divelab/Sys2Bench huggingface dataset:
Question: Ramesh completes a piece of work in 4 days, Ranjith completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)6 days
B)8 days
C)10 days
D)12 days
E)3.33 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days =4 × 20/24 = 3.33 days
Answer : E
Answer: E
Question: If x = 3y, where y is a prime number greater than 2, how many different positive even divisors does x have, including x?
Options:
A)0
B)1
C)2
D)3
E)It cannot be determined from the information given
Rationale: For x to have even divisors, xx has to be an even number.
We know that x=3y, where yy is a prime number greater than 2. As 2 is the only even prime number, y has to be an odd prime number.
This means that x must also be an odd number, since odd x odd = odd.
As x is odd, it cannot have any even divisors.
Therefore, A is the correct answer.
Answer: A
Question: 21 friends went to a hotel and decided to pay the bill amount equally. But 20 of them could pay Rs. 30 each as a result 21st has to pay Rs. 200 extra than his share. Find the amount paid by him.
Options:
A)120
B)250
C)110
D)220
E)None
Rationale: Explanation:
Average amount paid by 20 persons = Rs. 30
Increase in average due to Rs. 200 paid extra by the 21st men = Rs. 200/20= Rs. 10
Therefore, Average expenditure of 21 friends = Rs. 30 + Rs. 10 = Rs. 40
Therefore, Amount paid by the 21st men = Rs. 40 + Rs. 200 = Rs. 240
Correct Option: E
Answer: E
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 340 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40 sec
E)56
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 340 = 700 meter
Time taken to cross the platform = 700/(25/2) = 700 Ã— 2/25 = 56 seconds
ANSWER:E
Answer: E
Question: Bani has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
Options:
A)71
B)72
C)73
D)74
E)75
Rationale: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 75 that is c is the option which is divisible by 5.
so answer is E
Answer: E
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
Options:
A)333
B)144
C)188
D)199
E)121
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144.Answer: B
Answer: B
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance R between the two cities?
Options:
A)48
B)72
C)96
D)120
E)192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance R to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: E
Question: If 9 is a factor of 2y, then which of the following may not be an integer?
Options:
A)6y/54 + 2y/3
B)(4y-18)/9
C)(2y+27)/9
D)(81-4y^2)/81
E)(2y-3)/3
Rationale: I got the right answer A after plugging in 18 for y.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6y/54 + 2y/3 = 3/6 * 2y/9 + 2y/3.
Since 9 is a factor of 2y, 3 is also factor of 2y. So 2y/3 is an integer, as is 2y/9. But 3/6 = 1/2, so if 2y/9 is not even, the expression 3/6 * 2y/9 will not be even."
But, isn't 2y/9 always even? 9 is a factor of 2y, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2y/9 is even.A
Answer: A
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
Options:
A)10
B)12
C)13
D)18
E)21
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: D
Question: A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are
drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid
P was contained in the container initially?
Options:
A)23
B)21
C)19
D)17
E)18
Rationale: Explanation :
Let's initial quantity of P in the container be 7x and initial quantity of Q in the container be 5xNow 9
litres of mixture are drawn off from the containerQuantity of P in 9 litres of the mixtures drawn off =
9×712=6312=214Quantity of Q in 9 litres of the mixtures drawn off = 9×512=4512=154HenceQuantity of
P remains in the mixtures after 9 litres is drawn off =7x−214Quantity of Q remains in the mixtures after 9
litres is drawn off =5x−154Since the container is filled with Q after 9 litres of mixture is drawn
off,Quantity of Q in the mixtures=5x−154+9=5x+214Given that the ratio of P and Q becomes 7 :
9⇒(7x−214):(5x+214)=7:9⇒(7x−214)(5x+214)=7963x−(9×214)=35x+(7×214)28x=(16×214)x=(16×214×28)
litres of P contained in the container initially = 7x=(7×16×214×28)=16×214×4=21
Answer : Option B
Answer: B
Question: A certain university will select 2 of 3 candidates eligible to fill a position in the mathematics department and 4 of 5 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)42
B)10
C)40
D)65
E)15
Rationale: 3C2*5C4 = 3*5 = 15
the answer is (E)
Answer: E
Question: How many even integers n, such that 20<=n<=180 are of the form 3k+4, where k is any natural number?
