MU-NLPC/Calc-aqua_rat huggingface dataset:
In a partnership between A, B and C. A's capital is Rs.5500. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Choose the correct option:	A) 23676	B) 19766	C) 29172	D) 12925	E) 11267

Solution: Explanation:   200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5500   470 ---- ?=> 12925   Answer:12925
Answer: D
Virginia, Adrienne, and Dennis have taught history for a combined total of 96 years. If Virginia has taught for 9 more years than Adrienne and for 12 fewer years than Dennis, for how many years has Dennis taught?
Choose the correct option:
A) 23 B) 32 C) 35 D) 41 E) 42

Solution: Let number of years taught by Virginia = V   number of years taught by Adrienne = A   number of years taught by Dennis = D   V+A+D = 96   V= A+9   =>A = V-9   V= D-12   => A = (D-12)-9 = D-21   D-9 + D-21 + D = 96   => 3D = 96 + 30= 
96 + 30 = 126
126=> D = 42   Answer 42
Answer: E
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Seven years ago Jim was 13 times as old as Sam. How old is Jim now?  Pick one
A) 8 B) 12 C) 16 D) 20 E) 24

Solution: We're asked how old Jim is NOW. We're given three facts to work with:   1) Today, Jim is TWICE as old as Fred   2) Today, Sam is 2 years younger than Fred   3) 7 years ago, Jim was 13 times as old as Sam.   let's TEST Answer D: 20   IF....Jim is currently 20 years old....   Fred is 10 years old   Sam is 8 years old   7 years ago, Jim was 13 and Sam was 1, so Jim WAS 13 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.   20
Answer: D
In how many different ways can the letters B, E, N, E, F, I, C, I, A, L be arranged?	Choose the most appropriate option
A) 10×9×8×7×6×5×3×2  B) 10×9×8×7×6×5×4×3  C) 8!  D) 9!  E) 10!

Solution: Number of ways of arranging BENEFICIAL = 10! / 2! * 2! = 10×9×8×7×6×5×3×2. Hence 10×9×8×7×6×5×3×210  / 2  * 2= 
10  / 2  * 2 = 10
10×9×8×7×6×5×3×2. Hence 10×9×8×7×6×5×3×2
Answer: A
A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 12 on Wednesday, what would be the value of D calculated on the following Saturday?  Options:	A) 2140	B) 2520	C) 2960	D) 3360	E) 3710

Solution: On Saturday, the value would be   7*6*5*12= 
  7*6*5*12 = 2_520
2520   The answer is 2520.
Answer: B
4 is what percent of 50?	Answers:
A) 0.2%  B) 8%  C) 10%  D) 20%  E) 500%

Solution: 4= x*50/100   x = 8%   Ans; 8%
Answer: B
John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?  Choose the correct option
A) 1.39%	B) 1.40%	C) 1.41%	D) 1.42%	E) 1.43%

Solution: Sol.   Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.   Answer 1.42%
Answer: D
The monthly rent of a shop of dimension 20feet × 18feet is Rs.1440. What is the annual rent per square foot of the shop?	Options:
A) 48 B) 56 C) 68 D) 87 E) 92

Solution: Sol. Monthly rent per square feet = 1440/(20*18)= 
1440/(20*18) = 4
4   & 48nnual rent per square feet=12*4= 
12*4 = 48
48   48nswer : 48
Answer: A
1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series	Choose the correct option:
A) 2311
B) 2411
C) 2511
D) 2611
E) 2487

Solution: Start with making two series   1+1*2= 
1+1*2 = 3
3 terms 2   1+2*2= 
1+2*2 = 5
5. 3   1+3*2= 
1+3*2 = 7
7. 4   ....   ....   ....   1+47*2= 
1+47*2 = 95
95. 48   1+48*2= 
1+48*2 = 97
97. 49   And last term    1+5*2= 
 1+5*2 = 11
11. 6   Total sum= 48(3+97)/2+11=2411   ANSWER:2411
Answer: B
A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?  Options
A) (4Y/6)^(1/2) B) (Y/6)^(1/2) C) (Y/4)^(1/2) D) (2Y/3)^(1/2) E) (Y)^(1/2)

