mathewhe/aqua_rat huggingface dataset:
Question: In a certain game of dice, the player’s score is determined as a sum of three throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If John plays this game against 22 other players, what is the probability of the minimum score that will guarantee John some monetary payoff?
(A) 41/50
(B) 1/216
(C) 1/221
(D) 1/84
(E) 1/42
Rationale: To guarantee that John will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and John will get nothing.
P(18)=1/6^3=1/216.
Answer: B.
Answer: (B) 1/216
Question: Data sufficiency question:
If solution (x) with alcohol (14%) and solution (y) with alcohol (20%) mixed together to form 24 liters of mixture.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 3
Rationale: Explanation:
Let a liters of first solution, and 'b' liters of second solution has been taken.
So using weighted average formula = n1×a1+n2×a2n1+n2n1×a1+n2×a2n1+n2 = n1×14+n2×20n1+n2=15n1×14+n2×20n1+n2=15
⇒n1=5n2⇒n1n2=51⇒n1=5n2⇒n1n2=51
As total volume was given as 24 liters, first solution = 16×24=416×24=4
So statement 1 is sufficient.
Answer:A
Answer: (A) 1
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 157
(B) 197
(C) 152
(D) 1518
(E) 112
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: D
Answer: (D) 1518
Question: Some ladies can do a piece of work in 12 days. Two times the number of such ladies will do half of that
work in :
(A) 6 days
(B) 4 days
(C) 12 days
(D) 3 days
(E) 8 days
Rationale: Expl : Let x ladies can do the work in 12 days. More ladies, less days (Indirect)
Less work, less days (direct)
Ladies 2x : x Work 1 : ½
2x : x , 1 : ½ : : 12 : y
:. 2x * 1*y = x* ½ *12 or y = 3
Hence the required number of days = 3
Answer:D
Answer: (D) 3 days
Question: In Orange County, one ninth of the people are gathering mushrooms and one eighth of the people are collecting apples. What can be the number of people in Orange County?
(A) 244
(B) 260
(C) 275
(D) 288
(E) 292
Rationale: The number must be a multiple of both 9 and 8 so the answer is 288.
The answer is D.
Answer: (D) 288
Question: Find the numbers which are in the ratio 3:2:3 such that the sum of the first and the second added to the difference of the third and the second is 24?
(A) 4,3,22
(B) 4,4,22
(C) 9,3,32
(D) 9,6,12
(E) 18,12,18
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:3
Given, (a + b) + (c - b) = 24
=> a + c = 24
=> 3x + 3x = 24 => x = 6
a, b, c are 3x, 2x, 3x
a, b, c are 18, 12, 18.
Answer:E
Answer: (E) 18,12,18
Question: How many of the positive divisors D of 120 are also multiples of 4 not including 120?
(A) 3.
(B) 4.
(C) 5.
(D) 7.
(E) 8.
Rationale: 4,8,12,20,24,40,60. (7) is the answer
Other way : factors of 120 = 2^3 * 3*5
Separate 2^2 ( which means 4)
Now, calculate the number of other factors.
D=2*3*5 = total positive factors are 2*2*2 = 8
This 8 factors include 120
So subtract 1 from 8
Ans is 7=D
Answer: (D) 7.
Question: Ravi and sunil are partners in a business. Ravi invests Rs.20,000 for 8 months and Sunil invested Rs.16000 for 10 months then after one year ratio of their profits will be
(A) 1:1
(B) 2:3
(C) 3:2
(D) 3:1
(E) 3:4
Rationale: =(15000*8):(8000*10)
=160000:160000
=1:1
ANSWER:A
Answer: (A) 1:1
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
(A) 2 sq m
(B) 18 sq m
(C) 3 sq m
(D) 12 sq m
(E) 15 sq m
Rationale: Explanation:
Area S=(a+b+c)/2
S = (1 + 2 + 3)/2 = 3 sq m.
Answer : C
Answer: (C) 3 sq m
Question: 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
(A) 15%
(B) 20%
(C) 80%
(D) 70%
(E) 90%
Rationale: Explanation :
Let number of men = 100.
Then, 80 men are less than or equal to 50 years old i.e 20 men are greater than 50 years of age.
Now, the number of men above 50 years who play football = 20% of 20 = 4.
20% of all men play football i.e total no. of men who play football = 20, out of which 4 men are above 50 years old.
