divelab/Sys2Bench huggingface dataset:
Question: If x and y are positive integers, Choose which of the following CANNOT be the greatest common divisor of 35x and 20y?
Options:
A)5
B)5(x-y)
C)10x
D)20y
E)35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 35x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 35x/5 = 7x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 10x when x = 1 its 10 and 10 cannot be the greatest common divisor of 35x and 20y ...
or 35x/10x = 3.5 which is not a integer.
so answer is C.
Answer: C
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
Options:
A)386
B)378
C)396
D)395
E)394
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 1638 = Rs. 378
Answer: B
Answer: B
Question: Calculate the dividend from Caleb's stock, if Caleb he invested Rs. 2500 at 79 to obtain an income of Rs. 200.
Options:
A)6.32
B)5.32
C)7.32
D)2.32
E)1.32
Rationale: By investing Rs.2500, income = Rs.200
By investing Rs.79, income = 200Ã—79/2500=6.32
ie, dividend = 6.32%
Answer is A.
Answer: A
Question: X does a work in 40 days. Y does the same work in 60 days. In how many days they together will do the same work?
Options:
A)10
B)12
C)24
D)30
E)15
Rationale: X's 1day's work= 1/40
Y's 1 day's work=1/60
(X+Y)'s 1day's work= (1/40+1/60)=1/24
both together will finish the work in 24 days.
correct option is C
Answer: C
Question: Eighteen years ago,a father was three times as old as his son.Now the father is only twice as old as his son.Then the sum of the present ages of the son and the father is :
Options:
A)54
B)72
C)105
D)108
E)None of these
Rationale: Solution
Let the present ages of the father and son be 2x and x years respectively.
Then,(2x - 18)=3 (x - 18) ⇔ x = 36.
∴ Required sum = (2x + x) = 3x =108 years. Answer D
Answer: D
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)18%
B)19%
C)12%
D)32%
E)17%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: C
Question: 12 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work?
Options:
A)23
B)27
C)36
D)27
E)11
Rationale: 12 * 30 = 10 * x => x = 36 days
Answer:C
Answer: C
Question: If m is an integer such that (-2)^2m=2^(12-m) then m=?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2m = 12-m
3m = 12
m = 4
The answer is D.
Answer: D
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
Options:
A)50
B)40
C)20
D)30
E)10
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
answer is B.
Answer: B
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 70 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
Options:
A)50%
B)53%
C)54%
D)55%
E)57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.70=42 Democrats are expected to vote for Candidate A;
40*0.20=8 Republicans are expected to vote for Candidate A.
Thus total of 42+8=50 registered voters are expected to vote for Candidate A, which is 50% of the total number of registered voters.
Answer: A
Answer: A
Question: A family consists of two grandparents, two parents, and three grandchildren. The average age of the grandparents is 65 years, the average age of the parents is 36 years, and the average age of the grandchildren is 5 years. What is the average age (in years) of the family?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: Total age of the grandparents = 65 Ã— 2 = 130
Total age of the parents = 36 Ã— 2 = 72
Total age of the grandchildren = 5 Ã— 3 = 15
Average age of the family = (130+72+15)/7 = 217/7 = 31 years
The answer is A.
Answer: A
Question: What is 992*992?
Options:
A) 974,169
B) 974,219
C) 984,064
D) 985,219
E) 985,369
Rationale: if you take a base of 1000 then 992 is 8 less than 1000
to get the product of 992 x 992 write like this
992- 8( as 8 less than base1000)
992- 8
now 8 x 8 = 64
and 992-8 = 984
so 992 x 992 = 984064 ... (bingo the answer is C . you can even have a shortcut ...... 8 x 8 = 64 ... only answer choice has last three digits as 64.. so no need to calculate 992-8 . after you get 8 x 8 you can straight way pick answer choice C.
Answer: C
Question: A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.40 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?
Options:
A)$94.03
B)$96.75
C)$98.75
D)$102.07
E)$105.3
Rationale: there can be 2 cases
1)25+25+10+5=$98.75 or
2)25+25+25=$96.75
C
Answer: C
Question: If the 15th day of a month is three days earlier than Saturday, What day will it be on the 24th day of the month?
