mathewhe/aqua_rat huggingface dataset:
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 288. What is their H.C.F.?
(A) 18
(B) 24
(C) 36
(D) 42
(E) 48
Rationale: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 288
x = 24
HCF of 2x, 3x and 4x = x = 24
The answer is B.
Answer: (B) 24
Question: The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
(A) 1/64
(B) 1/9
(C) 1/16
(D) 1/25
(E) 1/2
Rationale: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128
We will add the cases to get 1/64
Answer: (A) 1/64
Question: A rectangular block 10cm by 20cm by 30cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
(A) 6
(B) 10
(C) 15
(D) 40
(E) 22
Rationale: Volume of the block = 10*20*30 = 6000 cm^3
Side of the largest cube = H.C.F of 10,20,30 = 10cm
Volume of the cube = 10*10*10 = 1000 cm^3
Number of cubes = 6000/1000 = 6
Answer is A
Answer: (A) 6
Question: There are 8 stores in town that had a total of 24 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 9 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 9 people visited 2 stores each for 18 visits.
To maximize the number of stores that one person visited, let's assume that 2 people visited 1 store each. The number of remaining visits is 24 - 18 - 2 = 4, which is the maximum that one person could have visited.
The answer is C.
Answer: (C) 4
Question: Which of the following is closest to (20!-19!)/(20!+19!)?
(A) 1.25
(B) 0.9
(C) 2.1
(D) 0.3
(E) 1.69
Rationale: (20!-19!)/(20!+19!)
19! (20-1)/19! (20+1)
19/21 = 0.9
B is the answer
Answer: (B) 0.9
Question: If we multiply the digits of a number until we get a single digit, then which is the only two digit number which require multiplication of digits more than 3 times?
(A) 77
(B) 67
(C) 87
(D) 97
(E) 57
Rationale: 77 =7*7 =49
49 =4*9 =36
36 =3*6 =18
18 =1*8 =8
ANSWER:A
Answer: (A) 77
Question: A departmental store has 5 managers and 25 associates. The 5 managers have an average salary of $1500. The 25 associates have an average salary of $20,000. What is the average salary for the departmental store?
(A) $14,000
(B) $12800
(C) $15,000
(D) $14,500
(E) $16,916.66
Rationale: Number of managers is 5
Their average salary is $1500
Number of associates is 25
Their average salary is $20,000
Total salary of managers is 5*1500=$7500
Total salary of associates is 25*20,000=$500,000
Total salary for the departmental store is 500,000+7500=50,7500
Average salary for the departmental store is 50,7500/5+25=16,916.66
Answer is E
Answer: (E) $16,916.66
Question: A man invests some money partly in 10% stock at 90 and partly in 5% stock at 90.To obtain equal dividends from both,he must invest the money in the ratio :
(A) 1 : 2
(B) 3 : 5
(C) 4 : 5
(D) 16 : 15
(E) None
Rationale: Solution
For an income of Rs. 1 in 10% stock at 90, investment = Rs. (90/10)= Rs. 9 .
For an income of Rs. 1 in 5% stock at 90, investment = Rs.(90/5) = Rs. 18.
∴ Ratio of investments = 9 :18 =1:2
Answer A
Answer: (A) 1 : 2
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 4 oranges.
The answer is D.
Answer: (D) 4
Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 1km
(B) 1.5km
(C) 5km
(D) 3.2km
(E) 2.4km
Rationale: Speed of down stream = 5+1 = 6kmph
speed of upstream = 5-1 = 4kmph
Let the required distance be xkm
x/6 + x/4 = 1
2x+3x = 12
x = 2.4 km
Answer is E
Answer: (E) 2.4km
Question: A FAIR AND LOVELY manufacturer produces 100 units of a certain model each month at a cost to the manufacturer of £10 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £10,000?
(A) 90
(B) 60
(C) 110
(D) 30
(E) 34
Rationale: 100(x-10)≥10,000
x-10≥100
x≥110
Answer: Option C
Answer: (C) 110
Question: How many integers are between 6 and 74/5, inclusive?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: 74/5 = 14.xx
We are not concerned about the exact value of 74/5 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 6 and 74/5 would be 6, 7, 8, 9, 10, 11, 12,13,14
Total number of integers = 9
Option E
Answer: (E) 9
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 7
(B) 5
(C) 4
(D) 2
(E) 1
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Answer: (B) 5
Question: A train 100 m long passed a pole in 20 sec. How long will it take to pass a platform 500 m long?