So, 20 - 4 = 16 men are less than or equal to 50 years old.
Therefore, percentage of football players less than or equal to 50 years = (16/20) x 100 = 80% .
Answer : C
Answer: (C) 80%
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 22
(B) 99
(C) 27
(D) 28
(E) 20
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m.Answer:D
Answer: (D) 28
Question: Rs. 4536 is divided among 4 men, 5 women and 2 boys. The ratio of share of a man, a woman and a boy is 7: 4: 3. What is the share of a woman?
(A) 236
(B) 336
(C) 346
(D) 356
(E) 426
Rationale: Ratio of the share of a man, a woman and a boy is 7:4:3
No of men, women and boys are 4, 5, 2
Thus effective ratio of men, women and boys is 7*4 : 4*5 : 3*2 = 28 : 20 : 6
so part of women = (20/54)* 4536 = 1680
so part of 1 woman = 1680/5 =336
ANSWER:B
Answer: (B) 336
Question: A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes half an hour and 3 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 5/4
(E) 3/7
Rationale: The rate of the basic system is 1 room/half hour = 2 rooms per hour
The rate of the advanced system is 1/3 of a room per hour
The combined rate is 7/3 rooms per hour.
The time to ventilate one room is 3/7 of an hour.
The answer is E.
Answer: (E) 3/7
Question: There are 840 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 140
(B) 100
(C) 125
(D) 175
(E) 225
Rationale: female = x
Male = 840-x
x/2 + 840-x/4 = 1/3* (840)= 280
x= 280
x/2 = 140 is supposed to be the answer
M is missing something
Correct Option A
Answer: (A) 140
Question: Robert spent $100 in buying raw materials, $125 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) $150
(B) $210
(C) $250
(D) $160
(E) $200
Rationale: Let the total amount be x
then, (100-10)% of x = 100+125
90% of x = 225
90x/100 = 225
x = $250
Answer is C
Answer: (C) $250
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.88 at the candy store. What is John’s weekly allowance?
(A) $2.70
(B) $3.00
(C) $3.30
(D) $3.60
(E) $3.90
Rationale: x = 3x/5 + 1/3*2x/5 + 88
4x/15 = 88
x = 330 = $3.30
The answer is C.
Answer: (C) $3.30
Question: A 10% stock yields 8%.The market value of the stock is :
(A) Rs. 72
(B) Rs. 125
(C) Rs. 112.50
(D) Rs. 116.50
(E) None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 10, investment = Rs.(100/8X10)= Rs. 125
∴ Market value of Rs. 100 stock = Rs.125
Answer B
Answer: (B) Rs. 125
Question: Two trains are moving in the same direction at 126 kmph and 54 kmph. The faster train crosses a man in the slower train in 14 seconds. Find the length of the faster train?
(A) 280
(B) 290
(C) 300
(D) 310
(E) 320
Rationale: Relative speed = (126 - 54) * 5/18 = 4 * 5
= 20 mps.
Distance covered in 27 sec
= 14 * 20
= 280 m.
The length of the faster train
= 280 m.
Answer:A
Answer: (A) 280
Question: If cost of sugar increases by 12%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
(A) 7.5
(B) 9.2
(C) 10.7
(D) 15.3
(E) 18.6
Rationale: 100
112
-----
112 ----- 12
100 ------ ? => 10.7%
Answer:C
Answer: (C) 10.7
Question: Sheena has a pet frog and it is growing fast and eating more flies each day. When she first brought it home on Monday it ate 3 flies, Tuesday it ate 6, Wednesday it ate 9, and Friday it ate 15.
How many flies did her frog eat on Thursday?
(A) 12
(B) 14
(C) 10
(D) 11
(E) 13
Rationale: A) 12. The frog started eating 3 more flies each day.
3 +3 =6
6+3=9
9+3=12
12+3=15
Answer: (A) 12
Question: 30.5 % of 2000
(A) 556
(B) 612.5
(C) 756.8
(D) 610
(E) 820
Rationale: 1 % of 2000 = 2030% of 2000 = 30*20 =6000.5% of 2000 = 0.5*2000 = 10Total =610Answer :D
Answer: (D) 610
Question: In how many ways can the letters of the word 'BANANA' be arranged?