Options:
A)Saturday
B)Monday
C)Sunday
D)Wednesday
E)Friday
Rationale: Explanation:
Given that 15th day of a month is three days earlier than Saturday
=> 15th day is Wednesday
=> 22nd is Wednesday
=> 24th is Friday
Answer: Option E
Answer: E
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120
B)775
C)555
D)288
E)278
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)Rs. 650
B)Rs. 690
C)Rs. 698
D)Rs. 700
E)Rs. 720
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: C
Question: An woman sitting in a train which is travelling at 25 kmph observes that a goods train travelling in a opposite direction, takes 3 seconds to pass him. If the goods train is 140 m long, find its speed.
Options:
A)141
B)142
C)143
D)144
E)145
Rationale: Relative speed = (140/3)m/s = (140/3)*(18/5) = 168 kmph
speed of goods train = 168-25 = 143 kmph
Answer is C
Answer: C
Question: Q as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P.
Options:
A)62%
B)50%
C)75%
D)66%
E)65%
Rationale: Explanation :
IF P+Q=62%
ANSWER IS A
Answer: A
Question: Find the least number must be subtracted from 899830 so that remaining no.is divisible by 16?
Options:
A)5
B)8
C)7
D)6
E)9
Rationale: On dividing 899830 by 16 we get the remainder 6, so 6 should be subtracted
D
Answer: D
Question: A candidate who gets 20% of the marks fails by 40 marks. But another candidate who gets 30% marks gets 20 marks more than necessary for passing. Find the number of marks for passing?
Options:
A)100 Marks
B)200 Marks
C)280 Marks
D)160 Marks
E)827 Marks
Rationale: 20% ------------ 40
30% ------------ 20
----------------------
10% ------------- 60
20% -------------- 120
120 + 40 = 160 Marks
Answer:D
Answer: D
Question: Find how many positive integers less than 10,000 are there such thatthe sum of the digits of the no. is divisible by 3?
Options:
A)2468
B)2789
C)2987
D)3334
E)3568
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: D
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 5 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
Options:
A)20cs
B)cs/2
C)60cs
D)(2cs)/12
E)(24c)/s
Rationale: Ans: C
Solution: simple multiplication s students , c classes , 5 books/ month= 60 books a year
total number of books = 60cs
Answer: C
Question: Which of the following is a multiple of 6!-120?
Options:
A)5!+80
B)6!+320
C)5!+380
D)5!+480
E)4!+24
Rationale: The factorial 6! mean 6*5*4*3*2
Therefore 6!-120 =(6*5*4*3*2)-120
This gives you 720-120=600
valculating all the options the only option that gives a factor of 6!-120 is option D) 5!+480
Answer: D
Question: A chef cuts a watermelon along its horizontal diameter once and then along its vertical diameter twice at right angle to each other. A slice is removed (other pieces remains intact). What will be the total surface area of the remaining portion?
Options:
A)4*pi*r^2
B)4*pi*r^3
C)4*pi*r^4
D)4*pi*r^5
E)4*pi*r^6
Rationale: surface area of sphare is (4*pi*r^2)
if 1/4th parth is removed (4*pi*r^2)-(pi*r^2)= 3*pi*r^2
and the cut surface is (1/2*pi*4^2)*2
so total surface area is 4*pi*r^2
ANSWER:A
Answer: A
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 28!
Options:
A)13
B)10
C)12
D)14
E)16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18,21,24,27
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
21=3x7->1
24=3x8->1
27=3x3x3->3
---- count 3's =13 so answer is 13
Answer : A
Answer: A
Question: How many integers between 1000 and 10000 have
no digits other than 4, 5 or 6?
Options:
A)91
B)51
C)81
D)71
E)61
Rationale: Any number between 1,000 and 10,000 is of 4 digits. The unit’s place can be filled up by 4,5 or 6, that is, in 3 ways.
Similarly, the ten’s place can be filled up by 4 or 5 or 6, that is in 3 ways. The hundred’s place can be filled up by 4, 5 or 6, that is in 3 ways and the thousand’s place can.be filled up by 4 or 5 or 6, that is, in 3 ways.