Options:
A)24
B)27
C)30
D)33
E)36
Rationale: The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 278 = 16+6(27)
There are 27 numbers in the list.
The answer is B.
Answer: B
Question: There are 12 dozen mangoes in a box. If there are 43
such boxes, how many mangoes are there in all the
boxes together?
Options:
A)516
B)3096
C)6192
D)628
E)None
Rationale: Number of mangoes = 12 dozens
= 12 × 12 = 144
∴ Number of mangoes in 43 boxes
= 43 × 144 = 6192
Answer C
Answer: C
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
A)34%
B)56%
C)57%
D)67%
E)78%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: C
Question: If 28a+30b+31c=395.
then a+b+c=?.a,b,c are natural numbers
Options:
A)5
B)8
C)12
D)13
E)42
Rationale: have a look on your calender
since,we all know 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*5+ 31*7..
hence values of a,b and c are 1, 5 and 7 respectively..
a+b+c=13
ANSWER:D
Answer: D
Question: K is a 3 digit number such that the the ratio of the number to the sum of its digits is least.What is the difference between the hundreds and tens digit?
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: Explanation :
This is only possible only when the hundreds digit has the least value and tens and units has the highest value.so we could get the highest possible sum but possible lowest number.so by this logic this number could only be 199.so the difference is 8.
note:remember a number given as abc i.e abc=aX100+bX10+c.
so 123=1X100+2X10+3.
Answer : B
Answer: B
Question: An inlet pipe can fill the tank in 30 minutes. B an outlet pipe can empty the tank in 45 minutes. In what time the tank be filled if both pipes work simultaneously?
Options:
A)90 minutes
B)80 minutes
C)70 minutes
D)60 minutes
E)50 minutes
Rationale: Time taken to fill the tank= LCM = 90
= Ratio= 30:45=2:3
= 90/(3 - 2) = 90/1 = 90 minutes
ANSWER:A
Answer: A
Question: The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
Options:
A)44
B)48
C)45
D)43
E)50
Rationale: Total age = 22 * 21
tot age of all stu + age of the teacher = 23*22
age of the teacher = 23*22-22*21 = 44
ANSWER A
Answer: A
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)Rs.530
B)Rs.540
C)Rs.550
D)Rs.560
E)Rs.570
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
B
Answer: B
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Options:
A)Rs.2166.67
B)Rs.2234
C)Rs.2345.13
D)Rs.2456.34
E)Rs.2550.34
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: A
Question: If two students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then three rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
Options:
A)0
B)3
C)4
D)5
E)9
Rationale: Let there be a rows.
Then 2a + 6 = 6(a-3) [equating the number of students]
=> a= 6
and total number of students = 18
Therefore 3 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (B)
Answer: B
Question: Find the value of k for which there are infinite solutions for the given set of equations.
5x + 2y = k and 10x + 4y = 3
Options:
A)3/0
B)3/2
C)3/1
D)3/8
E)3/4
Rationale: For the two sets of equation to have infinite solutions, we have 510=24=k3510=24=k3. Hence, k = 3/2
Answer:	B
Answer: B
Question: If n is an integer greater than 8, which of the following must be divisible by 3?
Options:
A)1. n (n+1) (n-4)
B)2. n (n+2) (n-1)
C)3. n (n+3) (n-5)
D)4. n (n+4) (n-2)
E)5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
C
Answer: C
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 1(2/9)
B)Rs. 2(2/9)
C)Rs. 2(1/9)
D)Rs. 4(2/9)
E)Rs. 3(1/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)8
B)9
C)10
D)20
E)30
Rationale: x ------- 6
(x + 10) ---- 3
x * 6 = (x + 10)3
x = 10
ANSWER:C
Answer: C
Question: 36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203. What is the first part?
Options:
A)19
B)88
C)267
D)26
E)28
Rationale: Explanation:
Let the first part be x.
8x + 3 (36 – x) = 203
8x + 108 – 3x = 203
5x + 108 = 203
5x = 95
x = 19
ANSWER: A
Answer: A
Question: In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/4 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
Options:
A)N/9
B)8N/9
C)19N/20
D)31N/40
E)37N/40
Rationale: The number of people who answered yes to both questions is (1/4)(1/5)N = N/20
The number of people who did not answer yes to both is 1 - N/20 = 19N/20
The answer is C.
