MU-NLPC/Calc-aqua_rat huggingface dataset:
In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 12 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?	Select:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: The class borrowed a total of 40*2= 
40*2 = 80
80 books.   The 26 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 12*2= 
12 + 12*2 = 36
36.   To maximize the number of books borrowed by 1 student, let's assume that 13 students borrowed 3 books and 1 student borrowed the rest.   80 - 36 - 3*13= 
80 - 36 - 3*13 = 5
5   The maximum number of books borrowed by any student is 5.   The answer is 5.
Answer: C
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?	Choices:
A) 12%
B) 10%
C) 90%
D) 80%
E) 20%

Solution: 2420 --- 242   100 --- ? => 10%   Answer: 10%
Answer: B
Rs.1690 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?  Choose the correct choice from the following answers:
A) s.528
B) s.542
C) s.780
D) s.540
E) s.549

Solution: A+B+s.780 = 1690   4A = 3B = 2s.780 = x   A:B:s.780 = 1/4:1/3:1/2 = 3:4:6   6/13 * 1690 = Rs.780   Answer: s.780
Answer: C
Three unbiased coins are tossed. What is the probability of getting at most two heads?
Choose the correct choice from the following:	A) 3/4	B) 7/8	C) 3/8	D) 5/6	E) 9/11

Solution: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting at most two heads.   Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.   P(E)=n(E)/n(S)   =7/8   The answer should be 7/8
Answer: B
A test has a mean of 110 and a standard deviation of 5, find the corresponding x score for: a) a test score of 116? Choose the correct choice from the following options:
A) A)6/5	B) B)2.4	C) C)5	D) D)5.6	E) E)7

Solution: 6/5 test has a mean of 110 and a standard deviation of 5,   find the corresponding x score for:   a) a test score of 116,   x(116) = (116-110)/5= 6/5   Option 6/5
Answer: A
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 13th and the 20th terms?  Pick: A) 324 B) 335 C) 346 D) 357 E) 368

Solution: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.   Thus, 11n – 3 describes the values in the sequence where n is the number of the term.   The 13th term is 13 × 11 – 3 = 140   The 20th term is 20 × 11 – 3 = 220 – 3 = 217.   The sum of these two values is 357   The correct answer is choice (357).
Answer: D
The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?	Options.
A) 76 cm2 B) 56 cm2 C) 18 cm2 D) 98 cm2 E) 50 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle   = 2.5 * 40/2= 
2.5 * 40/2 = 50
50 cm2   Answer:50 cm2
Answer: E
A train 440 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Choose the most appropriate option:	A) 40.33 sec	B) 41.33 sec	C) 42.33 sec	D) 40 sec	E) 44.33 sec

Solution: D = 440 + 180= 
440 + 180 = 620
620   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 620/15 = 41.33 sec   ANSWER:41.33 sec
Answer: B
The area of a triangle will be when a = 5m, b = 7m, c = 8m, a, b, c being lengths of respective sides?  Choose the correct answer:
A) 3	B) 6	C) 4	D) 9	E) 10

Solution: S = (5 + 7 + 8)/2= 
(5 + 7 + 8)/2 = 10
10 Answer:10
Answer: E
If p and q are two different prime numbers, which of the following cannot be true?	Choose the correct choice.
A) pq is odd.
B) p + q is even.
C) p + q is odd.
D) pq is even.
E) p/q is an integer

Solution: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q).   Answer: E.   All other options are possible:   A. pq is odd --> p=3 and q=5;   B. p + q is even --> p=3 and q=5;   C. p + q is odd --> p=2 and q=3;   D. pq is even --> p=2 and q=3;   p/q is an integer
Answer: E
Maney bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?	Pick:
A) $10
B) $11
C) $12
D) $13
E) $14

Solution: From the given information,we can conclude that Maney bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for  1000*.90= 
 1000*.90 = 900
$900 . With the remaining money ($1000 - $900= $100), he can buy 10 more shares. So, the reduced price per share = $100/10= 
100/10 = 10
$10.   Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=$11
Answer: B
Simplify: 99^48/49 * 245.  Pick one:
A) 23345  B) 26695  C) 24495  D) 25575  E) None of them

