mathewhe/aqua_rat huggingface dataset:
Question: Two ropes are given to you. Both of the ropes will take exactly an hour each to burn fully.
You are asked to measure forty five minutes using the two ropes. How will you achieve to do it?
(A) 30 minutes
(B) 40 minutes
(C) 50 minutes
(D) 60 minutes
(E) 70 minutes
Rationale: Solution:
Take both the ropes. Now light the first rope from both the ends. Light the second rope from just one end. In thirty minutes, the first rope will burn fully. At this point of time, the second rope will be left exactly half and you have to light it from the second end now. It will take half of the actual time (thirty minutes) to burn now i.e. fifteen minute.
Thirty Minutes + Fifteen minutes = Forty Minutes
Answer B
Answer: (B) 40 minutes
Question: If x and y are positive integers, and x^3*y^4 = 5488, which of the following is the value of xy?
(A) 6
(B) 10
(C) 14
(D) 15
(E) 21
Rationale: 5488 = 2*2744 = 2^2*1372 = 2^3*686 = 2^4*343 = 2^4*7^3
xy = 2*7 = 14
The answer is C.
Answer: (C) 14
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
(A) 2
(B) 1
(C) 6
(D) 7
(E) 9
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer: B
Answer: (B) 1
Question: A car takes 12 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/4th of the previous time?
(A) 25Kmph
(B) 60Kmph
(C) 100Kmph
(D) 120Kmph
(E) 180Kmph
Rationale: Time = 12
Distence = 540
3/4 of 12 hours = 12 * 3/4 = 9 Hours
Required speed = 540/9 = 60 Kmph
B)
Answer: (B) 60Kmph
Question: A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 200 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?
.
(A) (B + 200)/2.
(B) (B + 2)/6.
(C) (2B + 200)/3.
(D) (B + 2)/3.
(E) (B - 2)/6
Rationale: P: cost of 1 paint brush in cents; W: cost of 1 bucket of white wash in cents
P + W = 100*B cents (B dollars)
paintbrush costs 200 cents less than twice the price of a bucket of whitewash
So, P-200 = 2W ---> P=2W+200
P + W = 100*B cents (B dollars) ---> 2W+200+W = 100*B ---> 3W = 100*B - 200 ---> W = (100B - 200)/3
Price of half bucket of White wash = W/2 = (100B - 200)/6 dollars or (B-2)/6 in cents.
Answer is E.
Answer: (E) (B - 2)/6
Question: find two integers, neither of which ends in a zero, and whose product is exactly 10,000
(A) 64 and 15,625
(B) 60 and 15,625
(C) 64 and 15,620
(D) 16 and 625
(E) 64 and 16,625
Rationale: 10,000=10^4
=10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)
=(2^4)x(5^4)
= 16x625
so the numbers are 16 and 625
ANSWER:D
Answer: (D) 16 and 625
Question: If Tim had lunch at $50.50 and he gave 15% tip, how much did he spend?
(A) $58
(B) $60.60
(C) $70.60
(D) $40.60
(E) $50.60
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 15% of 50.50 = (15/100)*50.50 = $7.575
Total spent
50.50 + 7.575 = $58
correct answer A
Answer: (A) $58
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 19 years replaced by a new boy. The age of the new boy is?
(A) 15 years 8 months
(B) 15 years
(C) 16 years 4 months
(D) 17 years 10 months
(E) 17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 19 years - 3 years 4 months.
= 15 years 8 months.
ANSWER:A
Answer: (A) 15 years 8 months
Question: A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is
(A) 12Π cm3
(B) 15Π cm3
(C) 16Π cm3
(D) 20Π cm3
(E) None
Rationale: Solution
Clearly, we have r = 3cm and h = 4cm.
∴ Volume	= 1/3Πr2h
= (1/3 x Π x 32x4)cm3
= 12Πcm3.
Answer A
Answer: (A) 12Π cm3
Question: A number when divided by the sum of 555 and 445 gives two times their difference the quotient and 30 as the remainder. The number is
(A) 1220
(B) 1250
(C) 22030
(D) 220030
(E) None
Rationale: Solution
Required number	= (555+445)×2×110+30
220000+30
‹=›220030.
Answer D
Answer: (D) 220030
Question: A tap can fill a tank in 4 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 3 hr
(B) 1 hr 30 min
(C) 2 hr 30 min
(D) 2 hr
(E) 4 hr
Rationale: Explanation:
A tap can fill a tank in 4 hours.
Therefore the tap can fill half the tank in 2 hours.
Remaining part =1/2
After half the tank is filled, three more similar taps are opened.
