mathewhe/aqua_rat huggingface dataset:
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
(A) 3.34 sq m
(B) 3.94 sq m
(C) 7.34 sq m
(D) 3.35 sq m
(E) 3.44 sq m
Rationale: Explanation:
Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m
Answer: Option A
Answer: (A) 3.34 sq m
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 10x +5 = 0?
(A) 6
(B) 42
(C) 24
(D) 18
(E) 95
Rationale: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -10/1 = -10
ab = 5/1 = 5
Hence a/b + b/a = [(-10)2 - 2(5)]/5 = 90/5 = 18.
D)
Answer: (D) 18
Question: Find the least number must be subtracted from 531742 so that remaining no.is divisible by 3?
(A) 4
(B) 5
(C) 1
(D) 2
(E) 3
Rationale: On dividing 531742 by 3 we get the remainder 1, so 1 should be subtracted
C
Answer: (C) 1
Question: In racing over a given distance d at uniform speed, A can beat B by 10 meters, B can beat C by 6 meters, and A can beat C by 14 meters. What is the distance d in meters?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: When A is at the finish line, B is 10 meters back, and C is 14 meters back.
When B runs another 10 meters to the finish line, C is 6 meters back.
So B gains 2 meters every 10 meters covered.
To gain a final difference of 6 meters, B runs a total of 30 meters.
The answer is A.
Answer: (A) 30
Question: A,B,C can complete a piece of work in 24,6 and 12 days respectively. Working together, they will complete the same work in how many days?
(A) 13/8
(B) 26/11
(C) 24/7
(D) 12/13
(E) 1/2
Rationale: (A+B+C)'s 1day work = (1/24)+(1/6)+(1/12) = 7/24
A,B,C together will complete the work in 24/7 days
Answer is C
Answer: (C) 24/7
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/10, then what is the value of abc/def ?
(A)  27/4
(B)  27/8
(C)  3/4
(D)  3/20
(E)  1/4
Rationale: Say a = 2. Then:
a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1/10 --> f = 20.
abc/def = (2*6*3)/(6*2*20) = 3/20.
Answer: D.
Answer: (D)  3/20
Question: There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
(A) 3 1⁄4 days
(B) 4 1⁄3 days
(C) 5 1⁄6 days
(D) 6 1⁄5 days
(E) 7 1⁄5 days
Rationale: Explanation :
Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
…
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one.
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 1⁄6 days
Answer : Option C
Answer: (C) 5 1⁄6 days
Question: The temperature of a certain cup of coffee 5 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
(A) 65
(B) 61.875
(C) 80
(D) 85
(E) 90
Rationale: First, we have to find a.
We know that after t=5 minutes the temperature F=120 degrees.
Hence:
120 = 120*(2^-5a)+60
60 = 120*(2^-5a)
60/120 = 2^-5a
1/2 = 2^-5a
2^-1 = 2^-5a
-1 = -5a
1/5 = a
Now we need to find F after t=30 minutes:
F = 120*(2^-1/5*30)+60
F = 120* (2^-6) +60
F = 120* (1/2^6) +60
F = 120*1/64 +60
F = 1.875+60 = 61.875
Answer B!
Answer: (B) 61.875
Question: What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(2, 5) ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: C.
Answer: (C) 5
Question: A bicycle at Store P costs $200. The regular price of the same bicycle at Store Q is
15% more than it is at Store P. The bicycle is on sale at Store Q for 10% o of the
regular price. What is the sale price of the bicycle at Store Q?
(A) $230
(B) $201
(C) $199
(D) $207
(E) $210
Rationale: At Store Q, the bicycle's regular price is 15% more than the price at Store P, or 15% more than
$200.
Since 15% of 200 is 15
100 200 = 0:15200 = 30, then 15% more than $200 is $200+$30 or $230.
This bicycle is on sale at Store Q for 10% o of the regular price, $230.
Since 10% of 230 is 10
100 230 = 0:10 230 = 23, then 10% o of $230 is $230 􀀀 $23 or $207.
The sale price of the bicycle at Store Q is $207.
correct answer D
Answer: (D) $207
Question: A man buys a watch for Rs.1950 in cash and sells it for Rs. 2200 at a credit of 1 year.If the rate of interest is 10% per annum,the man :
(A) gains Rs. 55
(B) gains Rs. 50
(C) loses Rs. 30
(D) gains Rs. 30
(E) None of these
Rationale: Solution
S.P. = P.W. of Rs. 2200 due 1 year hence = Rs. [ 2200x100/100 + (10x 1) ]= Rs. 2000.
∴ Gain = Rs. (2000 - 1950) = Rs. 50.
