MU-NLPC/Calc-aqua_rat huggingface dataset:
A letter lock consists of three rings each marked with eight different letters. The number of distinct unsuccessful attempts to open the lock is at the most?  Choose the correct choice from the following options:
A) 176
B) 511
C) 518
D) 519
E) 172

Solution: Since each ring consists of eight different letters, the total number of attempts possible with the three rings is   = 8 * 8 * 8= 
8 * 8 * 8 = 512
512. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 512 - 1= 
512 - 1 = 511
511.   Answer: 511
Answer: B
What least value should be replaced by * in 223*431 so the number become divisible by 9	Choose the correct choice from the following answers
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Explanation:   Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9,   15+3 will be divisible by 9,   so that least number is 3.   3nswer: Option 3
Answer: A
In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included? Choose the correct choice from the following answers: A) 175 B) 190 C) 205 D) 220 E) 235

Solution: The total number of ways to choose 4 children is 10C4 = 210   The number of ways to choose only boys is 5C4 = 5   The number of groups which include at least one girl is 205.   The answer is 205.
Answer: C
What is the sum of the integers from -194 to 195 inclusive?
Options:  A) 0  B) 5  C) 195  D) 875  E) 965

Solution: sum/n= average.   sum=(average)(n)   average=a+b/2=194+195/2=0.5   number of items(n)=B-A+1=195-(-194)+1=195+195= 
195+195 = 390
390.   sum=average*n=0.5*390= 
0.5*390 = 195
195.   answer is 195
Answer: C
If a man buys 10 lollipops for $80 and sold them for $2 dollars determine his loss.  Choose the correct choice from the following
A) 50
B) 60
C) 70
D) 80
E) 90

Solution: Cost of 10 lollipops = $80   Sold each lollipop for $2   So, he sold 10 lollipops for $(10 × 2) = $20   Loss = $(80 – 20) = $60   answer :60   Therefore, loss = $ 60.
Answer: B
On flipping 3 coins together what is the outcomes for at least two tails?
Choose one.
A) {HHH, HHT, HTH, THH}  B) {HHT, HHT, HTH, THH}  C) {TTH, HHT, HTH, THH}  D) {TTH,THT, HTT,TTT}  E) None

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least two tails   = favorable outcomes for exactly two heads and favorable outcomes for more than two heads   = {TTH, THT, HTT, TTT}   {TTH,THT, HTT,TTT}
Answer: D
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?	Select the correct option.
A) 3 B) 4 C) 2 D) 5 E) 7

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer: 3
Answer: A
If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-6) ∆ (6 ∆ −6) ?
Choices
A) 36/25	B) 81/4	C) 25/4	D) 49/9	E) 25/9

Solution: (-6) ∆ (6 ∆ −6) =   (-6) ∆ (12^2/6^2) =   (-6) ∆ (4) =   (-10^2) / (-6)^2 = 100/36 = 25/9   The answer is 25/9.
Answer: E
The average of five results is 46 and that of the first four is 35. The fifth result is? Choose the correct choice from the following options:
A) 50
B) 90
C) 77
D) 66
E) 51

Solution: 5 * 46 â€“ 4 * 35   = 90   Answer: 90
Answer: B
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: Options.
A) 1by7 B) 1/8 C) 1/9 D) 7/8 E) 1/5

Solution: Original share of 1 person = 1/8   New share of 1 person = 1/7   Increase =(1/7-1/8) = 1/56   Required fraction = (1/56)/(1/8)   = (1/56)*8   = 1/7   1by7NSWER:1by7
Answer: A
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of r square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)	Choose the correct choice from the following answers
A) (5,280 mt) / 12 r B) (5,280 pt) / 12m C) (5,280 pmt) /12 D) (5,280)(12m) / pt E) (5,280)(12p) / mt

Solution: Given that: 1 gallon of paint covers an area ofrsquare feet. Question:how many gallonsof paint will be needed ...   In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/r, so r must be in the denominator: eliminate all but A and D.   Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.   (5,280 mt) / 12 rnswer: (5,280 mt) / 12 r.
Answer: A
The ratio of men to women in the Snyder community choir is 4 to 7. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir? Choose the most appropriate option.
A) 20
B) 24
C) 28
D) 32
E) 34

Solution: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.   We're told that the ratio of the Men to Women in the Snyder choir is 4 to 7, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 4 The question asks how many WOMEN are in the SNYDER choir, so the answer MUST be a multiple of 7. We can eliminate AnswersA, B, D and E (since they're NOT multiples of 7   Answer 28
Answer: C
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? Answers:
A) 78 B) 54 C) 96 D) Cannot be determined E) 56