Solution: Given expression = (100-1/49) * 245=(4899/49) * 245 = 4899 * 5= 
4899 * 5 = 24_495
24495.   Answer is 24495.
Answer: C
If x and y are integers and x=50y + 59, which of the following must be odd?	Choose the correct choice from the following answers: A) xy B) x +2y C) x + y D) 3x-1 E) 3x+1

Solution: x = 50y + 59, since y is integer, 50y will always be even hence 50y + 59 will be odd hence x = odd   you don't know whether Y is even or odd, so you need to try.   A: odd * even = even ; odd*odd= odd ->not true   C: odd + odd = even ; odd+even = odd -> not true   B: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, .   D&E WILL x +2yE EVEN IF X IS ODD   Answer x +2y
Answer: B
By selling an article at Rs.600, a profit of 25% is made. Find its cost price?	Options.
A) Rs.482
B) Rs.429
C) Rs.480
D) Rs.408
E) Rs.428

Solution: SP = 600   Rs.480P = (SP)*[100/(100+P)]   = 600 * [100/(100+25)]   = 600 * [100/125] = Rs.480   Answer:Rs.480
Answer: C
The diagonal of a rhombus are 62 m and 80 m. Its area is:
Answers.
A) 1940  B) 2480  C) 2460  D) 2500  E) 1980

Solution: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 62 Ã— 80) Cm(power)2   = 62 Ã— 40 = 2480 Cm(power)2   Answer is 2480.
Answer: B
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of $ 12,000 after 3 years at the same rate?  Choose the correct choice:
A) $2160
B) #3120
C) $3972
D) $6240
E) NONE OF THESE

Solution: Let P = $ 100. Then, S.I. $. 60 and T = 6 years.   R = 100 x 60 = 10% p.a.   100 x 6   Now, P = $ 12000. T = 3 years and R = 10% p.a.   $3972.I.	= $ 12000 x 1 +	10 3	- 1   100   = $ 12000 x	331   1000	=3972   ANSWEWR : $3972 3972
Answer: C
When 1/10 percent of 2,000 is subtracted from 1/10 of 2,000, the difference is	Choose one
A) 1980	B) 1998	C) 198	D) 200	E) 20

Solution: (1/10)*2000 - (1/10)%*2000 =   200 - (1/1000)*2000 =   200 - 2= 
200 - 2 = 198
198   The answer is 198.
Answer: C
The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 25%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?  Choose the correct choice from the following answers
A) 32.5  B) 77.78  C) 48  D) 65  E) 67.5

Solution: 1) Let the price of jacket initially be $100.   2) Then it is decreased by 25% , therefore bringing down the price to $75.   3) Again it is further discounted by 10%, therefore bringing down the price to $56.25   4) Now 56.25 has to be added byX %in order to equal the original price.   56.25 + ( X% ) 56.25 = 100.   Solving this eq for X, we get X = 77.78   Ans is 77.78.
Answer: B
A single discount equivalent to the discount series of 20%, 15% and 8% is?
Options:
A) 37.4  B) 31.8  C) 31.6  D) 31.3  E) 31.1

Solution: 100*(80/100)*(85/100)*(92/100)   = 62.6   100 - 62.6= 
100 - 62.6 = 37.4
37.4   37.4nswer:37.4
Answer: A
Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 2 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? Choose the correct answer.
A) 1.5 B) 2.5 C) 3.75 D) 5 E) 7.5

Solution: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.   The total time is 4 + 2= 
4 + 2 = 6
6 hours   The average speed= total distance/total time taken = 2x/6 = x/3   The average speed of the complete journey is 2 km/hour   x/3 = 2   x = 6 km   The average speed while climbing = distance/time = 6/4= 
6/4 = 3/2 = around 1.5
1.5 km/h   The answer is 1.5.
Answer: A
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 200-gram mixture, 50 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?
Choose the most appropriate option.
A) 84%
B) 85%
C) 86%
D) 87%
E) 88%

