mathewhe/aqua_rat huggingface dataset:
Question: If a 2 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: The area A of the large cube is 2*2*6 = 24 square cm.
The area of the 8 small cubes is 8*6 = 48 = 2A, an increase of 100%.
The answer is B.
Answer: (B) 100%
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 700
(B) 726
(C) 800
(D) 278
(E) 298
Rationale: n:
25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Answer: (C) 800
Question: The ratio of pens to pencils is 5 to 6. There are 7 more pencils than pens. How many pencils are there?
(A) 36
(B) 42
(C) 48
(D) 55
(E) 64
Rationale: Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 7
x = 7
The number of pencils is 42.
The answer is B.
Answer: (B) 42
Question: In a sports club with 30 members, 17 play badminton and 17 play tennis and 2 do not play either. How many members play both badminton and tennis?
(A) 7
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: Let x play both badminton and tennis so 17-x play only badminton and 17-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(17-x)+x+2=30
36-2x+x=30
36-x=30
x=6
So 6 members play both badminton and tennis.
B
Answer: (B) 6
Question: Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in
(A) 9
(B) 8
(C) 4
(D) 3
(E) 1
Rationale: Explanation:
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
Answer: D) 3 days
Answer: (D) 3
Question: What is the units digit of (147^21)^48 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 21 has the form 4n+1 so the units digit is 7 inside the bracket. The number 48 has the form 4n, so the units digit is 1. The answer is A.
Answer: (A) 1
Question: There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
(A) 2!*7!
(B) 2!*8!
(C) 3!*7!
(D) 3!*8!
(E) None of these
Rationale: Solution: Total number of ways = 7!*2!.
Answer: Option A
Answer: (A) 2!*7!
Question: Express a speed of 414 kmph in meters per second?
(A) 201 mps
(B) 114 mps
(C) 118 mps
(D) 115mps
(E) 111 mps
Rationale: 414* 5/18 = 115 mps
Answer: D
Answer: (D) 115mps
Question: Ramesh purchased a refrigerator for Rs. 13500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 2899
(D) 18975
(E) 12778
Rationale: Price at which the TV set is bought = Rs. 13,500
Discount offered = 20%
Marked Price = 13500 * 100/80 = Rs. 16875
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 17250 * 110/100
= Rs. 18975
Answer: D
Answer: (D) 18975
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
(A) Rs. 80
(B) Rs. 96
(C) Rs. 106
(D) Rs. 108
(E) Rs. 118
Rationale: Michel earns Rs 135 by investing Rs1620
To earn Rs 8 how much he have to invest?
=(8*1620)/135=Rs 96
ANSWER:B
Answer: (B) Rs. 96
Question: Of the four-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 6048
(B) 3648
(C) 7248
(D) 1448
(E) 2168
Rationale: Of the four-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7ways;
# of permutations of 3 digits in ppqr - 4!/2!
Total: 9*8*7*4!/2!=6048.
Answer: A.
Answer: (A) 6048
Question: The average weight of 8 persons increases by 5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 65 kg
(C) 55 kg
(D) 85 kg
(E) 105 kg
Rationale: Total weight increased = (8 x 5) kg = 40 kg.
Weight of new person = (65 + 40) kg = 105 kg.
Answer: E
Answer: (E) 105 kg
Question: Yali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?
(A) 82
(B) 96
(C) 110
(D) 120
(E) 192
Rationale: Yali want to double the original amount of blocks, not just the red blocks
the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).
192-82 = 110
so 110 bricks need to be added to the new 82 brick tower to double the original.
They worded the question ashow many red bricks need to be addedbut really it could be any colour just that 110 more bricks need to be there to equal 192=E
Answer: (E) 192
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1 : 96
(B) 1 : 97
(C) 1 : 98
(D) 1 : 99
(E) 1 : 93
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: (A) 1 : 96
Question: Gao earns $25.00 for each house she cleans. She refuses to work weekends. Monday she cleaned 2 houses 1 on Tuesday and only 3 more for the rest of the week. How much money did Gao earn this week?
(A) $160
(B) $140
(C) $170
(D) $165
(E) $135
Rationale: Adding all the houses together is 2+1+3=6. If she gets $25 for each house then you must multiply 25 and 6. 25 x 6 =160. She got $160 this week.
Answer: (A) $160
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 65 Kmph
(B) 70 Kmph
(C) 72 Kmph
(D) 75 Kmph
(E) 73 Kmph
Rationale: Explanation:
Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER IS C
Answer: (C) 72 Kmph
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements Q.