Solution: Answer: Option D   Let the ten's digit be x and unit's digit by y   Then, x + y = 15 and x - y = 3 or y - x = 3   Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6   Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9   So, the number is either 96 or 69.   Hence, the number cannot be determined.
Answer: D
If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 25 =  Choose the correct answer.
A) 6
B) 10
C) 12
D) 5
E) 8

Solution: 5 5
Answer: D
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? Select:
A) 22 B) 32 C) 77 D) 66 E) 8

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   nswer: 32
Answer: B
In store A there are 10 pairs of pants for every 50 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?	Choose the correct option
A) 3:16.	B) 2:3.	C) 4:15.	D) 3:4.	E) 2:5.

Solution: 1st statement : ratio of pants   Store A : Store B   10x : 50x   X:5X   Price :   4y:3y   Total revenue   4xy : 15xy   4:15   Answer : 4:15.
Answer: C
The area of one square is x^2 + 6x + 9 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 52, what is the value of x? Answers:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: The areas are (x+3)^2 and (2x-5)^2.   The lengths of the sides are x+3 and 2x-5.   If we add the two perimeters:   4(x+3) + 4(2x-5) = 52   12x = 60   x = 5   The answer is 5.
Answer: C
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is? Choose the correct choice from the following answers
A) 6	B) 12	C) 24	D) 36	E) 48

Solution: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is:   A 6, B 12, C 24, D 36, E 48   n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.12
Answer: B
When positive integer D is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when D is divided by B?  Pick one:	A) 13	B) 14	C) 15	D) 16	E) 17

Solution: the remainder will be obtained from the decimal part when D is divided by B i.e. 0.35   0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option 14-14 satisfies this   PS: for 14-14 D=174 and 14=40
Answer: B
Jancy invested an amount of Rs. 9,000 at the rate of 10% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested? Choose the correct option
A) 15800	B) 12800	C) 11800	D) 16800	E) 17800

Solution: Let the second amount be Rs. x. Then,   (9000 * 10 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100   9000+ 15x= 16800 + 14x   x = 7800   Total investment = 10000 + 7800 = Rs. 17,800.Answer: 17800
Answer: E
How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?  Choose the most appropriate option:  A) 59  B) 11!/(2!*2!*2!)  C) 56  D) 76  E) 11!/(3!*2!*2!*2!)

Solution: E- -R   We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.   We should consider two cases:   1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.   2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.   Total = 56 + 3 = 76.   Answer: 76.
Answer: D
Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following R must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.	Choose the correct answer:  A) I only  B) II only  C) III only  D) I and III only  E) R=None of the above

Solution: Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3.   Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect.   Even if not, we can rule them both out. So, R=None of the above.
Answer: E
Tom, working alone, can paint a room in 8 hours. Peter and John, working independently, can paint the same room in 4 hours and 2 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Choose the correct choice from the following choices.
A) 4/7	B) 5/7	C) 6/7	D) 1/7	E) 3/7

Solution: Let the time when all three were working together be t hours. Then:   Tom worked for t+4 hour and has done 1/8*(t+4) part of the job;   Peter worked for t+2 hour and has done 1/4*(t+2) part of the job;   John worked for t hours and has done 1/2*t part of the job:   1/8*(t+4)+1/4*(t+2)+1/2*t=1 --> multiply by 8 --> (t+4)+(2t+2)+4t=8 --> t=2/7;   Hence Peter has done 1/4*(2/7+2)=1/4 *16/7=16/28 =8/14 =4/7   4/7nswer: 4/7
Answer: A
1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now? Options:
A) 76 days  B) 98 days  C) 32 days  D) 45 days  E) 24 days

Solution: 1600 ---- 28 days   1600 ---- 24   1200 ---- ?   1600*24 = 1200*x   x = 32 days   Answer: 32 days
Answer: C
Calculate the largest 3 digit number which is exactly divisible by 89?  Choose the correct choice from the following options.
A) 911  B) 969  C) 979  D) 977  E) 971

Solution: Largest 4 digit number is 999   After doing 999 ÷ 89 we get remainder 20   Hence largest 3 digit number exactly divisible by 89 = 999 - 20= 
999 - 20 = 979
979   979
Answer: C
If a, b are integers and |a-b|=12, which of the following is the smallest possible value of ab? Choose the correct choice from the following answers
A) -16  B) 0  C) -36  D) 7  E) 40