Solution: The amount of milk is 0.8(200) + 50 = 210 grams.   The proportion is 210/250= 
210/250 = 21/25 = around 0.84
0.84 which is 84%   The answer is 84%.
Answer: A
On multiplying a number X by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result. Choose the correct choice from the following answers
A) 104345	B) 107375	C) 108385	D) 109395	E) 105355

Solution: The only thing you actually know about the correct number X is that it is divisible by 153 and has 5 as a factor.   You should immediately try to find the factors of 153 and look for them in the options.   153 = 9*17   Divisibility by 9 is easy to check. Only (109395) satisfies.
Answer: D
A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?  Choose the correct choice from the following choices
A) 40	B) 32	C) 26	D) 21	E) 14

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 260 + 140= 
260 + 140 = 400
400 m   Required time= 400 * 2/25= 
400 * 2/25 = 32
32 sec   Answer:32
Answer: B
Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2-12y+32=0 Options
A) If x>y  B) If x>=y  C) If x < y  D) If X<= Y  E) x=y or relationship cannot be established

Solution: Solution:-   X=3,4 and Y= 4,8   X<= Y   If X<= Y
Answer: D
The smallest prime number is:
Choose the correct option.
A) 1
B) 6
C) 3
D) 4
E) 2

Solution: 2   2
Answer: E
Jonathan can type a 30 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Answers.
A) 5 minutes	B) 10 minutes	C) 15 minutes	D) 18 minutes	E) 20 minutes

Solution: You may set up common equation like this:   job/A+job/B+job/C=job/x   Memorize this universal formula, you will need it definitely for GMAT.   and find x from this equation   In this specific case, the equation will look like this:   30/40+30/30+30/24=30/x   If you solve this equation, you get the same answer 10 minutes (10)
Answer: B
In how many years Rs 200 will produce the same interest at 10% as Rs. 1000 produce in 2 years at 12%  Choose the correct choice from the following answers.
A) 13
B) 9
C) 11
D) 12
E) 10

Solution: Explanation:   Clue:   Firstly we need to calculate the SI with prinical 1000,Time 2 years and Rate 12%, it will be Rs. 240   Then we can get the Time as   Time = (100*240)/(200*10)= 
(100*240)/(200*10) = 12
12   Option 12
Answer: D
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?	Choose the correct answer:
A) $ 280,000  B) $ 320,000  C) $ 360,000  D) $ 480,000  E) $ 540,000

Solution: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?   The investment gets doubled in 70/p years. Therefore, the investment gets doubled in   70/5= 
  70/5 = 14
every 14 years. After 42 years, the investment will get doubled 42/14= 
42/14 = 3
3 times.   So the amount invested will get doubled thrice.   So, 60000 *2^3= 480000   Hence, the answer is $ 480,000.
Answer: D
A invested some money in 8% stock at 96.If B wants to invest in an equally good 10% stock ,he must purchase a stock worth of :  Choose the correct choice from the following options.
A) Rs. 120
B) Rs. 60
C) Rs. 128
D) Rs. 130
E) Rs. 140

Solution: Solution   For an income of Rs. 8, investment = Rs. 96.   For an income of Rs. 10, investment = Rs.(96/8x10) = Rs. 120   Rs. 120nswer Rs. 120
Answer: A
The fourth proportional to 18, 14 and 18 is?	Pick one.
A) 14  B) 66  C) 77  D) 88  E) 99

Solution: (14*18)/18= 
(14*18)/18 = 14
14   14nswer: 14
Answer: A
17200 x 223 + 17200 x 77 = ?
Choose the most appropriate option
A) 2736900 B) 2738800 C) 2658560 D) 5160000 E) None of them

Solution: =17200 x (223+77) (by distributive law)   =17200 x 300   =5160000   Answer is 5160000
Answer: D
Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
Choose the most appropriate option:
A) 1/2	B) 3/2	C) 3/2	D) 2/2	E) 5/2

Solution: A   1/2   one of two is the possibility   1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.   2. If any of the first 99 people sit in 1/2ishwarya's seat, 1/2bhishek will get to sit in his seat.
Answer: A
A person want to give his money of $15800 to his 4 children A,B,C,D in the ratio 5:9:6:5. What is the A+C share? Select:
A) $4000
B) $2890
C) $3005
D) $6952
E) $6003