Solution: We are given width = 3, depth = 2, height = 4.   Then Volume = Width x Depth x Height = 3*2*4= 
3*2*4 = 24
24   i.e. Y= 24   The correct option should result in 4 (the height) on substituting the value of Y=24.   Checking options with Y=24:   (4Y/6)^(1/2)) (4Y/6)^(1/2) = (96/6)^(1/2) = 4 CORRECT (4Y/6)^(1/2)NSWER   B) (Y/6)^(1/2) = (24/6)^(1/2) = 2 INCORRECT (4Y/6)^(1/2)NSWER   C) (6Y/4)^(1/2) = (144/4)^(1/2) = 6 INCORRECT (4Y/6)^(1/2)NSWER   D) (Y/3)^(1/2) = (24/3)^(1/2) = 8^(1/2) INCORRECT (4Y/6)^(1/2)NSWER   E) (Y)^(1/2) = (24)^(1/2) INCORRECT (4Y/6)^(1/2)NSWER   (4Y/6)^(1/2)nswer: Option (4Y/6)^(1/2)
Answer: A
Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
Pick:
A) Rs. 200
B) Rs. 209
C) Rs. 202
D) Rs. 238
E) Rs. 218

Solution: Explanation:   SI in 2 years = Rs. 20, SI in 1 year = Rs. 10   CI in 2 years = Rs. 21   % rate per annum = [(CI – SI) / (SI in 1 year)] *100   = [(21 – 20) / 20] * 100   = 5 % p.a.   Let the principal be Rs. X   Time = T = 2 years   % rate = 5% p.a.   SI = (PRT/100)   20 = (X*5*2) / 100   X = Rs. 200   Rs. 200NSWER: Rs. 200
Answer: A
The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Select the correct option:
A) 7N
B) 8N
C) 9N
D) 12N
E) 15N

Solution: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.   In 1993, the total assets were 400% GR15NAT15NR, which means 1992 PLUS 400% of 1992:   $100 + 4x$100 = $100 + $400 =$500   In 1994, the total assets were 200% GR15NAT15NR than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 +2x$500 100 +  400= 
100 +  400 = 500
$500   In 1994, the total assets were 200% GR15NAT15NR than they were in 1993, which means 1993 PLUS 300% of 1993:   $500 +2x$500= $500 + $1000 =$1500   This is 15 times the 1992 number, so the correct answer is 15N.500 +  1000= 
500 +  1000 = 1_500
$1500   This is 15 times the 1992 number, so the correct answer is 15N.
Answer: E
How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?  Choose the correct choice from the following options.
A) 55  B) 56  C) 4  D) 5  E) 3

Solution: Solution:   At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.   During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].   For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.   Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.   i.e. 5 positions.   Answer 5
Answer: D
A bag contains 4 red, 3 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? Choose the most appropriate option:
A) 1/13
B) 2/23
C) 1/6
D) 4/27
E) 3/23

Solution: P(Both are red),   =41/6291/62=41/6291/62   =6/36=1/6   1/6
Answer: C
20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. Choose one:
A) 19
B) 20
C) 21
D) 22
E) 23

Solution: in case of cycle no of handshakes = no of persons   hence ans = 20   ANSWER:20
Answer: B
In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 240 votes. What was the total number of votes?
Select the correct option:	A) 400	B) 600	C) 800	D) 1000	E) 1200

Solution: Let V be the total number of votes.   0.4V = 240   V = 600   The answer is 600.
Answer: B
In the manufacture of a certain product, 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale? Choose the correct answer:
A) 0.125%	B) 0.2%	C) 0.8%	D) 1.25%	E) 2.0%