Hence the required numbers = 3 x 3 x 3 x 3 = 81
ANSWER:C
Answer: C
Question: United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
Options:
A)200 minutes
B)100 minutes
C)120 minutes
D)140 minutes
E)160 minutes
Rationale: Lets take number of minutesx.
Given that, 7+0.25x=12+0.2x ->0.05x=2 -> x=100minutes
ANS B
Answer: B
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability Q that the team will have exactly 2 women?
Options:
A)1/14
B)1/7
C)2/7
D)3/7
E)1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: D
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
Options:
A)1/8
B)1/1
C)1/5
D)1/4
E)1/0
Rationale: Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: C
Question: Is a given rectangular block, a cube?
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: EXPLANATION
I gives, any two of l, b, h are equal.
II gives, lbh = 64.
From I and II, the values of l, b, h may be (1 ,1 , 64), (2 ,2 ,16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
Correct answer is (D).
Answer: D
Question: If s is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
Options:
A)z - w = 3(y - x)
B)s is divisible by 8
C)The average of w, x, y, and z is odd
D)s is divisible by 4
E)w + x + 8 = y + z
Rationale: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
s = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that s is not divisible by 8. Answer (B)
Answer: B
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 80%?
Options:
A)10.8
B)20.8
C)28.8
D)18.8
E)17.8
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 480% of Re. 1 = Rs.24/5
For Rs. 24/5 , toffees sold = 6.
For Re. 1, toffees sold = 6 x 24/5 =28.8.
Answer C
Answer: C
Question: 5. Find the value for log58 + 5(1/1000)
Options:
A)3
B)-3
C)4
D)-4
E)5
Rationale: Solution:
log58 + 5(1/1000) = loglog5(8 x 1/1000)
= log5(1/125)
= log5(1/5)3
= log5(5)-3
= -3log5(5)
= -3 x 1
= -3
ANSWER IS B
Answer: B
Question: If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible?
Options:
A)120
B)240
C)12
D)360
E)720
Rationale: We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=3!*2!=12 ways
Answer C
Answer: C
Question: here are 5 Rock songs, 6 karnatic songs and 3 Indi pop songs. How many different albums can be formed using the above albums should contain at least 1 Rock song and 1 karnatic song?
Options:
A)36254
B)45124
C)15624
D)45654
E)36254
Rationale: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.
In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1 = 31 ways.
Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1 = 64 - 1 = 63 ways.
And the 3 Indi pop can be selected in 23 = 8 ways. Here the option of not selecting even one Indi Pop is allowed.
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Ans: C
Answer: C
Question: 3 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?
Options:
A)1/2
B)9/24
C)15/24
D)18/24
E)21/24
Rationale: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*1*1=3
and total possible outcomes =3!=6
probability of the favourable outcome=1/2. A
Answer: A
Question: Average of six numbers comes out to be 3.95. Average of two of the numbers is 3.4 while the average of other two is 3.85. Determine the average of the two numbers left.
Options:
A)4.7
B)4.8
C)4.3
D)4.6
E)4.9
Rationale: Explanation:
In the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers.
=> 3.95 (Average of 1st and 2nd number)
=> 3.85 (Average of 3rd and 4th number)
=> 3.4 (Average of 5th and 6th number)
3.95 = (3.4 + 3.85 + x)/3
x = 4.6
ANSWER D
Answer: D
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical E present. If the concentration of chemical E is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
Options:
A)100% decrease
B)50% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: Let A and E be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/E
Since new E is increased by 100%
Rate = A^2/(2E)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: D
Question: Peter read R books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
Options:
A)R > 35N
B)R < N − 35
C)R > N + 35
D)R = N − 35
E)R = N + 35
Rationale: Peter read R books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. R > 35N
B. R < N − 35
C. R > N + 35
D. R = N − 35
E. R = N + 35
Since Peter read more books than Nikki we have R>N. Moreover since Peter reads 35 more books than Nikki easily we can have R=N+35.
So the answer is (E).
