
Answer: D
Question: If the radius of a cylinder is made 3 times and height is doubled, what is the new volume of the cylinder divided by the old one?
Options:
A)18.
B)2.
C)6.
D)4.
E)10.
Rationale: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(3r)^2(2h)
v'=18v
A) 18
Answer: A
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is
Options:
A)420
B)520
C)620
D)720
E)820
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 200
=> x = 40
Total students = 8x+5x = 13x = 13(40) = 520
Option B
Answer: B
Question: In an election, candidate Smith won 52% of the total vote in Counties A and S. He won 61% of the vote in County A. If the ratio of people who voted in County A to County S is 3:1, what percent of the vote did candidate Smith win in County S ?
Options:
A)A.25%
B)B.27%
C)C.34%
D)D.43%
E)E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County S
hence answer is A.
Answer: A
Question: The marks obtained by Polly and Sandy are in the ratio 3:5 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?
Options:
A)3:4
B)5:6
C)7:8
D)9:10
E)11:12
Rationale: Polly : Sandy = 3:5 = 9:15
Sandy : Willy = 3:2 = 15:10
Polly : Sandy : Willy = 9:15:10
Polly : Willy = 9:10
The answer is D.
Answer: D
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A)2
B)2 1/2
C)3
D)3 1/2
E)4
Rationale: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Answer: B
Question: If x^2 = 231, which of the following is closest to a potential value of x?
Options:
A)-127
B)-11
C)12
D)13
E)15
Rationale: Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √231 => +- 15 (approx)
this value is closer to 15
Hence E is correct.
Answer: E
Question: A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?
Options:
A)5/8
B)3/4
C)7/8
D)57/64
E)15/16
Rationale: It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.
Probability of getting no tails: 1/2^6=1/64
Probability of getting 1 tail: 6C1∗1/2^6=6/64, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways;
Probability of getting 6 tails: 1/2^6=1/6^4
P=1−(1/64+6/64+1/64)=56/64=7/8
Answer: C.
Answer: C
Question: Each shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
Options:
A)A)4
B)B)5
C)C)6
D)D)8
E)E)9
Rationale: Denoting x the number of the shelves,
we can build an equation: 24x=16(x−1)+22+34
Solving the equation, we get x=5
Answer: B
Answer: B
Question: A 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds. What is the length of the platform?
Options:
A)120
B)840
C)350
D)420
E)210
Rationale: Speed = [420 / 30] m/sec =14 m/sec.
Let the length of the platform be x meters.
Then, x + 420/ 60 = 14
x + 420 = 840 è x = 420m. Answer: D
Answer: D
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/81%
B)18 2/11%
C)18 3/11%
D)18 1/11%
E)18 2/15%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: B
Question: "I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years.
Options:
A)47 years and 28 years.
B)40 years and 24 years.
C)48 years and 27 years.
D)46 years and 26 years.
E)none of these
Rationale: Let the present age of the man be ’a’ and son be ’b’,
Given, a + b = 64 or b = (64 - a)
Now the man says "I am five times as old as you were, when I was as old as you are",
So, a = 5[b - (a - b)]
We get 6a = 10b,
Substitute value for b,
6a = 10(64 - a),
Therefore a = 40, b = 24.
ANSWER:B
Answer: B
Question: If 12% of x is equal to 6% of y, then 18% of x will be equal to how much % of y ?
Options:
A)7%
B)9%
C)11%
D)12%
E)none of these
Rationale: We have ,
12% of X = 6% of Y
=> 2% of X = 1% of Y
=>(2 x 9)% of X = ( 1 x 9)% of Y
Thus, 18% of X = 9% of Y.
ANSWER:B
Answer: B
Question: Train G and H, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train G left at 4 pm traveling at a speed of 60 miles per hour, and train H left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
Options:
A)9.05Am
B)9.11pm
C)8.05pm
D)7.05pm
E)9.05pm
Rationale: First, since G has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is D
Answer: D
Question: a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?
Options:
A)50 %
B)60 %
C)70 %
D)80 %
E)40 %
Rationale: let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit.
Nw he adds 10% milk ie total milk z 110 lit.
Now he will get 132 rs. by selling 110 lit f milk (120*110/100)
total profit = 32 rs
increased profit =12 rs
%age increase= 12/20= 60 %
ANSWER:B
Answer: B
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 48?