Hence, total number of taps becomes 4.
Part filled by one tap in 1 hour =1/4
Part filled by four taps in 1 hour =4×14=1
i.e., 4 taps can fill remaining half in 30 minutes.
Total time taken= 2 hour + 30 minute = 2 hour 30 minutes
Answer: Option C
Answer: (C) 2 hr 30 min
Question: Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money Q would he earn per month?
(A) $700
(B) $754
(C) $770
(D) $782
(E) $893
Rationale: OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
Q=$700 + $70 = $770.
The correct answer is choice (C).
Answer: (C) $770
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 298 m
(B) 279 m
(C) 827 m
(D) 150 m
(E) 165 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer:D
Answer: (D) 150 m
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were TWO times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 6/7
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=2E=2(I-S)
=> 14S = 2I => Savings = 1/7 I
Hence Expenditure = 1-(1/7)I = 6/7 I
Answer (A)
Answer: (A) 6/7
Question: A certain high school has 500 students. Of these students, 50 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
(A) 430
(B) 440
(C) 450
(D) 460
(E) 470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 50
Y = 20
Z = 10
So, we have 50 students taking music, 20 taking art and 10 taking BOTH music and art.
40 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 60 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 60 = 440.
B
Answer: (B) 440
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 1/2
(B) 2/3
(C) 1/4
(D) 4/5
(E) 5/6
Rationale: Let Mary's monthly savings = S
Mary's monthly pay = P
Mary's monthly expenditure = P-S
Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month
12S = 3*(P-S)
=>4S = P-S
=> P = 5S
Mary's monthly expenditure = P-S = 5S-S = 4S
fraction of her salary that Mary spent each month = 4S / 5S = 4/5
Answer D
Answer: (D) 4/5
Question: Evaluate : 986 x 237 - 986 x 37
(A) 197600
(B) 168000
(C) 278000
(D) 192700
(E) None of them
Rationale: 986 x 237 - 986 x 37 = 986 x (237 - 37) = 986 x 200 = 197200.
Answer is D.
Answer: (D) 192700
Question: Using all the letters of the word "QUESTION", how many words can be formed, which begin with Q and end with N?
(A) 713
(B) 650
(C) 720
(D) 700
(E) 456
Rationale: There are five letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with Q and N all the remaining three blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
Answer:C
Answer: (C) 720
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.6 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
(A) 24 years
(B) 44 years
(C) 34 years
(D) 48 years
(E) 84 years
Rationale: If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 6 = 11
4A + 6 = 9
9(5A + 6)=11(4A + 6)
A = 12
Thomasâ€™s current age = 4A
= 48 years.
D
Answer: (D) 48 years
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 34 is subtracted and divided by 10?
(A) 4
(B) 7
(C) 8
(D) 2
(E) 3
Rationale: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 34)/10 = (54 - 34)/10 = 2
Answer: Option D
Answer: (D) 2
Question: If the sales tax be reduced from 4 (1/3) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 8000?
(A) Rs. 156.66
(B) Rs. 150.23
(C) Rs. 146.66
(D) Rs. 135.06
(E) None of these
Rationale: Explanation:
Required difference = (4 (1/3) of Rs. 8000) - (2 (1/2) of Rs. 8000)
= (13/3 – 5/2) % of Rs. 8000
= (11/6) x (1/100) x 8000
= Rs. 146.66
ANSWER C
Answer: (C) Rs. 146.66
Question: Of the 14,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
(A) 14.3%
(B) 16.67%
(C) 33%
(D) 28.6%
(E) 49.67%
Rationale: the number of employees is not reqd...
1/2 of 2/7 are shunted out so 1/7 left... there are another 5 equal parts(5/7)..
so total remaining parts=6, in which 1 part is journeyman....
therefore %=1/6*100=16.67%
ANSWER:B
Answer: (B) 16.67%
Question: One hour before John started walking from P to Q, a distance of 23 miles, Ann had started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met?
(A) 6 miles
(B) 8,4 miles
(C) 9 miles
(D) 9,6 miles
(E) 15 miles
Rationale: Ann walks from Q to P at a speed of 3 miles/hr for one hour. She covers 3 miles in 1 hour and now distance between John and Ann is 23 - 3 = 20 miles.
Ann walks at 3 mph and John at 2 mph so their relative speed is 3+2 = 5 mph.
They have to cover 20 miles so it will take them 20/5 =4 hours to meet.
In 4 hrs, Ann would have covered 4 hrs * 3 miles per hour = 12 miles.