Answer: E
Question: Simplify
25âˆ’[2âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
Options:
A)37
B)25
C)28
D)30
E)32
Rationale: Explanation:
=25âˆ’[2âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=25âˆ’[2âˆ’(6+2Ã—4))]
=25âˆ’[âˆ’12]=25+12=37
Option A
Answer: A
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 6km on foot. His total journey is
Options:
A)16km
B)10km
C)12km
D)24km
E)36km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +6 =x
5x +36 =6x
X = 36km
Answer: Option E
Answer: E
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Options:
A)10
B)35
C)25
D)45
E)15
Rationale: 2/5 of 25 = 10
ANSWER:A
Answer: A
Question: The average expenditure of a labourer for 6 months was 95 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
Options:
A)70
B)72
C)75
D)78
E)84
Rationale: Income of 6 months = (6 × 95) – debt
= 570 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 840
Average monthly income = 840 ÷ 10 = 84
Answer E
Answer: E
Question: A four-character password consists of one letter of the alphabet and three different digits between 0 and 7, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
Options:
A)5,040
B)18,720
C)17,472
D)37,440
E)52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 8 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 7 ways.
Next digit can be chosen in 6 ways.
This gives us 8*26*7*6ways
Now, the letter can also be DDLD so there will be another 8*26*7*6 ways
Total = 8*26*7*6*2 = 17,472 ways C
Answer: C
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
Options:
A)20
B)99
C)7878
D)656
E)27
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20% Answer: A
Answer: A
Question: If p/8 = r/2 and r = 0.75s, what is the ratio of p to r to s?
Options:
A)2 : 3 : 4
B)8 : 12 : 9
C)24 : 6 : 8
D)6 : 4 : 3
E)12 : 8 : 3
Rationale: p/8=r/2, r=0.75s, what is p:r:s?
we get p/r=8/2 and r/s=3/4, so
8/3*3/2 and 2/2*3/4
24/6 and 6/8
C
Answer: C
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 190 kilometers?
Options:
A)3.5 gallons
B)2.7 gallons
C)5.7 gallons
D)4.75 gallons
E)7.5 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 190 kilometers?
190 Ã· 40 = 4.75 Ã— 1 gallon = 4.75 gallons
correct answer is D) 4.75 gallons
Answer: D
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 34 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
Options:
A)33 years
B)34 years
C)35 years
D)36 years
E)29 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*25 + 3*28 + 3*34 + x + x + 11 = 11*28.
=> 75+84+102+2x+11=308
so 2x = 36
so x = 18.
Age of the captain = (x+11)
= 29 years.
Answer : E
Answer: E
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Options:
A)8000
B)8077
C)2776
D)2976
E)2971
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000.Answer: A
Answer: A
Question: How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?
Options:
A)51
B)56
C)58
D)62
E)63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind	CP of 1 kg sugar of 2nd kind
Rs. 9	Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4	9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: E
Question: By how much does the larger root of the equation 2q^2+5q = 12 exceed the smaller root?
Options:
A) 5/2
B) 10/3
C) 7/2
D) 14/3
E) 11/2
Rationale: For 2q^2+5q = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: E
Question: A basketball player succeeds with 80% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Options:
A)0.972
B)0.978
C)0.984
D)0.992
E)0.998
Rationale: P(missing all 3 free throws) = 0.2^3 = 0.008
P(succeeding at least once) = 1 - 0.008 = 0.992
The answer is D.
Answer: D
Question: What is x if x + 2y = 10 and y = 4?
Options:
A)A)10
B)B)8
C)C)6
D)D)4
E)E)2
Rationale: x = 10 - 2y
x = 10 - 8.
x = 2
Answer : E
Answer: E
Question: A batsman scored 150runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets.
Options:
A)40%
B)50%
C)60%
D)66.66%
E)70%
Rationale: Explanation:
Number of runs made by running = 150 - (5 x 4 + 5 x 6)
= 150 - (50)
= 100
Now, we need to calculate 100 is what percent of 150.
=> 100/150 * 100 = 66.66 %
Option D
Answer: D
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)1:2
Rationale: profit=time*capital
so 400:600=2:3
ANSWER:B
Answer: B