Answer B
Answer: (B) gains Rs. 50
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
(A) 5/18
(B) 5/12
(C) 5/112
(D) 5/17
(E) 5/11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: (B) 5/12
Question: Diana works 10 hours per day on Monday, Wednesday and Friday, and 15 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $1800 per week. How much does she earn in dollars per hour?
(A) 20
(B) 22
(C) 30
(D) 24
(E) 25
Rationale: So, she works 30 hours in 3 days
So, she works 30 hours in 2 days
So in a week she works 60 hours ( 30 + 30 ) and earns $1800
So, Hourly wage is 1800/60 => 30
Hence answer will be (C) 30
Answer: (C) 30
Question: Two pipes A and B can separately fill a cistern in 80 minutes and 160 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 40 minutes. In how much time, the third pipe alone can empty the cistern?
(A) 90 min
(B) 160 min
(C) 110 min
(D) 120 min
(E) 130 min
Rationale: 1/40-(1/80+1/160)=-1/160
third pipe can empty in 160 minutes
ANSWER:B
Answer: (B) 160 min
Question: Two numbers N and 10 have LCM = 36 and GCF = 5. Find N.
(A) 35
(B) 56
(C) 76
(D) 18
(E) 24
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
10* N = 36 * 5
N = 36*5 / 10 = 18 correct answer D
Answer: (D) 18
Question: Meera purchased two three items from a shop. Total price for three items is Rs.2000/- She have given Rs. 3000/- What is the balance amount meera got?
(A) 650
(B) 1000
(C) 1500
(D) 800
(E) 750
Rationale: Total cost of Items : 2000/-
amount Paid : 3000/-
Balance receivable : 3000- 2000= 1000/-
Answer is B
Answer: (B) 1000
Question: If logn48 = a and logn108 = b. What is the value of logn1296 in terms of a and b?
(A) 2(2a + b)/5
(B) (a + 3b)/5
(C) 4(2a + b)/5
(D) 2(a + 3b)/5
(E) None of these
Rationale: Given logn48 = 4logn2 + logn3 = a and
logn108 = 2.logn2 + 3logn3 = b
Let logn 2 = X and logn3 = Y.
=> 4X + Y = a
2X +3Y = b.
2 x (ii) - (i) gives
6Y - Y = 2b - a
Y = (2b - a)/5
Similarly, X = (3a - b)/10.
logn1296 = 4(logn2 + logn3).
= 4[(2b - a)/5 + (3a - b)/10].
= 4[(a + 3b)/10] = 2(a + 3b)/5.
ANSWER:D
Answer: (D) 2(a + 3b)/5
Question: A courtyard is 28 meter long and 13 meter board is to be paved with bricks of dimensions 22 cm by 12 cm. The total number of bricks required is :
(A) 16000
(B) 14567
(C) 13787
(D) 13456
(E) None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(2800Ã—1300 /22Ã—12)=13787
Option C
Answer: (C) 13787
Question: There are two numbers. If 80% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) A)3/7
(B) B)5/16
(C) C)6
(D) D)6/7
(E) E)7
Rationale: Let the two numbers be x and y.
80/100 * x + y = 5/4y
=> 4/5 x = 1/4 y => x/y = 5/16
B)
Answer: (B) B)5/16
Question: 175 × 11 - 50 × 3 ÷ (75 - 50) = ?
(A) 1915
(B) 1917
(C) 1918
(D) 1919
(E) 1921
Rationale: Explanation:
=> ? = (175 × 11) - (50 × 3) ÷ (75 - 50)
= 1925 - (150/25) = 1925 - 6 = 1919
Answer: Option D
Answer: (D) 1919
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 759
(B) 750
(C) 278
(D) 267
(E) 187
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: B
Answer: (B) 750
Question: Deepak is 4 times as old as his son. four years hence the sum of their ages will be 43 years. How old is deepak's son now ?
(A) 5 years
(B) 7 years
(C) 8 years
(D) 9 years
(E) 10 years
Rationale: Let the son's present age be x years
Then, (x + 4 ) + (4x + 4) = 43
5x = 35
x = 7 years
Answer : B
Answer: (B) 7 years
Question: How many numbers between 0 and 1570 have a prime tens digit and a prime units digit?
(A) 268
(B) 272
(C) 202
(D) 112
(E) 252
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1500, there 16*15 = 240 such numbers.
From 1501 to 1570, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 240+12 = 252
The answer is E.
Answer: (E) 252
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder D of Y divided by 5?
(A) D=1.
(B) D=2.
(C) D=3.
(D) 4.