Solution: A's share = 15800*5/25= 
15800*5/25 = 3_160
$3160   C's share= 15800*6/25= 
15800*6/25 = 3_792
$3792   A+C= $6952   Answer is $6952
Answer: D
Pipe A can fill a tank in 3 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?	Choose the correct choice from the following choices
A) 1.1  B) 1.3  C) 1.5  D) 1.7  E) 1.9

Solution: The part filled by A + B + C in 1 hour is 1/3 + 1/4 + 1/12 = 2/3   All the three pipes together will fill the tank in 1.5 hours.   The answer is 1.5.
Answer: C
If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.68 per litre then what is the rate of mixed oil per litre?	Choose one:  A) Rs.49.17  B) Rs.51.03  C) Rs.56  D) Rs.55.33  E) None of the above

Solution: 50*10= 
50*10 = 500
500   68*5= 
68*5 = 340
340   840/15= 
840/15 = 56
56   ANSWER:Rs.56
Answer: C
The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?  Choices.
A) 22887 B) 28779 C) 27677 D) 13500 E) 17971

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]   P = 13500   Answer:13500
Answer: D
Ashley and Betty start a business with $9000 each, and after 3 months, Betty adds another $5000. How should they share the profits at the end of the 24 months? Answers.
A) 72:107
B) 4:5
C) 17:23
D) 3:4
E) 68:95

Solution: Ashley invests $9000 for 24 months, but Betty invests $9000 for the first 3 months and then adds $5000. So, the investment of Betty for remaining 21 months is $14000.   72:107shley:Betty   9000*24 : (9000*3) + (14000*21)   216000 : 321000   72:107:B = 72:107   72:107nswer: 72:107
Answer: A
A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? Choose the correct choice from the following answers: A) 2 3/2 hours B) 2 1/3 hours C) 2 1/5 hours D) 2 9/2 hours E) 2 1/2 hours

Solution: Required time   = (5 1/4)/3 + (5 1/4)/7   = 2 1/2 hours.   Answer: 2 1/2 hours
Answer: E
The profit earned by selling an article for 872 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?  Choose the correct choice from the following choices
A) 960 B) 990 C) 1,200 D) 920 E) None of these

Solution: Let the profit or loss be x   and 872 – x = 448 + x or, x = 424⁄2 = 212   \ Cost price of the article = 872 – x = 448 + x = 660   \ SP of the article = 660 × 150⁄100 = 990   Answer 990
Answer: B
x is the product of each integer from 1 to 75, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?	Select the correct option:
A) 8  B) 7  C) 6  D) 9  E) 10

Solution: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:   n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n   x = 1*2*3....*75 = 50!   No. of trailing zeros in 75! = 75/5 + 75/5^2 = 15+3= 
15+3 = 18
18   100^k= 10^2k → k = 18/2= 
18/2 = 9
9   9
Answer: D
Each of the numbers x1, x2...., xn, n > 4, is equal to 1 or –1.
Suppose, x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, then,
Options:
A) n is even  B) n is odd.  C) n is an odd multiple of 3.  D) n is prime  E) None

Solution: Explanation :   Every term of the eq : x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, would either be 1 or -1 (product of 1's and -1's would never be anything else).   Now for the equation to be true number of 1's would have to be equal to number -1's thus there would always be even number of terms in the equation. Now for that to be true n would have to be even.   Say for example n=6: x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + x6x1x2x3.   We see there are 4 terms in the equation, we can have 2 1's and 2 -1's. So , n is even.   n is evennswer : n is even
Answer: A
A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even? Pick: A) 1/3 B) 2/3 C) 5/9 D) 6/11 E) 5/11

Solution: Probability of getting an even number = 2/3   Probability of getting an odd number = 1/3   since the dice is biased.   The sum is even if   (even,even) or (odd,odd)   [P(even).P(even)] + [P(odd).P(odd)]   2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9   ANSWER:5/9
Answer: C
Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?	Choose the correct choice from the following answers
A) 85 B) 97 C) 109 D) 178 E) 112