Answer: C
Question: The cost price of 60 articles is the same as the selling price of x articles. If the profit is 20%, what is x?
Options:
A)42
B)45
C)48
D)50
E)54
Rationale: Let the cost price = y
The cost price of 60 articles = 60y
The selling price of x articles = 1.20y*x
1.20y*x = 60y
x = 60 / 1.2 = 50
The answer is D.
Answer: D
Question: The grade point average of the entire class is 84. If the average of one fourth of the class is 96, what is the average of the rest of the class?
Options:
A)76
B)77
C)78
D)79
E)80
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
84x = (1/4)96x + (3/4)(P)x
336 = 96 + 3P
3P = 240
P = 80.
The answer is E.
Answer: E
Question: 2 – [2 – {2 – 2 (2 + 2)}] = ?
Options:
A)-4
B)4
C)6
D)None of these
E)Cannot be determined
Rationale: Solution
Given exp. = 2 - [2-{2-2×4}]
= 2 -[2-{2-8}]
= 2-[2-(-6)]
= 2-[2+6]
= 2-8
= -6
Answer D
Answer: D
Question: How many D ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
Options:
A)6C4
B)6P4
C)4^6
D)6^4
E)6!
Rationale: Each marble has 4 options, so there are total of D=4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: C
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for 75 cents, and Zachary buys a pencil and an eraser for 35 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)285
B)295
C)305
D)315
E)325
Rationale: pencil + notebook = 80
notebook + eraser = 75
pencil + eraser = 35
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 190 cents
The cost to buy 3 of each would be (3/2)(190) = 285
The answer is A.
Answer: A
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 8th position from either end of the row.
Can you find out how many girls are practicing together?
Options:
A)4
B)9
C)15
D)16
E)18
Rationale: As judith is 8th from either end of the row, it means that 7 girls are on one of her sides and 7 are present on the other.
7 + 7 + 1(judith herself) =15.
Hence, 15 girls are practicing the dance together.
correct answer is C)15
Answer: C
Question: One hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 300 selected numbers are odd?
Options:
A)34.33%
B)16.67%
C)35.33%
D)36.33%
E)37.33%
Rationale: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 100 multiples are odd i.e 50 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (50+0)/(100+200)= 50/300=(1/6) = 16.67%
Answer B
Answer: B
Question: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad hari in 15 days and by hari and ram in 20 days. Ram alone can complete the work in how much days ?
Options:
A)30
B)35
C)25
D)32
E)28
Rationale: Rate*Time = Work
Since the work done is same throughout the question so we can take the work done as 1
Let Rate of Ram be R, Hari be H and Shaym be S
A piece of work can be done by Ram and shyam in 12 days
When Ram and Shyam will work together then their rate will be added. So combined rate will be R+S
(R+S)*12 = 1
R+S = 1/12 ...(1)
By shyam And hari in 15 days
Similarly
S+H = 1/15 ...(2)
hari and ram in 20 days
Similarly
H+R = 1/20 ...(3)
(2)-(3)
S+H - (H+R) = 1/15 - 1/20
=> S-R = 1/60 ..(4)
(1) - (4)
R + S - (S - R) = 1/12 - 1/60 = 4/60 = 1/15
2R = 1/15 => R = 1/30
Ram alone can complete the work in how much days ?
R * t = 1
t = 1/R = 1/ (1/30) = 30 days
So, Answer will be A
Answer: A
Question: There are 97 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
Options:
A)29
B)49
C)39
D)59
E)69
Rationale: Editing my solution:
Number of switches = 97
Number of switches turned on by A: 3, 6, ... 96 = 32
Number of switches turned on by B: 5, 10, ....95 = 19
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (32 - 6) + (19 - 6) = 39
Answer: C
Answer: C
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 20 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$9,240
C)$10,500
D)$11,500
E)$12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.8 = 10,395
Answer B is correct.
Answer: B
Question: A portion of the 50% solution of chemicals was replaced with an equal amount of 60% solution of chemicals. As a result, 55% solution of chemicals resulted. What part of the original solution was replaced?
Options:
A)3/4
B)1/4
C)3/4
D)2/5
E)1/2
Rationale: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.5(1-x)+0.6*x=0.55 --> x=1/2.
Answer: E.
Answer: E
Question: If Harsh sold a match ticket for Rs.340 at a profit of 25%, at what price did he purchased the ticket?