Options:
A)12
B)18
C)24
D)30
E)36
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
48=2*3*8 is divisible by 12. therefore the greatest common divisor is 12
A
Answer: A
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are?
Options:
A)60, 120, and 30
B)60, 30, and 120
C)30, 60, and 120
D)30, 120, and 60
E)120, 30, and 60
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 70
7x/3 = 70
x = 30
The numbers in order are 60, 30, and 120
The answer is B.
Answer: B
Question: Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 40 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled?
Options:
A)6
B)9
C)10
D)27
E)48
Rationale: If 3 Machines can do the work in 40 hr then 4 Machines can do the work in 3/4*40 = 30 Hrs. hence time saved will be 10hr
option C is the correct answer
Answer: C
Question: X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:
Options:
A)200
B)250
C)300
D)350
E)400
Rationale: X = Rs.5000/-
Y = Rs.15000/-
X share 1 part & Y share 3 parts
Total 4 parts -----> Rs.1600/-
----> 1 part -------> Rs.400/-
X share = 1 part -----> Rs.400/-
E
Answer: E
Question: In how many ways letters of the word RSCUPERATE be arranged?
Options:
A)357687
B)247886
C)284757
D)456788
E)302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: E
Question: A and B complete a work in 16 days. A alone can do it in 40 days. If both together can do the work in how many days?
Options:
A)1.0875 days
B)0.1875 days
C)0.0675 days
D)0.0875 days
E)0.0775 days
Rationale: 1/16 + 1/40 = 0.0875 days
ANSWER:D
Answer: D
Question: In how many ways can the letters of the word 'LEADER' be arranged?
Options:
A)72
B)144
C)360
D)720
E)None of these
Rationale: Explanation:
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =	6! / (1!)(2!)(1!)(1!)(1!) =360.
ANSWER IS C
Answer: C
Question: A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If25 were to be added to each score, which of these three statistics would change?
Options:
A)The mean only
B)The mean and the median
C)The standard deviation only
D)The median only
E)The mean and the standard deviation
Rationale: The correct answer is B.
Answer: B
Question: In how many ways can 5 boys and 2 ladiesbe arranged at a table if 2 ladies are never together?
Options:
A)245
B)278
C)390
D)420
E)480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: E
Question: A farm has chickens, cows and sheep. There are five times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?
Options:
A)5
B)8
C)10
D)4
E)17
Rationale: Chicken - ch
Cows - C
Sheep -S
ch+C=6S
C> ch and c>s
Each cow has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5c+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
c=11 and ch=9 or
c=14 and ch=10
Since from first equation where ch+c=5s
The sum of ch and c should be divisbile by 5. 24 is not so the only possible solution is c=11 and ch=9. So s=4
Answer : D
Answer: D
Question: If m is an integer, what is the greatest possible value for m that would still make the following statement true: 11*10^m < 1/10 ?
Options:
A) –4
B) –3
C) –2
D) –1
E) 0
Rationale: Just putting values, the LHS becomes
m =0 --> 11
m =-1 --> 11/10
m =-2 --> 11/100
m =-3 --> 11/1000
Anything lower will be smaller than 11/1000. m =-2, equality doesn't hold but it does for m =-3.
Answer is B.
Answer: B
Question: Two men A and B start from place X walking at 4 1/2 kmph and 5 1/2 kmph respectively. How many km apart they are at the end of 3 1/2 hours if they are walking in the same direction?
Options:
A)4 3/9
B)4 3/5
C)4 3/8
D)4 3/2
E)4 3/1
Rationale: RS = 5 3/2 - 4 1/2 = 1 1/4
T = 3 1/2 h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: C
Answer: C
Question: A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per kg and 6 kg of salt worth Rs.5 per kg. For what amount of money should he sell 4 kg of the mixed variety of salt in order to make a profit of 12½%?