Solution: Percent of defective produced = 5%   Percent of the defective units that are shipped for sale = 4%   Percent of units produced are defective units that are shipped for sale = (4/100)*(5/100)*100%   = (20/10000)*100%   = (20/100)= 
(20/100) = 1/5 = around 0.2
.2 %   Answer 0.2%
Answer: B
The weight of a glass of jar is 10% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar? Choose the correct choice from the following choices:
A) 1/5  B) 1/3  C) 2/5  D) 1/2  E) 5/9

Solution: Let weight of jar filled with beans = 100 g   Weight of jar = 10 g   Weight of coffee beans = 90 g   Weight of jar and remaining beans = 60 g   Weight of remaining beans = 50 g   Fraction remaining = 50/90 = 5/9   Answer is 5/9.
Answer: E
A number is increased by 50 % and then decreased by 50 %. Find the net increase or decrease per cent.	Options:	A) 25%	B) 18%	C) 17%	D) 13%	E) 16%

Solution: Let the number be 100.   Increase in the number = 50 % = 50 % of 100   = (50/100 Ã— 100)   = 50   Therefore, increased number = 100 + 50= 
100 + 50 = 150
150   This number is decreased by 50 %   Therefore, decrease in number= 50 % of 150   = (50/100 Ã— 150)   = 7500/100= 
7500/100 = 75
75   Therefore, new number= 150 - 75= 
150 - 75 = 75
75   Thus, net decreases= 100 - 75= 
100 - 75 = 25
25   Hence, net percentage decrease= (25/100 Ã— 100) %   = (2500/100)= 
(2500/100) = 25
25 %   25%nswer:25%
Answer: A
A certain fraction is equivalent to 3/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?  Choose one
A) 49  B) 35  C) 28  D) 56  E) 21

Solution: x/y = 3/5 -> 1   (x+4)/2y = 1/3 -> 2   56ivide 1 by 2 :   => 2x/(x+4) = 9/5   => 10x = 9x + 36   => x = 36   => y = 5/3 * 12= 
5/3 * 12 = 20
20   so x + y= 56   The answer is 56.
Answer: D
Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much?
Pick.
A) 9680  B) 8130  C) 8134  D) 8556  E) 9808

Solution: (6200*5*3)/100= 
(6200*5*3)/100 = 930
930   7200   --------   8130   Answer: 8130
Answer: B
From the given choices select the odd man out	Pick.
A) 37, 14, 19, 8  B) 37, 14, 19, 0  C) 37, 14, 19, 2  D) 37, 14, 19, 7  E) 37, 14, 19, 1

Solution: Explanation:   All the numbers in those options are prime numbers except 14 in option 4.   Answer:37, 14, 19, 7
Answer: D
If x is a positive integer, which of the following must be odd?	Select the correct option
A) x+1  B) x^2+x  C) x^2+x+1  D) x^2−1  E) 3x^2−3

Solution: A. X+1 = can be odd or even. Since O + O =E or E + O = O   B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]   C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 1 = ODD   Hence x^2+x+1.
Answer: C
If |x – 9/2| = 5/2, and if y is the median of a set of s consecutive integers, where s is odd, which of the following must be true?
I. xys is odd
II. xy(s^2 + s) is even
III. x^2y^2s^2 is even  Choose the correct choice from the following answers:  A) II only is true  B) III only is true  C) I and III  D) II and III  E) I, II, and III

Solution: given:   s is Odd   y is the median of odd numbers, hence y is Odd   x = solving the modulus you get 7 and 2. Hence x is Even or Odd   Therefore: s = O, y = O and x = O or E   Statement I = x*y*s = y*s*x = O x O x O/E = O x O/E = Odd or even. So False   Statement II = xy(s^2 + s) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true   Statement III. x^2y^2s^2 is even. E/O x O x O = Odd or even. Hence False.   II only is truenswer = II only is true.
Answer: A
When the positive integer p is divided by 9, the remainder is 5. What is the remainder when 3p is divided by 9?  Choose the correct choice from the following options
A) 0	B) 1	C) 3	D) 4	E) 6