(E) 5.
Rationale: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4 . X+Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
Answer: (B) D=2.
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20
ANSWER B
Answer: (B) 20
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 5,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
(A) 1/9
(B) 29/180
(C) 26/143
(D) 1/5
(E) 31/220
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 5.5*2 = 11 hours;
In 1 hour 15 journeymen can finish 1/11 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/11=31/220 of the job.
Answer: E
Answer: (E) 31/220
Question: If the cost price of 30 pens is equal to the selling price of 25 pens, the gain percent is:
(A) 9%
(B) 20%
(C) 50%
(D) 80%
(E) 34%
Rationale: Solution :
Let cost price of the price be Rs.1
25 pens C.P. = 25
30 pens S.P. = 30
Gain = 5/25*100 = 20 %
Answer :B
Answer: (B) 20%
Question: In how many ways can three members be selected from a group of five members?
(A) 5C6
(B) 5C3
(C) 5C4
(D) 10C3
(E) 10C1
Rationale: three members can be selected from five members in
5C3
= 5C3 ways.
Answer: B
Answer: (B) 5C3
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was :
(A) 14
(B) 19
(C) 33
(D) 38
(E) 56
Rationale: Explanation:
Let the son's present age be x years .Then, (38 - x) = x x= 19.
Son's age 5 years back = (19 - 5) = 14 years. Answer: A
Answer: (A) 14
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) 27
(B) 50
(C) 22
(D) 26
(E) 28
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:B
Answer: (B) 50
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $119,000 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
(A)  $1,568,000
(B)  $448,000
(C)  $406,000
(D)  $313,600
(E)  $116,000
Rationale: My take is E.
(119000*4 + 112000*3)/7 = 116000
Answer: (E)  $116,000
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
(A) 59kg
(B) 58.85kg
(C) 59.75kg
(D) 60kg
(E) None of these
Rationale: Explanation:
Actual total weight is (20X 58.4 – 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85kgs
Answer B
Answer: (B) 58.85kg
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 120 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
(A) 1 hr 20 min
(B) 1 hr 45 min
(C) 2 hr
(D) 2 hr 20 min
(E) 1 hr
Rationale: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/120
converting it to hrs P+M= 1/(60/120) => 2
second equation => M+2M =>1/20
converting it to hrs 3M=1/(20/60) =>1/(1/3) =>3
therefore M= 1 and P=1
Rate of Perry = 1
time= work/rate (work = 1 job)
Time= 1 hrs
Answer : E
Answer: (E) 1 hr
Question: Darius and Daniel each had an equal amount of money to spend. After Darius spent 360.00 and Daniel spent 150.00. Daniel had 8 times as much money as what Darius had left. How much money did each boy have to begin with
(A) $390
(B) $380
(C) $370
(D) $360
(E) $350
Rationale: Since Darius and Daniel each had an equal amount of money to spend (and because this is the amount we are wanting to find) we can let "d" denote the variable for this amount. Now it is given to us that Darius spent $360 and Daniel spent $150. So, we can let "d - 360" denote the amount of money Darius has left, and we can let "d - 150" denote the amount of money Daniel has left. Finally, we are given that the amount of money Daniel has left (d - 150) is equal to 8 times the amount of money Darius had left (d - 360). Therefore,
d - 150 = 8(d - 360)
d - 150 = 8d - 2880
-150 = 7d - 2880
7d = 2730
d = 390
So, the amount of money each boy had to begin with is $390.00.
Answer A
Answer: (A) $390
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 10092 sq. m, the cost of fencing the field @ 25 paise per metre is
(A) Rs. 55.50
(B) Rs. 67.50
(C) Rs. 86.50
(D) Rs. 101.50
(E) None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 10092⇔ 12x2 = 10092 ⇔ x2 = 841 ⇔ x = 29.
So, length = 87 m and breadth = 116 m.
Perimeter = [2(87 + 116)] m = 406 m.
∴ Cost of fencing = Rs. (0.25 × 406) = Rs. 101.50. Answer D
Answer: (D) Rs. 101.50
Question: If b is a positive integer and b^2 is divisible by 12, then the largest positive integer that must divide b ^3 is
(A)  2^3
(B)  2^6
(C)  3^3
(D)  6^3
(E)  12^2
Rationale: Since b is an integer so b cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making b^2 as a multiple of 12))
b^2 is divisible by 12 (12 = 2*2*3), So, b should have at least one 2 and one 3 so that b^2 has a 2^2 and two 3
So, b will have a 2 and a 3. Or b will be a multiple of 6
So, largest possible integer than should divide b^3 is 6^3
So, Answer will be D
Answer: (D)  6^3
Question: A clock store sold a certain clock to a collector for 45 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 25 percent of what the collector had paid. The shop then sold the clock again at a profit of 55 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $180, for how much did the shop sell the clock the second time?