(A) 60
(B) 50
(C) 48
(D) 96
(E) 78
Rationale: The word BANANA contains 6 letters
1B,3A,2N
required number of ways = 6!/(1!*3!*2!) = 60
Answer is A
Answer: (A) 60
Question: If 30/x is an integer and 3/x is an integer, which of the following must be true?
I. 10/x is an integer
II. 3/x is an integer
III. 6/x is an integer
(A) II only
(B) I only
(C) III only
(D) II,III only
(E) I,III only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 3, GCD of 30 and 3, and if x=3 then ONLY II is true.
Answer: A
Answer: (A) II only
Question: The average of marks obtained by 120 boys was 38. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
(A) 100
(B) 110
(C) 115
(D) 125
(E) 140
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 38
24X = 4560 - 1800
=> X = 2760/24
X = 115.
Hence, the number of boys passed = 115.
ANSWER:C
Answer: (C) 115
Question: How many words can be formed by using all letters of the word “LOVE”
(A) 12
(B) 24
(C) 15
(D) 16
(E) 140
Rationale: The word LOVE contains 4 different letters.
Required number of words = 4p4 = 4! = (4x3x2x1) = 24.
Answer B
Answer: (B) 24
Question: man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14years
(B) 26 years
(C) 17 years
(D) 18 years
(E) 22 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
answer :E
Answer: (E) 22 years
Question: When the positive integer c is divided by 11, the quotient is d and the remainder 3. When c is divided by 19, the remainder is also 3. What is the remainder when d is divided by 19?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r
where k = LCM (d1,d2)
In this case the divisors are 1119 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also c=d1q+3 ; which means d1q=209d1=11 therefore q=19
And ( d divided by 19)19/19 leaves remainder 0.
Answer is E
Answer: (E) 0
Question: Vikas can cover a distance in 1hr 24min by covering 2/3 of
the distance at 4 kmph and the rest at 5kmph.the total
distance is?
(A) 8km
(B) 6 km
(C) 2km
(D) 11km
(E) 7km
Rationale: Let total distance be S
total time=1hr24min
A to T :: speed=4kmph
diistance=2/3S
T to S :: speed=5km
distance=1-(2/3S)=1/3S
21/15 hr=(2/3 S)/4 + (1/3s) /5
84=(14/3S)*3
S=(84*3)/14*3
= 6km
Answer is B.
Answer: (B) 6 km
Question: The ratio between Sumit's and Prakash's age at present is 2:3. Sumit is 6 years younger than Prakash. The ratio of Sumit's age to Prakash's age after 6 years will be :
(A) 1 : 2
(B) 2 : 3
(C) 3 : 4
(D) 3 : 8
(E) None
Rationale: Explanation:
Let their ages be 2x and 3x years.
3x-2x=6 or x=6
Sumit's age = 12 years, Prakash's age = 24 years
Ratio of their ages = 18 : 24 = 3 :4.
Correct Option: C
Answer: (C) 3 : 4
Question: If 8 men or 12 women can do a piece of work in 20 days, in how many days can the same work be done by 6 men and 11 women?
(A) 10 days
(B) 11 days
(C) 12 days
(D) 15 days
(E) 17 days
Rationale: 8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/20
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*20= 1/240
so, 20 women work= 20/240=1/12
ans: 12days
ANSWER:C
Answer: (C) 12 days
Question: Sabrina gave Samantha as many dollars as Samantha started out with. Samantha then gave Sabrina back as much as Sabrina had left.
Sabrina then gave Samantha back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00. How much did Sabrina and Samantha have at the beginning of their exchange?
(A) $50
(B) $40
(C) $30
(D) $20
(E) $10
Rationale: Sabrina had $50 and Samantha had $30.
This can be solved by setting up two simultaneous equations, but it’s easier just to work backwards.
At each step, the person who is receiving the money gets the amount that they were already holding. In other words, they double their money.
Therefore, just before the last exchange, Samantha must have had $40 and was given another $40 to get to her total of $80.
Just before the second exchange, Sabrina must have had half of her $40. Therefore, Sabrina had $20 and Samantha had $60.
After the first exchange Samantha doubled her money, so she must have had $30 before the exchange, leaving Sabrina with $50 at the start.