(A) 90 sec
(B) 100 sec
(C) 110 sec
(D) 120 sec
(E) 130 sec
Rationale: Speed = 100/20 = 5 m/sec.
Required time = (100 + 500)/5 = 120 sec
Answer:D
Answer: (D) 120 sec
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: B
2
If the number 1056 is completely divisible by 23 means, remainder should come zero.
But if we divide 1056 by 23, the remainder is 2.
So if 2 is added to the 1056, we get remainder 0.
Therefore solution is 2
Answer: (B) 2
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost Z for a course at the gym's highest level?
(A) $175
(B) $245
(C) $425
(D) $675
(E) $725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost Z of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: (A) $175
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1230
(B) 1280
(C) 1290
(D) 1340
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: 39! is divided by 41. Then what is the remainder?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: (A) 1
Question: What percent of a day is 5 hours?
(A) 12%
(B) 12.5%
(C) 13%
(D) 20.8%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (5/100 * 24) = 20.8%
Answer : D
Answer: (D) 20.8%
Question: Find the highest common factor of 36 and 84.
(A) 12
(B) 10
(C) 16
(D) 19
(E) 18
Rationale: 36 = 2^2 x 3^2
84 = 2^2 x 3 x 7
H.C.F. = 2^2 x 3 = 12.
Answer: Option A
Answer: (A) 12
Question: A passenger train takes two hours less for a journey of 300km if its speed is increased by 5 kmph from its normal speed. The normal speed is
(A) 35 kmph
(B) 50 kmph
(C) 25kmph
(D) 30 kmph
(E) 38 kmph
Rationale: let normal speed = x
Increased speed = x + 5
Initial => x = 300/t1
=> t1 = 300/x
After => (x + 5) = 300/(t1 - 2)
=> (x + 5) = 300 / [ (300/x) - 2]
=> x = 25kmph
ANSWER:C
Answer: (C) 25kmph
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 9 days
(C) 12 days
(D) 14 days
(E) 16 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 = 10 × 40/50 = 8 days.
A)
Answer: (A) 8 days
Question: A card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox. Find the total number of pins used .
(A) 135
(B) 136
(C) 137
(D) 138
(E) 139
Rationale: (35*4)-4=136
ANSWER:B
Answer: (B) 136
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is?
(A) 11 years
(B) 88 years
(C) 38 years
(D) 17 years
(E) 18 years
Rationale: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
Answer: C
Answer: (C) 38 years
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 15?
(A) A)100
(B) B)150
(C) C)250
(D) D)200
(E) E)160
Rationale: Then, 10% of x= 15
(10/100)x = 15
x = (15*100*)/10= 150
Answer is B
Answer: (B) B)150
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 13
(B) 18
(C) 40
(D) 82
(E) 43
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 63)
=> x/2 = 20
=> x = 40
Answer:C
Answer: (C) 40
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 7
(B) 9
(C) 8
(D) 6
(E) 4
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 6 boys when a boy gets any no. of prizes?
(A) 1296
(B) 1678
(C) 1456
(D) 1200
(E) 1340
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the 4 prizes can be given in 6 ways, i.e. (6 x 6 x 6 x 6) ways = 64 ways = 1296 ways Or nr ways = 64 ways = 1296 ways
Answer: (A) 1296
Question: A train running at the speed of 60 km/hr crosses a pole in 3 sec. What is the length of the train?
(A) 50
(B) 75
(C) 100
(D) 120
(E) 25
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 3 = 50 m
Answer: A
Answer: (A) 50
Question: From a nine-member dance group, six will be chosen at random to volunteer at a youth dance event. If Kori and Jason are three of the nine members, what is the probability that three will be chosen to volunteer?
(A) a) 1/21
(B) b) 100/7
(C) c) 4/21
(D) d) 2/7
(E) e) 3/7
Rationale: Total number of ways to choose 6 out of 9 = 9C6 = 21/5.
Number of ways to choose 3 (any but Kori and Jason) out of 6 (excluding Kori and Jason) = 6C3 = 60.
P = favorable/total = 60/(21/5) = 100/7.
Answer: B.
Answer: (B) b) 100/7
Question: 400 + 5 × 4 = ?