(A) a) Q=48
(B) b) Q=144
(C) c) Q=240
(D) d) 288
(E) e) 120
Rationale: One specificboy is seated to either of end seat, lets call him b1
One specificgirl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Answer: (C) c) Q=240
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
(A) 4
(B) 8
(C) 16
(D) 12
(E) 14
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
answer :B
Answer: (B) 8
Question: An empty wooden vessel weighs 8% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
(A) 3/5
(B) 5/9
(C) 1/24
(D) 4/9
(E) 3/7
Rationale: An empty wooden vessel weighs 8% of its total weight when filled with paint:
Vessel = 0.08(Vessel + Paint);
8V = V + P (so the weight of completely filled vessel is 8V)
P = 7V (so the weight of the paint when the vessels is completely filled is 7V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*8V;
P' = 3V (so the weight of the paint when the vessels is partially filled is 3V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 3V/7V = 3/7.
Answer: E
Answer: (E) 3/7
Question: If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to:
(A) 55/601
(B) 601/55
(C) 11/120
(D) 120/11
(E) 120/13
Rationale: Let the numbers be a and b.
Then, a + b = 55 and ab = 5 * 120 = 600.
Required sum = 1/a + 1/b = (a + b)/ab = 55/600 = 11/120.
ANSWER:C
Answer: (C) 11/120
Question: In what time will a railway train 90 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 1 sec
(C) 9 sec
(D) 6 sec
(E) 2 sec
Rationale: T = 90/36 * 18/5
= 9 sec
Answer:C
Answer: (C) 9 sec
Question: Dawson professes to sell his goods at the cost price but he made use of 600 grams instead of a kg, what is the gain percent?
(A) 13 2/3%
(B) 14 2/3%
(C) 15 2/3%
(D) 16 2/3%
(E) 17 2/3%
Rationale: Answer:	600 --- 100
100 --- ? => 16 2/3%
Answer:D
Answer: (D) 16 2/3%
Question: Three friends (Fred, James and Kelly) are employees of a company. Their respective salaries are in the ratio of 4 : 6 : 7. James and Kelly's salaries together is Rs. 8840. By what percent is Kelly's salary than that of Sarah?
(A) 40%
(B) 60%
(C) 90%
(D) 70%
(E) 80%
Rationale: Explanation:
Let the salaries be 4x, 6x and 7x respectively.
Then,6x + 7x = 8840 => x = 680.
Fred's salary = Rs. 2800, James's salary = Rs. 4080, and Kelly's salary Rs. 4760.
Excess of Kelly's salary over Fred's=[ (1960 /2800) x 100] = 70%.
Answer: D
Answer: (D) 70%
Question: In order to complete a reading assignment on time, Terry planned to read 100 pages per day. However, she read only 50 pages per day at first, leaving 800 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
(A) 12
(B) 14
(C) 16
(D) 10
(E) 18
Rationale: D=100*X - according to the plan, assignment to be completed on time reading 100 pages per day for next X days. But, Terry's plans changed so she read as follow:
50 pages for first Y days and 800 pages for last 6 days, we get these equations:
50*Y+800=100*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 60 pages per day and 6 leftover days used to complete a lump 780 pages
From above we find that X=Y+6 and 50Y+800=100Y+600 or 50Y=200 --->>>>> Y=4, hence X=10
Answer : D
Answer: (D) 10
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 8/15
(B) 7/15
(C) 6/15
(D) 5/15
(E) 4/15
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
Answer is A.
Answer: (A) 8/15
Question: Given that x = 2^b – (8^32 + 16^5), which of the following values for b yields the lowest value for |x|?
(A) 94
(B) 95
(C) 96
(D) 97
(E) 116
Rationale: 8^32 + 16^5 = 2^96 + 2^20
Compared to 2^96, the value of 2^20 is negligible.
2^96 - (2^96 +2^20) will minimize the value of |x|.
The answer is C.
Answer: (C) 96
Question: In how many ways can the letters of the word "COMPUTER" be arranged?
(A) 36480
(B) 40320
(C) 44290
(D) 48360
(E) 52810
Rationale: The total ways of arranging the letters = 8! = 40320
The answer is B.