Options:
A)22.95
B)23.95
C)24.95
D)25.95
E)26.95
Rationale: 7kg*Rs6---- Rs 42
5 kg*Rs4---- Rs 20
6kg*Rs5---- Rs 30
18kg for Rs--92 cost price of 1 kg=92/18=>Rs5.11111
cost of 4 kg ---- 4*5.11111=Rs 20.4444
Profit=12.5%
SP={(100+Gain%)/100}*CP
={(100+25/2)/100}*20.444
=22.95
ANSWER:A
Answer: A
Question: If 28a+30b+31c=427.
then a+b+c=?.a,b,c are natural numbers
Options:
A)6
B)14
C)12
D)45
E)28
Rationale: have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*4 + 31*9..
hence values of a,b and c are 1, 4 and 9 respectively..
a+b+c=14
ANSWER:B
Answer: B
Question: Find the odd one out:
125, 106, 83, 76, 65, 58, 53
Options:
A)33
B)83
C)26
D)18
E)222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 83 is the answer.
ANSWER: B
Answer: B
Question: P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
Options:
A)12 days
B)12.5 days
C)13 days
D)14.5 days
E)15.5 days
Rationale: Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
B
Answer: B
Question: If 4^x = 8^y, then the value of (x/y)-1 is equal to :
Options:
A)1/2
B)0
C)1/4
D)3/4
E)2/3
Rationale: 4^x = 8^y,
2^2x= 2^3y
so
2x=3y
x/y = 3/2
(x/y)-1 = (3/2)-1= 1/2
ANSWER:A
Answer: A
Question: complete the numerical series with the correct number
5+3+2=151022
9+2+4=183652
8+6+3=482466
5+4+5=202541
9+5+5= ?
Options:
A)468645
B)454586
C)454585
D)454386
E)444586
Rationale: Correct Answer : C
number is formed as
5+3+2
5*3 3*2 2*5 = 151022
similarly,
9*5 9*5 (9*5+9*5-5)= 454585
Answer: C
Question: A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
Options:
A)6.4 days
B)4.4 days
C)5.4 days
D)8.4 days
E)2.4 days
Rationale: A
6.4 days
1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300
So, all three together will complete the work in 300/47 = 6.4 days.-
Answer: A
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)17
B)19
C)16
D)12
E)14
Rationale: 63 + 83 + 103
= a3 => a
= 12
Answer:D
Answer: D
Question: The average age of a husband and his wife was 26 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
Options:
A)11
B)18
C)21
D)287
E)27
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (26 * 2 + 5 * 2) + 1 = 63 years.
Required average = (63/3) = 21 years.
Answer: C) 21
Answer: C
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage?
Options:
A)65%
B)50%
C)59%
D)40%
E)53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 165 (33 * 5)
Profit percentage
= (165 - 100)/100 * 100 = 65%
Answer: A
Answer: A
Question: A soccer team played 158 games and won 40 percent of them. How many games did it win?
Options:
A)84
B)63.2
C)104
D)50.8
E)15.8
Rationale: 40% of 158=x
0.40*158= x
63.2=x
answer :B
Answer: B
Question: Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow?
Options:
A)1/2
B)1/5
C)3/4
D)1/3
E)3/5
Rationale: This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow.
So, possible options for this other ball would be: W, W, B, B (as one yellow is already picked)
So the probability for that ball to be yellow too is 2/4=1/2.
Option A
Answer: A
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m, what is its area?
Options:
A)2510
B)2535
C)2530
D)2030
E)2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=186 m
⇒ breadth =35 m
length =35+23=58 m
Area =58×35=2030 m2
Answer is D.
Answer: D
Question: Sequence P is defined by pn=pn−1+3, p1=11, sequence Q is defined as qn=qn−1–4, q3=103. If pk>qk+2, what is the smallest value k can take?
Options:
A)6
B)9
C)11
D)14
E)15
Rationale: Set P = {11, 14, 17,.....}
Set Q = {110, 107, 103,....}
For Arithmetic progression a(n)=a(1)+(n−1)d
Started with C) 11 does not satisfy pk > qk+2
and D) 14, pk = qk+2
So Answer is E
Answer: E
Question: Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is
Options:
A)3
B)4
C)7
D)11
E)12
Rationale: (a+b+c+d)/4=4
=>(a+b+c+d)=16...........(1)
(d+e+f+g)/4=4
=>(d+e+f+g)=16
=>(e+f+g)=16-d...........(2)
Also, (a+b+c+d+e+f+g)/7=3 (Given)
using (1) and (2) equations
16+16-d=21
=> d=11
ANSWER:D
Answer: D