(A) 820
(B) 202
(C) 420
(D) 209
(E) None of these
Rationale: 400 + 5 × 4 = ?
or, ? = 400 + 20 = 420
Answer C
Answer: (C) 420
Question: A certain team has 10 members, including Joey. A three-member relay team will be selected as follows: one of the 10 members is to be chosen at random to run first, one of the remaining 9 members is to be chosen at random to run second, and one of the remaining 8 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/1320
(B) 1/132
(C) 1/110
(D) 1/12
(E) 1/5
Rationale: Total outcomes= 10*9*8
Favorable Outcomes= 9*1*8 and 9*8*1
P=2*9*8*1/10*9*8
P=1/5
Ans E
Answer: (E) 1/5
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 28, what is the common ratio of the G.P?
(A) 3
(B) 1/3
(C) 2
(D) 9
(E) 1/9
Rationale: 28=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
28=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
28=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
27=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
27=r^3
r=3
A
Answer: (A) 3
Question: A trader sells 23 meters of cloth for Rs. 529 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?
(A) 26
(B) 88
(C) 90
(D) 42
(E) 18
Rationale: SP of 1m of cloth = 529/23 = Rs. 23
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 23 - Rs. 5 = Rs. 18
Answer:E
Answer: (E) 18
Question: How many natural numbers are there between 43 and 200 which are exactly divisible by 6?
(A) 28
(B) 26
(C) 24
(D) 22
(E) 21
Rationale: Explanation :
43/6 = 7, remainder = 1. Hence 5 more should be added to 43 to get the minimum
number divisible by 6 between 43 and 200.
=> Minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48
200/6 = 33, remainder = 2. Hence 2 should be decreased from 200 to get the maximum
number divisible by 6 between 43 and 200.
=> Maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198
Hence, natural numbers numbers divisible by 6 between 43 and 200 are 48, 54, 60,...198
This is Arithmetic Progression with a = 48, d = 6, l=198
Number of terms = (l − a)/d + 1 = (198 − 48)/6 + 1 = 150/6 + 1 = 25 + 1 = 26. Answer : Option B
Answer: (B) 26
Question: Jack and Christina are standing 360 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 7 feet per second. Lindy runs at a constant speed of 12 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
(A) 270
(B) 300
(C) 330
(D) 360
(E) 390
Rationale: The relative speed of Jack and Christina is 5+ 7 = 12 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 360/12 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 12*30 = 360 feet.
Answer: D.
Answer: (D) 360
Question: The product of x and y is a constant. If the value of x is increased by 40%, by what percentage must the value of y be decreased?
(A) 34%
(B) 36%
(C) 28.57%
(D) 30%
(E) 32%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.4x (140)
i.e. 140*New 'y' = 10000
i.e. New 'y' = 10000/140 = 71.43
i.e. y decreases from 100 to 71.43 i.e. Decrease of 28.57%
C
Answer: (C) 28.57%
Question: Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 10
Rationale: We have 5, 10, 10 and 20 to work with
From least to greatest, we have...
5 (the least)
10
15
20
25
30
35
40
45 (the greatest)
Total options = 9
Final Answer:D
Answer: (D) 9
Question: M is the sum of the reciprocals of the consecutive integers from 301 to 400, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/4< M < 1/3
Rationale: M = 1/301 + 1/302 + 1/303 + ...... + 1/400
If we replace the first 99 terms by 1/400, then we get a sum = 100/400 = 1/4. Since the actual terms are larger than 1/400, the sum is larger than 1/4.
If we replace the all the 100 terms by 1/300, we get a sum = 100/300 = 1/3. Since the actual terms are smaller than 1/200, the sum is less than 1/3.
Therefore 1/4 < M < 1/3
Choice E
Answer: (E) 1/4< M < 1/3
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 240*80 / 60 + 40 / 10 = ?
(A) -2305
(B) -2407
(C) 2509
(D) -2101
(E) None of these
Rationale: Explanation:
Given : 240*80 / 60 + 40 / 10 = ?
Substituting the coded symbols for mathematical operations, we get,
240 / 80 - 60 * 40 - 10 = ?
3 - 2400 - 10 = -2407
ANSWER : B
Answer: (B) -2407
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?
(A) 178.88
(B) 178.29
(C) 188.29
(D) 178.2
(E) 178.12
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35
= 180 cm - 60 /35 cm
= 180 cm - 1.71 cm
= 178.29 cm.