Adding this to the 3 miles she covered before John, Ann covered a total of 3 + 12 = 15 miles.
Answer (E)
Answer: (E) 15 miles
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 15.5 days
(B) 19.5 days
(C) 10 days
(D) 16.5 days
(E) 18.5 days
Rationale: C = 1/5 – 1/10 = 5/50 => 10 days
ANSWER:C
Answer: (C) 10 days
Question: Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 3000, what is the area of the side face of the box?
(A) 300
(B) 150
(C) 180
(D) 109
(E) 200
Rationale: Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 3000
l*1.5l*2l= 3000
l=10
Side face area= l*d= l*2l= 10*2*10=200
E is the answer
Answer: (E) 200
Question: How many positive integers less than 5,000 are evenly divisible by neither 15 nor 23?
(A) 4,514
(B) 4,475
(C) 4,521
(D) 4,428
(E) 4,349
Rationale: integers less than 5000 divisible by 15 5000/15 =333.something , so 333
integers less than 5000 divisible by 23 5000/23 = 238.## , so 238
we have double counted some, so take LCM of 15 and 23 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 23 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4521 answer C.
Answer: (C) 4,521
Question: Which of the following is closer to (3!+2!)+(3!-2!)?
(A) 8
(B) 22
(C) 10
(D) 14
(E) 12
Rationale: (3!+2!)+(3!-12!)=6+2+6-2
= 12
Answer: E
Answer: (E) 12
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 1:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
(A) 20% or 70%
(B) 40%
(C) 50%
(D) 55%
(E) 70%
Rationale: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 1:4:8
Initial Total dogs = 13X ( x assumed; 1+4+8= 13), Since the total dogs are less than 30 therefore initial total value has to be 13
L = 1, A = 4 E = 8
L:A= 1:4
This ratio doubles
Hence New Dog count is
L= 2 , A = 4 E= X: Also 2+4+x<30
We need to Find X*100/(2+4+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 2*100/(6+x) %A = 4*100/(6+x); Only Value for X is 4 or 14; 6+x<30 and % integer
Therefore, Enormus Dogs % is = 4*100/(20) = 20% or 14*100/20 % =70%
20% or 70%
A
Answer: (A) 20% or 70%
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 12 inches long, how wide is Jordan's rectangle, in inches?
(A) 25
(B) 23
(C) 22
(D) 20
(E) 10
Rationale: Area of Carol's rectangle = 24*5 = 120
Let width of Jordan's rectangle= w
Since , the areas are equal
12w = 120
=>w = 10
Answer E
Answer: (E) 10
Question: What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2.
(A) 35
(B) 66
(C) 77
(D) 88
(E) 99
Rationale: Ans. 35
Answer: (A) 35
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 7 hours. How long would it take for both hoses to fill up two-thirds of the pool?
(A) 5/12 hours
(B) 5/8 hours
(C) 28/13 hours
(D) 12/7 hours
(E) 12/5 hours
Rationale: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 7 hours
i.e. 1 Hour work of Hose 2 = 1/7
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/7) = (13/42)
i.e. (13/42) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(42/13)*(2/3) = 28/13 hour
Answer: Option C
Answer: (C) 28/13 hours
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 175/256
(B) 256/175
(C) 451/784
(D) 451/864
(E) 145/562
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: A
Answer: (A) 175/256
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15
(B) 66
(C) 77
(D) 88
(E) 12
Rationale: 90 * 10/60 = 15 kmph
Answer:A
Answer: (A) 15
Question: A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $45,000 in property taxes, but did not pay until October 15th?
(A) $1,400
(B) $1,800
(C) $2,400
(D) $21,400
(E) $12,150
Rationale: Original amount = 20,000
Fine for July = 20,000 * 1% = 450
Fine for August = lesser of the 2 , 450+600= 1050 or 450*3=1350 . Pick 1350
Fine for September = 1350+600=1950 or 1350*3 = 4050. Pick 4050
Fine for October = 4050+600=4650 or 4050*3 = 12150. Pick 12150.
The wording of the question should be have been clearer as total fines should be = 12150+4050+1350+450 = 18000 and NOT 12150.
12150 is the fine ONLY for the month of October!
E
Answer: (E) $12,150
Question: 34.	The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 9 feet, and the diagonal of the rectangular plate was 15 ft. What is height of the of the cylinder?
(A) 12
(B) 15
(C) 10
(D) 8
(E) 14
Rationale: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 12. Correct answer A
Answer: (A) 12
Question: The cost price of an article is 56% of the marked price. Calculate the gain percent after allowing a discount of 13%.