Solution: Answer: Option 178   This is an alternating division and addition series: First, divide by 2, and then add 8.
Answer: D
If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before?	Choose the correct choice from the following answers
A) 11 1/8%	B) 11 1/5%	C) 11 1/9%	D) 13 7/11%	E) 21 1/9%

Solution: 100 â€“ 12 = 88   88------12   100------? => 13 7/11%   Answer: 13 7/11%
Answer: D
What is the greatest 6-digit number when divided by 8 , 9, and 10 leaves a remainder of 6, 7, and 8 respectively?	Choose the correct choice from the following answers:	A) 456780	B) 678918	C) 997479	D) 997916	E) 997920

Solution: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so 678918 is the only possible answer.
Answer: B
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words?	Choose the correct choice from the following answers:
A) 5 to 4  B) 3 to 2  C) 42 to 1  D) 5 to 1  E) 6 to 1

Solution: Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6   Number of ways to form 3-letter code: 10!/7! = 10*9*8   Ratio: 42 to 1   Answer : 42 to 1
Answer: C
Population of a city in 20004 was 1100000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007	Choose the correct answer
A) 354354
B) 545454
C) 465785
D) 456573
E) 2384525/2

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 2384525/2   2384525/2
Answer: E
After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount
Select the correct option:
A) 22%
B) 23%
C) 21%
D) 20%
E) 17%

Solution: Let the first discount be x%   Then,87.5% of (100-x)% of 150= 105   87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)= 
(105*100*100)/(150*87.5) = 80
80   x=(100-80)= 
(100-80) = 20
20   first discount= 20%   Option 20%
Answer: D
A 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Pick.
A) 220 meter	B) 225 meter	C) 140 meter	D) 235 meter	E) None of these

Solution: Explanation:   As trains are running in opposite directions so their relative speed will get added   So, Relative speed = 120 +80= 
120 +80 = 200
200 kmph= 200*(5/18) = 500/9 m/sec   Let the length of other train is x meter then   x+360 /9=500 /9   =>x+360=500   =>x=140   So the length of the train is 140 meters   Option 140 meter
Answer: C
If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 1)?	Choose the correct choice:	A) 3	B) P + 2	C) p – 1	D) 2p – 1	E) 2p + 1

Solution: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is  (5-1)-1= 
 (5-1)-1 = 3
3: 2, 3, and 4.   Thus, the number of integers between pq and p(q+1)=pq+p is (pq+p-pq)-1=p-1.   Answer: p – 1.
Answer: C
The speed of a boat in still water is 15 km/hr and the rate of the current is 3 km/hr. The distance travelled downstream in 12 minutes is	Choose the correct choice.
A) 1.2 km  B) 1.8 km  C) 2.4 km  D) 3.6 km  E) None

Solution: Speed Downstream = (15 + 3) km/hr   = 18 km/hr.   Distance travelled = (18 x 12/60) hours   = 3.6km.   Answer 3.6 km
Answer: D
At what rate percent of simple interest will a sum of money double itself in 12 years?  Options
A) 8 1/6 %	B) 8 1/3 %	C) 8 8/3 %	D) 8 3/3 %	E) 8 1/2 %

Solution: Let sum = x. Then, S.I. = x.   Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)   = 25/3 = 8 1/3 %.Answer: 8 1/3 %
Answer: B
A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?  Answers:
A) 400  B) 600  C) 287  D) 278  E) 281

Solution: Explanation:   Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways   = (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5= 
(4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5 = 600
600 ways.   Answer:600
Answer: B
If a - b = 3 and a^2 + b^2 = 28, find the value of ab.	Choose the correct choice from the following choices:
A) 19  B) 15  C) 10  D) 8  E) 13

Solution: 2ab = (a^2 + b^2) - (a - b)^2   = 25 - 9= 
25 - 9 = 16
16   ab= 8.   Answer is 8.
Answer: D
At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Options:  A) 70%  B) 90%  C) 80%  D) 75%  E) 85%

Solution: A B 80% D   90 100 80 100   A D   90 ----- 100   360 ------ ? = 400   500 ------ 400   100 ------- ? => 80%   ANSWER:80%
Answer: C