Solution: Lets take the number as p   when p is divided by 9 the remainder is 5 hence p can be written as   p=9k +5   Multiplying by 3 will give   3p = 27k + 15   we can also write   3p = 27k + 9 + 6   Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence 6 is the answer.
Answer: E
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?	Choose the correct choice from the following options:
A) 2480	B) 3490	C) 6785	D) 8245	E) 9255

Solution: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:   16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2   Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.   = (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)   Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:   2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15= 
15*2*8*15 = 3_600
3600   So the sum must be  3375 + 1240 + 3600= 
 3375 + 1240 + 3600 = 8_215
8215   Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of   30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)   then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)   and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have   = 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)   In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals     15*15*62/2= 
  15*15*62/2 = 6_975
6975   and adding back the 1270, we get the answer of 8245. (ANS 8245)
Answer: D
Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present salary. Choose the correct answer:
A) 32000	B) 34000	C) 38000	D) 40000	E) None of these

Solution: Explanation:   Let the original Salaries of Ravi and Sumit is 2x and 3x.   So as per question   2x+4000/3x+4000=40/57   =>57(2x+4000)=40(3x+4000)   =>6x=68000   =>3x=34000   Sumit Salary =3x+4000   34000+4000= 
34000+4000 = 38_000
38000   Option 38000
Answer: C
A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?	Choose the correct choice from the following answers:
A) $10  B) $16  C) $20  D) $24  E) $25

Solution: Let P be the original price paid by the retailer.   1.25*P = 100   P = 80   The profit is $20.   The answer is $20.
Answer: C
Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
Choose the correct option: A) Rs.345 B) Rs.350 C) Rs.352 D) Rs.362 E) Rs.368

Solution: Suresh : Rohan : Sudhir   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rohan’s and Sudhir’s share = 1 share   :.i.e. = Rs. 3982 × 1/11 = Rs.362.   Rs.362
Answer: D
six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select?	Pick
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: 6c2 then ans is 6*5/1*2=15   ANSW15R:15
Answer: E
A card player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many hearts as clubs and twice as many diamonds as hearts. How many spades does he hold?  Choose the correct choice from the following answers
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Sol.   The player holds 1 club, 2 hearts and 4 diamonds.   As he holds 13 cards (or seven black cards), it follows that there must be 6 spades.   6nswer : 6
Answer: A
A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
Choose the correct choice from the following choices.
A) 0.9
B) 0.75
C) 0.6
D) 0.8
E) 0.5

Solution: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.   0.9nswer is 0.9
Answer: A
y and z represents 2 gas stations which are 270 km apart. if two cars leave each gas station and drive towards each other, at what time will they meet each other given that the first car left the gas station at 10 a.m. and travels at a speed of 75 kmph while the second car left the station at 11 a.m. and travels at a speed of 55 kmph.	Answers
A) 12.00 p.m	B) 11.30 p.m	C) 2.30 p.m	D) 12.30 p.m	E) 1.30 p.m

Solution: Suppose they meet x hours after 10 a.m.   Distance moved by first car in x hours + distance moved by 2nd car in x-1 hrs = 270   75x+55(x-1) = 270   75x+55x-55= 270   130x= 325   x = 2.5   So they meet 2.5 hr after 10 a.m. which is at 12.30 p.m.   Answer is 12.30 p.m
Answer: D
What should come in place of question mark (?) in the following equation?
5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = ?  Choose the correct choice from the following choices: A) 7 B) 8 1⁄2 C) 7 1⁄2 D) 6 1⁄2 E) None of these

Solution: ? = 5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = 28⁄5 ÷ 56⁄15 + 11⁄2   = 28⁄5 × 15⁄56 + 11⁄2 = 3⁄2 + 11⁄2 = 14⁄2 = 7   7nswer 7
Answer: A
The cost of 2 chairs and 3 tables is Rs.1500. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? Pick
A) 228 B) 287 C) 277 D) 188 E) 300