(A) $149.55
(B) $134.56
(C) $175.43
(D) $158.65
(E) $255.45
Rationale: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 45% profit.
This means the clocks' selling price was C (1.45) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 25% the price at which the collector bought it.
Thus, you get = 1.45*0.25*C = 0.3625 C
Furthermore, the store sells the clock for the second time for 55% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.55 = 1.55 * 0.3625 C
Finally given that C - 0.3625 C = 180 ----> C = 282.35$
Thus, the cost of the clock the second time around = 1.55*0.3625 C = 1.55 * 0.3625 * 282.35 = 158.65$. Hence D is the correct answer.
Answer: (D) $158.65
Question: Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 50 people bought tickets to the concert, what was the total revenue from ticket sales?
(A) $600
(B) $740
(C) $860
(D) $980
(E) $1,140
Rationale: Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 20 tickets = 20 * 20
= 400
Revenue generated from sales of 50 tickets = 120 + 340 + 400
= 860 $
Answer C
Answer: (C) $860
Question: If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ?
(A) 40 kms
(B) 70 kms
(C) 80 kms
(D) 50 kms
(E) 10 kms
Rationale: Explanation:
Let the actual distance travelled be x km.
Then x/8=(x+20)/12
=> 12x = 8x + 160
=> 4x = 160
=> x = 40 km.
Answer: A
Answer: (A) 40 kms
Question: A certain bacteria colony doubles in size every day for 21 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) 10 
(D) 20
(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 21 – 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, 20 is the answer
D
Answer: (D) 20
Question: If a person walks at 20 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
(A) 20 km
(B) 56 km
(C) 60 km
(D) 70 km
(E) 80 km
Rationale: Let the actual distance travelled be x km.
x/10 = (x+20)/14
20x = 10x + 200
10x = 200
x = 20 km.
answer :A
Answer: (A) 20 km
Question: How much space, in cubic units, is left vacant when maximum number of 2x2x2 cubes are fitted in a rectangular box measuring 8x10x9 ?
(A) 60
(B) 65
(C) 70
(D) 75
(E) 80
Rationale: No of cubes that can be accommodated in box = (8*10*9)/(2*2*2)
8*10 in numerator can be perfectly divided by 2*2 in denominator.
side with length 9 can't be perfectly divided by 2 and hence is the limiting factor. Closet multiple of 2 less that 9 is 8. so vacant area in cube =
=10*8 (9-8)
=10*8*1
=80
Ans - E
Answer: (E) 80
Question: Find the sum of prime numbers lying between 60 and 75.
(A) 199
(B) 201
(C) 211
(D) 272
(E) NOne
Rationale: Sol.
Required sum = ( 61 + 67 + 71 + 73)
= 272.
Answer D
Answer: (D) 272
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 28
(B) 99
(C) 27
(D) 26
(E) 11
Rationale: Explanation:
1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:A
Answer: (A) 28
Question: On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor.
(A) A)11
(B) B)14
(C) C)16
(D) D)18
(E) E)22
Rationale: d = (D-R)/Q
= (144 - 1)/13
= 143/13 = 11
A)
Answer: (A) A)11
Question: Find large number from given question. The difference of 2 numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1345
(B) 1450
(C) 1440
(D) 1546
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is
(A) 40000
(B) 50000
(C) 60000
(D) 70000
(E) None of these
Rationale: Explanation :
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000. Answer : Option C
Answer: (C) 60000
Question: What is the largest 4 digit number exactly divisible by 50?
(A) 4676
(B) 4678
(C) 9950
(D) 9504
(E) 9936
Rationale: Largest 4 digit number = 9999
9999 ÷ 50 = 199, remainder = 49
Hence largest 4 digit number exactly divisible by 50
= 9999 - 49 = 9950
answer :C
Answer: (C) 9950
Question: 2500÷10÷5=?
(A) 43
(B) 37
(C) 50
(D) 33
(E) 32
Rationale: 2500 ÷ 10 = 250
250 ÷ 5= 50
Answer is C
Answer: (C) 50
Question: A football field is 7200 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
(A) 450
(B) 600
(C) 750
(D) 2400
(E) 3200
Rationale: Answer A) 9600 yards need 1200 lbs
1 Yard will need 1200/7200 = 1/6 lbs
3600 Yards will need 1/6* 3600 Yards = 600lbs
B
Answer: (B) 600