(A) 23.4%
(B) 44.5%
(C) 55.3%
(D) 57.4%
(E) none
Rationale: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 56. S.P = Rs. 87.
âˆ´ Gain % = [31/56 * 100]% = 55.3%.
Answer C
Answer: (C) 55.3%
Question: How many three letter combinations can be formed using the letters of the word STARE?
(A) 6
(B) 25
(C) 45
(D) 60
(E) 120
Rationale: The number of letters in the given word is five.
The number of three letter combinations that can be formed using these five letters is
= 5 * 4 * 3 = 60.
Answer: D
Answer: (D) 60
Question: At what price must an article costing Rs.85.5 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 122.5
(B) 142.5
(C) 162.5
(D) 182.5
(E) 112.5
Rationale: CP = 85.50
SP = 85.5*(125/100) = 106.875
MP*(95/100) = 106.875
MP = 112.5
Answer:E
Answer: (E) 112.5
Question: A, B and C have Rs.400 between them, A and C together have Rs.300 and B and C Rs.150. How much does C have?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 100
Rationale: A+B+C = 400
A+C = 300
B+C = 150
--------------
A+B+2C = 450
A+B+C = 400
----------------
C = 50
Answer : B
Answer: (B) 50
Question: Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
(A) Rs. 22000
(B) Rs. 24000
(C) Rs. 26000
(D) Rs. 28000
(E) None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Option B
Answer: (B) Rs. 24000
Question: If b does not equal zero, and ab = b/4, what is the value of a?
(A) 1/8
(B) 1/4
(C) 1/3
(D) 1/2
(E) None of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/4
(ab)/b = (b/4)/b
a = (b/4)*1/b
a = 1/4
Answer: (B).
Answer: (B) 1/4
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
(A) $38,796.
(B) $40,000.
(C) $38,976.
(D) $29,232.
(E) $36,796.
Rationale: 30,000 *1.16*.84=29,232
Answer D
Answer: (D) $29,232.
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Y would it have taken for him to walk both ways.
(A) 8 h 45 min
(B) 7 h 45 min
(C) 6 h 45 min
(D) 5 h 30 min
(E) None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back Y=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: (A) 8 h 45 min
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 150?
(A) 3
(B) 14
(C) 30
(D) 42
(E) 30
Rationale: Greatest common factor n and 16 is 4 = 2*2 * 2*2
Greatest common factor n and 45 is 3 = 3*3 *5
Greatest common factor n and 150 is = 2*3*5 =30
Answer: E.
Answer: (E) 30
Question: There are 35 students in a hostel. If the no. of students increases by 2, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) s. 234.50
(B) s. 239.50
(C) s. 242.50
(D) s. 248.50
(E) s. 249.50
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 2) = x – 1
or, 35x + 42 = 37x – 37
or, x = 39.50
Thus the original expenditure of the mess = 35 x 39.5 =1382.50
Therefore x-1 = 38.5
hence 42 x 38.5 = 1617
1617-1382.50 = Rs. 234.50
A
Answer: (A) s. 234.50
Question: In a box, there are 4 green, 5 black and 7 red pencils. One pen is picked up randomly. What is the probability that it is neither black nor red?
(A) 2/5
(B) 1/5
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: Explanation :
Neither black nor red means the pencils drawn is green.
Total number of outcomes = (4+5+7) = 16.
Number of Favourable outcomes = 4 = Number of green pencils.
Hence, Probability of the event = 4/16 = 1/4.
Answer : E
Answer: (E) 1/4
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,220, what was the total number of pairs of contact lenses that she sold?
(A)  9
(B)  13
(C)  15
(D)  17
(E)  19
Rationale: (x+5)*150 +x*85=1220
=>x=2
total lens=2+(2+5)= 9
Answer A
Answer: (A)  9
Question: The average age of three boys is 18 years and their ages are in the proportion 3 : 3 : 6. The age of the youngest boy is:
(A) 21 years
(B) 18 years
(C) 15.5 years
(D) 13.5 years
(E) None of these
Rationale: Total age of 3 boys = (18 Ã— 3) years = 54 years. Ratio of their ages = 3 : 3 : 6.
Age of the youngest = (54 Ã— 3â„12) years = 13.5 years.
Answer D
Answer: (D) 13.5 years
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 20 seconds. The ratio of their speeds is?
(A) 3/7
(B) 3/2
(C) 3/5
(D) 3/1
(E) 3/3
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 20
==> 27 x + 17 y = 20 x + 20 y ==> 7 x = 3 y ==> x/y
= 3/7.
Answer: A
Answer: (A) 3/7