Answer A
Answer: (A) $50
Question: The average age of a class of 20 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 40
(B) 41
(C) 42
(D) 45
(E) 43
Rationale: Total age of all students =20Ã—21
Total age of all students + Age of the teacher =21Ã—22
Age of the teacher
=21Ã—22âˆ’21Ã—20=21(22âˆ’20)=21Ã—2=42
Answer is C.
Answer: (C) 42
Question: If the integer N = 139k53 where k is the hundreds digit, N can never be divisible by which of the following?
(A) 5
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: Apply the rule here that for a number to be divisible by 5 the last digits must be 0 or 5
Since in 'N' integer last digit is 3
This is never divisible by 5.
hence A is correct
Answer: (A) 5
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 150 marks, the no of questions he attempts correctly is :
(A) 35
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 150
=> 5x = 210
=> x = 42
Answer: D
Answer: (D) 42
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 9 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 1240
(D) 1480
(E) 1080
Rationale: Total # of outfits = 12 * 10 * 9 = 960
Answer - D
Answer: (D) 1480
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
(A) 8%
(B) 9%
(C) 11%
(D) 12.5%
(E) 20%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 75 :(75/15)) then typical dosage would be 2 *5 = 10 cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 10)*100 = 20 %
E is the answer.
Answer: (E) 20%
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent R above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 = 200%=R
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: The circulation for magazine M in 1961 was 3 times the average (arithmetic mean) yearly circulation for magazine M for the years 1962-1970. What is the ratio of the circulation in 1961 to the total circulation during 1961-1970 for magazine M ?
(A) 9/4
(B) 5/4
(C) 7/4
(D) 3/4
(E) 1/4
Rationale: There are 9 years from 1962-1970, inclusive. Let's say the average circulation every year between 1962-1970 inclusive is x.
So the total circulation is 9x from 1962-1970, inclusive.
In 1961, the circulation is 3x.
So total circulation for 1961-1970 is 3x + 9x = 12x.
Ratio of circulation in 1961 to total circulation during 1961-1970 is 3x to 12x or 3/12=1/4
Answer :E
Answer: (E) 1/4
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 4
(B) 6
(C) 8
(D) 9
(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) 6
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 5 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
(A) 19 3/4 days
(B) 29 3/4 days
(C) 9 3/4 days
(D) 16 days
(E) 39 3/4 days
Rationale: 4/18 + (x -5)/27 + x/36 = 1
x = 29 3/4 days
ANSWER:B
Answer: (B) 29 3/4 days
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 4:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
(A) $24960
(B) $25920
(C) $28080
(D) $28500
(E) $29160
Rationale: From 9:00 in the morning to 4:55 in the afternoon, inclusive there are 8*12=96 five-minute intervals, thus total of 96*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=96*30 --> x=24*30 and 3x=3*(24*30)=24*90.
Therefore, the total revenue from ticket sales that day was 24*30*6+24*90*10=$25,920.
Answer: B.
Answer: (B) $25920
Question: In the quadratic equation x2 - bx + 20 = 0, if the product of two roots is 20, what is the sum of the two roots?
(A) 20
(B) 12
(C) 16
(D) 14
(E) 18
Rationale: Explanation:
The sum of the roots of the quadratic equation ax2 + ax + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation x2 - ax + 20 = 0, where a = 1, b = - a and c = 20.
we get, product of the roots = 20
sum of the roots = -(-12)/ 1 = 12
ANSWER: B
Answer: (B) 12
Question: A number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?
(A) 60
(B) 8
(C) 7
(D) 12
(E) 13
Rationale: x * 3/5 * 1/5 = 9
x = 75 => 7 + 5 = 12
ANSWER:D
Answer: (D) 12
Question: A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system?
(A) 90
(B) 150
(C) 270
(D) 300
(E) 450
Rationale: We have ratio in 5:3:1 and this is shifted to 2:4:3 ( C:S:T )
If we observe the ratio of the tobacco increased by 2 times (3-1)
T = 1/9*1350 = 150.
Since tobacco increased by 2 times..we get 150*2 = 300.
Answer D is the answer..
Answer: (D) 300
Question: If 30 and 12 are factors of K, which of the following is the largest number that must divide evenly into K?
(A) 21
(B) 36
(C) 90
(D) 60
(E) 42
Rationale: In order to solve this, you can calculate the LCM(30,12) (Least common multiple of 30 and 12)
After the calculations you will find that the LCM(30,12)= 60.