Answer: (B) 40320
Question: Alex deposited x dollars into a new account that earned 4 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.08+1.16)
(C) w/(1.16+1.24)
(D) w/(1.04+1.04^2)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.04x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.04x+x) dollars. Account at the end of the second year would be (1.04x+x)*1.04=w --> x(1.04^2+1.04)=w --> x=w/(1.04+1.04^2).
Answer: D.
Answer: (D) w/(1.04+1.04^2)
Question: Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?
(A) 72
(B) 84
(C) 136
(D) 140
(E) None of these
Rationale: Explanation:
Let the number be x. Then,
2/5 of 1/3 of 3/7 of
x = 15 => x = (15 * 5/3 * 3 * 5/2) = 525/2
40% of 525/2 = (40/100 * 525/2) = 105
Answer IS E
Answer: (E) None of these
Question: A certain bacteria colony doubles in size every day for 22 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
(A) 6.33 
(B) 7.5 
(C) 21
(D) 15 
(E) 19 
Rationale: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be
Day 1 – B
Day 2 – 2B
Day 3 – 4B
Day 4 – 8B
.
.
.
Day 22 – 2^19 B
It can be implied that the capacity of the habitat is 2^19 B.
Case 2: There are 2 bacteria which keep doubling every day. So, the count would be
Day 1 – 2B
Day 2 – 4B
Day 3 – 8B
.
.
.
Day 18 – 2^18 B
Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.
Hence, 21 is the answer
C
Answer: (C) 21
Question: A toy store sells small, medium, and large toy trucks in each of the colors red, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
(A) 1/4
(B) 1/3
(C) 5/9
(D) 7/12
(E) 2/3
Rationale: Probability of NOT selecting medium out of 3 sizes = 2/3
Probability of NOT selecting red out of 3 colours = 2/3
Total probability of NOT selecting red and medium = (2/3)*(2/3) = 4/9
Required probability = 1 - 4/9 (this will select at least one of red and medium)
= 5/9
The answer is C.
Answer: (C) 5/9
Question: A sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
(A) $3,000
(B) $3,150
(C) $4,000
(D) $2,500
(E) $5,000
Rationale: We're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600.
Since the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 20% of $1,000 = $200
20% of $4,000 = 4($200) = $800
This is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure.
Let's TEST Answer D: $2,500
Since 20% of $1,000 = $200
20% of $2,500 = 2.5($200) = $500
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Answer: (D) $2,500
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?
(A) 22
(B) 27
(C) 20
(D) 21
(E) 12
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20
Discount % = 124.2/621 * 100 = 20%.Answer: C
Answer: (C) 20
Question: The perimeter of one face of a cube is 48 cm. Its volume will be:
(A) 125cm3
(B) 400cm3
(C) 250cm3
(D) 625cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 48/4 = 12 cm
Volume = a*a*a = 12*12*12 = 1728 cm cube
Option E
Answer: (E) None of these
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 17 sec
(B) 14 sec
(C) 48 sec
(D) 87 sec
(E) 25 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Answer: (C) 48 sec
Question: 30% of a number is more than 60% of 50 by 30. Find the number?
(A) 120
(B) 200
(C) 180
(D) 300
(E) 140
Rationale: (30/100) * X – (60/100) * 50 = 30
2/7 X = 60
X = 200
Answer:B
Answer: (B) 200
Question: N and B are integers. The expression (N+1)(B+1) is even. What can be said about N and B?
(A) They are both even numbers.
(B) At least one of them is even.
(C) At least one of them is odd.
(D) They are both odd.
(E) Nothing can be said surly on N and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (N+1) or (B+1) needs to be Even
So either N or B needs to be odd
Or At least one of them is odd.
At least one of them is odd=C
Answer: (C) At least one of them is odd.
Question: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 32
(B) 87
(C) 30
(D) 99
(E) 77
Rationale: 3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30
Answer: C
Answer: (C) 30
Question: If log4X + log4(1/6) = 1/2 then the value of X is?
(A) 18
(B) 24
(C) 16
(D) 12
(E) 10
Rationale: log4X +log4(1/6) = 1/2
=> log4[X x 1/6] = 1/2
=>log4 [X/6] = 1/2
=> 41/2 = X/6
=> 2 = X/6
Therefore, X = 12
ANSWER:D
Answer: (D) 12
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
(A) 11
(B) 67
(C) 88
(D) 25
(E) 12
Rationale: [50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer:D
Answer: (D) 25
Question: Sum of the squares of 3 no.'s is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: A certain manufacturer of cake, muffin, and bread mixes has 120 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) a. 1/10
(B) b. 3/10
(C) c. 1/4
(D) d. 7/10
(E) e. 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 120
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 120
B-CB-MB-2CMB = 30
hence the probability = 30/120 = 1/4.