Options:
A)280
B)255
C)300
D)272
E)None of these
Rationale: Explanation:
Cost price = Selling price/(1 + profit percent)
= 340/(1 + 0.25) = 340/1.25
= Rs.272
ANSWER D
Answer: D
Question: The ratio of the volumes of two cubes is 125 : 216. What is the ratio of their total surface areas?
Options:
A)13:18
B)8:12
C)1:12
D)8:17
E)1:11
Rationale: Ratio of the sides = ³√125 : ³√216
= 5 : 6
Ratio of surface areas = 52:62
= 13:18
Answer: A
Answer: A
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
Options:
A)25x^2 + 4 = y^2
B)75x^2 = 3y^2 - 12
C)25x^2 = (y + 2)(y - 2)
D)5x = y - 2
E)x^2 = (y^2 - 4)/25
Rationale: Let's Solve the given equation first
25x^2 = y^2 - 4
i.e. (5x)^2 - y^2 = -4
i.e. y^2 - (5x)^2 = 4
Let's Check the Options:
A) 25x^2 + 4 = y^2
This equation can be re-written as
25x^2 = y^2 - 4 which is same as Equation given in question hence Option ELIMINATED
B) 75x^2 = 3y^2 - 12
Divide the equation by 3 on both sides, we get
25x^2 = y^2 - 4 which is same as Equation given in question hence Option ELIMINATED
C) 25x^2 = (y + 2)(y - 2)
This equation can be re-written as
25x^2 = y^2 -2y+2y - 4
i.e. 25x^2 = y^2 - 4 which is same as Equation given in question hence Option ELIMINATED
D) 5x = y - 2 Hence, The correct Answer Option
E) x^2 = (y^2 - 4)/25
Multiply the equation on both sides by 25
i.e. 25x^2 = y^2 - 4 which is same as Equation given in question hence Option ELIMINATED
ANSWER:D
Answer: D
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13970 ?
Options:
A)3200
B)4064
C)3250
D)3825
E)3985
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 13970 Ã— 16/55 = Rs.4064.
Share of Z in the profit is Rs.4064.
Option B
Answer: B
Question: If a= 3b, where b is a prime number greater than 2, how many different positive even divisors does a have, including a?
Options:
A)0
B)1
C)2
D)3
E)It cannot be determined from the information given
Rationale: b is prime greater than 2 thus b is odd
3b is odd
Thus no even factors
Ans:A
Answer: A
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 3 : 3 : 4 what will be the age of C after 5 years?
Options:
A)45 years
B)42 years
C)40 years
D)41 years
E)None of the above
Rationale: 3+3+4=10
4*(90/10)=36yrs
after 5yrs=41
ANSWER:D
Answer: D
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: B
12
Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: B
Question: If f(x)=5x+6 and g(y)=2y^2+ 8y-5 then g(f(x))
Options:
A)52x^2+36x+85
B)50x^2+160x+115
C)85x^2+85x+85
D)68x^2+87x+69
E)87x^2+85x+58
Rationale: g(f(x))=2(5x+6)^2+8(5x+6)-5 =2(25x^2+60x+36)+40x+48-5 = 50x^2+120x+72+40x+43
=50x^2+160x+115
Answer is B
Answer: B
Question: Simplify :(log 75/16-2 log 5/9+log 32/243)
Options:
A)log 1
B)log 2
C)log 3
D)log 4
E)log 10
Rationale: log 75/16-2 log 5/9+log 32/243
= log 75/16-log(5/9)^2+log32/243
= log 75/16-log25/81+log 32/243
=log((75/16*32/243)/(25/81))
= log(75/16*32/243*81/25)=log 2
ANSWER:B
Answer: B
Question: A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be
Options:
A)12.5 m
B)10m
C)17.5m
D)21.25m
E)9.8m
Rationale: Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
40.25 : 28.75 :: 17.5 : x
40.25 * x = 28.75 * 17.5
x =	(28.75 x 17.5)/40.25
x = 12.5
Answer is A.
Answer: A
Question: Find the average of first 20 multiples of 7?
Options:
A)73.5
B)65.8
C)75.9
D)75
E)71.5
Rationale: Required average = 7(1+2+3---+20)/20 = 7*20*21/20*2 = 147/2 = 73.5
Answer is A
Answer: A