Solution: 300xplanation:   2C + 3T = 1500 --- (1)   3C + 2T = 1200 --- (2)   Subtracting 2nd from 1st, we get   -C + T = 300 => T - C = 300   Answer:300
Answer: E
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 30 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad? Pick
A) 16	B) 18	C) 20	D) 24	E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 30 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken= 30 / 10= 
30 / 10 = 3
3 hrs   Distance traveled by Brad= Brad's speed * time taken = 6 * 3= 
6 * 3 = 18
18 kms... Answer - 18
Answer: B
If x^2+(1/x^2)=3, x^4+(1/x^4)=?
Options:
A) 7
B) 11
C) 12
D) 14
E) 15

Solution: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=3^2-2=7.   Thus, the answer is 7.
Answer: A
A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?  Choices:  A) 2  B) 5  C) 9  D) 6  E) 3

Solution: 9 a.m.   Answer: 9
Answer: C
Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year? Pick:
A) 4225 B) 4096 C) 4356 D) Insufficient Data E) None of these

Solution: DETAILED SOLUTION   Let the area of backyard be x2 this year and y2 last year   ∴ X2- Y2 = 131   =) (X+Y) (X-Y) = 131   Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.   =) (X+Y) (X-Y) = 131 x 1   =) X+Y = 131   X-Y = 1   =) 2X = 132 =) X = 66   and Y = 65   ∴ Number of tomatoes produced this year = 662 = 4356   4356orrect 4356hoice (4356)
Answer: C
A football team lost 5 yards and then gained 9. What is the team's progress? Choose the correct choice from the following choices.
A) 2	B) 4	C) 5	D) 6	E) 8

Solution: For lost, use negative. For gain, use positive.   Progress = -5 + 9= 
-5 + 9 = 4
4 yards
Answer: B
Pipe A can fill a tank in 8 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Choose the correct choice from the following.
A) 5  B) 24  C) 78  D) 90  E) 54

Solution: Let the leak can empty the full tank in x hours 1/8 - 1/x = 1/12   => 1/x = 1/8 - 1/12 = (3 - 2)/24 = 1/24   => x = 24.   Answer: 24
Answer: B
How many odd three-digit integers smaller than 500 are there such that all their digits are different?	Answers: A) 72 B) 88 C) 112 D) 122 E) 144

Solution: Case 1: Numbers starting with 1   1 _ _   The unit digit can take 4 numbers (3,5,7,9) to be ODD so 4 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total = 8*4= 
8*4 = 32
32   Case 2: Numbers starting with 2   2 _ _   The unit digit can take 5 numbers (1,3,5,7,9) to be ODD so 5 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total= 8 *5= 
8 *5 = 40
40   Case 3: Numbers starting with 3   3 _ _   The unit digit can take 4 numbers (1,5,7,9) to be ODD so 4 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total= 8 *4= 
8 *4 = 32
32   Case 4: Numbers starting with 4   4 _ _   The unit digit can take 5 numbers (1,3,5,7,9) to be ODD so 5 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total= 8 *5= 
8 *5 = 40
40   Hence 32+40+32+40= 
32+40+32+40 = 144
144, correct answer is 144
Answer: E
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?  Pick one:
A) 10 hours  B) 23 hours  C) 18 hours  D) 20 hours  E) 12 hours

Solution: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.   x + y = 7 --- (1) ; 2x = 4 --- (2)   solving both the equations, we get y = 5   So, time taken to cover both ways by cycle = 2y hours =10 hours.   10 hoursnswer: 10 hours
Answer: A
A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? Choose one:
A) 115
B) 117
C) 116
D) 114
E) NONE OF THESE

Solution: Explanation:   Length = 6 m 24 cm = 624 cm   Width = 4 m 32 cm = 432 cm   HCF of 624 and 432 = 48   Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.   ANSWER IS 117
Answer: B
If a - b = 3 and a2 + b2 = 29, find the value of ab.	Answers.
A) 10
B) 12
C) 15
D) 18
E) 19

Solution: 2ab = (a2 + b2) - (a - b)2   = 29 - 9= 
29 - 9 = 20
20   ab= 10.   10nswer: 10
Answer: A