You will then check which of the numbers given in the alternatives are divisible by 60 and choose the largest of them.
In this case, the largest divisible number is 60.
Answer D
Answer: (D) 60
Question: In how many years does a sum of Rs. 7000 yield a simple interest of Rs. 16000 at 15% p.a.?
(A) 15.23 years
(B) 16.23 years
(C) 17.23 years
(D) 18.23 years
(E) 19.23 years
Rationale: T = (100 * 16000)/(15 * 7000) = 15.23 years
ANSWER:A
Answer: (A) 15.23 years
Question: if remainder is 1 , quotient is 54 and dividend is 217 then what is divisor ?
(A) 2
(B) 4
(C) 6
(D) 14
(E) 16
Rationale: we know
dividend = divisor * quotient + remainder===> 217 = divisor * 54 + 1 =====> 216/54 = divisor ===> divisor = 4 Ans - B
Answer: (B) 4
Question: {(476 + 424)2 - 4 x 476 x 424} = ?
(A) 2135
(B) 6551
(C) 2704
(D) 6466
(E) 1113
Rationale: Given Exp.	= [(a + b)2 - 4ab], where a = 476 and b = 424
= [(476 + 424)2 - 4 x 476 x 424]
= [(900)2 - 807296]
= 810000 - 807296
= 2704.
Correct Option is C
Answer: (C) 2704
Question: A hollow iron pipe is 42 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 3 g/cm3, then the weight of the pipe is:
(A) 2.172 kg
(B) 2.272 kg
(C) 2.282 kg
(D) 2.992 kg
(E) 2.772 kg
Rationale: External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron	=22/7x ((4 SQUARE)-(3 SQUARE))X42
=(22/7)X7X1X42 cm3.
= 924cm3.
Weight of iron = (924 x 3) gm = 2772 gm = 2.772 kg
answer :E
Answer: (E) 2.772 kg
Question: The least number which when divided by 3, 4, 5 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
(A) 167
(B) 243
(C) 252
(D) 336
(E) None of these
Rationale: Explanation:
L.C.M of 3, 4, 5, 8 = 120
therefore Required Number is of the form 120k+3.
Least value of k for which (120k+3) is divisible by 9 is k = 2
therefore Required Number = (120 x 2+3)=243
Answer: B
Answer: (B) 243
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 45
(B) 50
(C) 54
(D) 56
(E) 55
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: Option B
Answer: (B) 50
Question: A small company reduced its faculty by approximately 14 percent to 195 employees. What was the original number of employees?
(A) A)182
(B) B)227
(C) C)220
(D) D)224
(E) E)302
Rationale: If x is the original number of employees, then after 14% reduction in employees number is .86x
but we are given .86x = 195
x = 227
So the original number of employees is 227
Correct Answer - B
Answer: (B) B)227
Question: 5358 x 51 = ?
(A) 272258
(B) 272358
(C) 273258
(D) 274258
(E) 274358
Rationale: 5358 x 51	= 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
C)
Answer: (C) 273258
Question: The ratio of men to women in a class is 4 to 3. If 4 men drop out of the class and the ratio of men to women after the drop out is 10 to 9, then how many men are currently in the class?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Equation on the basis of question
4x-4/3x=10/9
x=6
Original number of men = 4*6=24
Original Number of Women = 3*6=18
Current number of men = 24-4=20 (Answer)
Current number of women = 18
Ratio = 20/18= 10/9 ( Just to verify)
Ans D
Answer: (D) 20
Question: At a small company, 64 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
(A) 5/16
(B) 3/4
(C) 9/20
(D) 7/10
(E) 5/7
Rationale: Lets take total employees are 100.
Given that,Total Women= 64 and Total Married = 60.
Total Men = 100 - 64 = 36 and Single men = 2/3*36 = 24.
Married men = total men - single men = 36 - 24 = 12.
Married women= Total married - Married men = 60 - 12 = 48.
Fraction of women are married = Married women / Total Women = 48 / 64 = 3/4. ANS B
Answer: (B) 3/4
Question: If 102x = 25, then 10-x equals:
(A) A)3
(B) B)2
(C) C)6
(D) D)9
(E) E)1/5
Rationale: 102x = 25
(10x)2 = 52
10x = 5
1/10x = 1/5
10-x = 1/5
Answer :E
Answer: (E) E)1/5