C
Answer: (C) c. 1/4
Question: Jason's team scored 60 points in a game basketball and he accounted for 60 percent of their points. How much did he score?
(A) 42
(B) 38
(C) 36
(D) 44
(E) 40
Rationale: 600/10 x (6/10) = 3600/100 or 36
Answer is C
Answer: (C) 36
Question: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 360, 300, and 360 as the side’s lengths, what is the triangle’s area?
(A) 34,200
(B) 36,200
(C) 38,200
(D) 49,089
(E) 43,200
Rationale: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2,
-> P=(360+300+360)/2=510, area=√(510(510-360)(510-300)(510-360))=49,089. Therefore, the answer is D.
Answer: (D) 49,089
Question: The number 0.5 is how much greater than 1/3 ?
(A) 1/6
(B) 2/10
(C) 1/50
(D) 1/500
(E) 2/500
Rationale: let x be the difference
then
.5-1/3=x
5/10-1/3=x
x=1/6
ans A
Answer: (A) 1/6
Question: If E and F are non-zero integers, and E/F > 1, then which of the following must be true?
(A) E > F
(B) EF>F
(C) E^2< F^2
(D) 2E< F
(E) E^3 < F^3
Rationale: B
Answer: (B) EF>F
Question: A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ?
(A) 130feet
(B) 22feet
(C) 20feet
(D) 15feet
(E) 10feet
Rationale: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 10 * Breadth = 600
=> Breadth = 60 feet
Area to be fenced = 2B + L = 2*60 + 10
= 130 feet
Answer: Option A
Answer: (A) 130feet
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/213
(B) 1/215
(C) 1/216
(D) 2/113
(E) 3/114
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.2%
(B) 0.4%
(C) 0.6%
(D) 0.8%
(E) 1%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (105/100)*x * (96/100)*y = (504/500 )(xy)
Error In measurement = (504/500)xy- xy= (4/500)xy
Error % = [(4/500)xy*(1/xy) *100] % = (4/5) % = 0.8%.
ANSWER D 0.8%
Answer: (D) 0.8%
Question: If 2x + y = 5 and 3x-2y = 7, then what is the value of 5x - y?
(A) 1/7
(B) 3
(C) 15
(D) 52/7
(E) 12
Rationale: 2x+y=5 ...equation 1
3x-2y=7 ...equation 2
adding both the equations
5x-y=12
correct answer option E
Answer: (E) 12
Question: x is the 9 digit largest number(digits are 1 to 9 with out repeat) which is divisible by 11 and y second largest number which also divisible by 11 then difference between x and y is?
(A) 160
(B) 170
(C) 188
(D) 198
(E) 208
Rationale: "sum of digit at even place and sum of digit at odd places must be adjusted such that their difference is 0 or divisible by 11.
we have 9 digit without repetition,
so sum of digit from 1 to 9 =45
Let sum of digit at odd place will be 'w' and sum of even place will be 'Z'.
W + Z= 45
W - Z = 11
2W = 56
So W = 28 and Z = 17
now the digits at odd place are 2, 4, 6, 7, 9
sum of digit at odd place is 2+4+6+7+9 = 28
the digits at even place are 1,3,5,8
sum of digits at even place is 1+3+5+8 =17
so the largest no will be find by put no. of odd and even places in increasing order accordingly
1st lasrgest no is 987563412
and 2nd largest no is 987563214
diference between them
X-Y=198
ANSWER:D
Answer: (D) 198
Question: For what value of x, is |x – 5| + |x + 4| + |x| = 14?
(A)  0
(B)  3
(C)  4
(D)  -4
(E)  5
Rationale: For what value of x, is |x – 5| + |x + 4| + |x| = 14?
It's easiest just to plug in answer choices:
(E): 5
|x – 5| + |x + 4| + |x| = 14?
|5 - 5| + |5 + 4| + |5| = 14?
|0| + |9| + |5| = 14
(E)
Answer: (E)  5
Question: A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
(A) 0.35 days
(B) 0.45 days
(C) 0.55 days
(D) 0.25 days
(E) 0.2 days
Rationale: B = 1/4 – 1/20 =0.2 days
ANSWER:E
Answer: (E) 0.2 days