Answer:B
Answer: (B) 178.29
Question: A rectangular with dimensions 10 inches by 15 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
(A) a) 4 inches
(B) b) 6 inches
(C) c) 7 inches
(D) d) 8 inches
(E) e) 5 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
10=2*5
15=3*5
GCF = 5
P.S you can make squares with side of 5
Answer : E
Answer: (E) e) 5 inches
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
(A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
(B) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.759
(C) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.758
(D) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.752
(E) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.122
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Answer: (A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Question: A lady who lived in a shoe had to buy Christmas gifts for her big family. She selected the cheapest stocking stuffers. The bill was still high. There was an addition of 15 percent of the sales tax and an addition of the 5 percent of the luxury tax to the actual amount. She paid $100.
Find out the original price of the stuffers without the taxes ?
(A) $55.26
(B) $83.33
(C) $45.87
(D) $90.12
(E) $95>50
Rationale: B
The original price is $83.33.
(20 percent of the taxes are added to the selling price.)
Answer: (B) $83.33
Question: A number when divided by 133 leaves 16 as a remainder. What will be the remainder if the number is divided by 50?
(A) 51
(B) 56
(C) 49
(D) 17
(E) 7
Rationale: 133+16=149
Dividing 149 evenly into whole numbers is 2 and leaves 49 remaining.
The correct answer is C.
Answer: (C) 49
Question: Two-third of a positive number and 25/216 of its reciprocal are equal. The number is:
(A) 5/12
(B) 12/5
(C) 25/144
(D) 144/25
(E) 146/25
Rationale: Let the number be x. Then,
2/3 x = 25/216 * 1/x
x2 = 25/216 * 3/2 = 25/144
x = 5/12
ANSWER:A
Answer: (A) 5/12
Question: If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x / y from options below?
(A) 1
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: B. x=27, y=9
27^2=729
9^3=729
x / y=27 / 9=3
My Answer is (B) 3
Answer: (B) 3
Question: 39! is divided by 41 then find the remainder?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: (A) 1
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $Q could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
(A) dQ / C
(B) Q / (C-d)
(C) d / (C-dQ)
(D) Q / (C(C-d))
(E) dQ/C(C - d)
Rationale: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = Q
n = Q/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dQ/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dQ/C(C - d)
Answer: E
Answer: (E) dQ/C(C - d)
Question: Two cubes each with side b are joined to form a cuboids. What is the surface area of this cuboids?
(A) 12b^2
(B) 10b^2
(C) 6b^2
(D) 4b^2
(E) 2b^2
Rationale: l=2b; b=b; h=b;
surface area=2*(lb+bh+hl)
=2*(2b^2+b^2+2b^2)
=10 b^2
ANSWER:B
Answer: (B) 10b^2
Question: 10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?
(A) 22
(B) 20
(C) 10
(D) 15
(E) none
Rationale: it is written that 10 men and 10 women dance with each other. so there is no chance of matching more than 2 partners at a time. so 2 men & 1 women is not possible.
ANSWER:E
Answer: (E) none
Question: Tom read a book containing 1000 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 15 pages a day more, how many days did Tom spend reading the book?
(A) 20
(B) 18
(C) 16
(D) 15
(E) 15.39
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=480 (we want to find the Days, soP=480/D)
2) (P+15)(D-5)=1000=> PD-5P+15D-75=1000
as the 1) stated u can put 1) into 2)
=> 1000-5P+15D-75=1000 => 15D-5P=75
put the bold one into it => 15D-5(480/D)=75the we get the final equation 16D^2-2400=80D (divide 16)
=> D^2-5D-160=0
so D=15.39days. Ans: (E)
Answer: (E) 15.39
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 7 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 1/3
(B) 2/5
(C) 3/7
(D) 1/2
(E) 7/13
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 7*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 7x
=13x
August tips as a fraction of total tips = 7x/13x =7/13. So E
Answer: (E) 7/13
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 195 m
(B) 145 m
(C) 175 m
(D) 179 m
(E) 125 m
Rationale: Explanation:
RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: Option C
Answer: (C) 175 m
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
(A) 40%
(B) 60%
(C) 80%
(D) 20%
(E) 28%
Rationale: A B C D
90 100 80 100
A D
90 ---------100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer:C
Answer: (C) 80%