Solution: a=6, b=-6. Hence, the answer is -36.
Answer: C
Find the sum of first 80 odd numbers Pick one
A) 6400 B) 8000 C) 5000 D) 4980 E) 4960

Solution: Explanation:   n2 = 802 = 6400   6400nswer: Option 6400
Answer: A
Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.? Select:
A) 17 kmph B) 19 kmph C) 15 kmph D) 12 kmph E) 16 kmph

Solution: D   12 kmph   Let the distance traveled be x km.   Then, x/10 - x/15 = 2   3x - 2x = 60 => x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.   Required speed= 60/5= 
60/5 = 12
12 kmph.
Answer: D
Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King  Choose one:
A) 1/29	B) 1/26	C) 1/26	D) 1/25	E) 1/22

Solution: Explanation:   Let X be the event that cards are in a club which is not king and other is the king of club.   Let Y be the event that one is any club card and other is a non-club king.   Hence, required probability:   =P(A)+P(1/26)   =\inline {\color{1/26lack}[(12C_{1}\times 1C_{1})/52C_{2}]+[(13C_{1}\times 3C_{1})/52C_{2}]}   Answer: 1/26) 1/26   == =
Answer: B
Find the constant k so that : -x2 - (k + 10)x - 8 = -(x - 2)(x - 4) Select the correct option.
A) 11	B) 12	C) 16	D) 14	E) 15

Solution: -x2 - (k + 10)x - 8 = -(x - 2)(x - 4) : given   -x2 - (k + 10)x - 8 = -x2 + 6x - 8   -(k + 10) = 6 : two polynomials are equal if their corresponding coefficients are equal.   k = -16 : solve the above for k   correct answer 16
Answer: C
Multiply: (x – 4)(x + 5)
Options.
A) (a) x2 + 5x - 20 B) (b) x2 - 4x - 20 C) (c) x2 - x - 20 D) (d) x2 + x - 20 E) (e) x2 + x + 20

Solution: (x – 4)(x + 5).   = x(x + 5) -4(x + 5).   = x2 + 5x – 4x – 20.   = x2 + x - 20   the answer is ((d) x2 + x - 20)
Answer: D
A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?
Choose the correct choice from the following:
A) d/800  B) 5d/1000  C) 125d  D) d/1000 + 25  E) 125/(1000d)

Solution: Since you're choosing to approach this algebraically, I'm going to add some labeling to your work....   1,000 purchased for a total of D dollars.....   Each modem costs D/1,000 dollars....   Each modem is then sold for 25% ABOVE the cost:   (1.25)(D/1,000) = 1.25D/1,000   1.25D/1,000 = 125D/100,000   125/1,000 = 1/8 so....   125/100,000 = 1/800   So the sell price of each modem is D/800   Final d/800nswer:   d/800
Answer: A
John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Select
A) A)19.7
B) B)21
C) C)21.4
D) D)21.5
E) E)22.5

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total ta x incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7
Answer: A
A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 4 minutes?  Choose the correct choice from the following choices
A) 36
B) 54
C) 108
D) 216
E) 324

Solution: 216irect Relationship:-   1 standard Veggiematik machine - 36 Carrots - 4 minutes,   1 standard Veggiematik machine - 9 Carrots - 1 minute,   Now   6 standard Veggiematik machine - ? Carrots - 4 minutes,   Hence = 9X6X4 =216 Carrots   Answer 216
Answer: D
In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m? Choose the correct choice from the following answers: A) 6 m/sec; 18 sec B) 5 m/s; 18 sec C) 4 m/s; 15 sec D) 3 m/s; 12 secs E) 2 m/s; 6 secs

Solution: A can allow B to start the race 10 metres ahead, so the time A need to cover 100 meters equals to the time B needs to cover 90 meters --> 100/a = 90/b, where a and b are the rates of A and B, respectively.   A can allow B to start the race 2 seconds before A, so the time A need to cover 100 meters is 2 seconds less than the time B needs to cover 100 meters --> 100/a + 2 = 100/b.   Subtract one from another: 2 = 100/b - 90/b --> b = 5.   Answer: B.   Or directly: 5 m/s; 18 sec needs 2 seconds more to cover 100 meters than to cover 90 meters --> 2 = 100/b - 90/b --> b = 5.
Answer: B
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 21 months?
Options.
A) 18:11	B) 18:15	C) 21:11	D) 18:121	E) 18:112

Solution: A invests Rs.8000 for 21 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   A : B   8000*21 : (8000*4) + (4000*14)   168000 : 88000   A:B = 21:11.Answer:21:11
Answer: C
In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?
Choose the correct choice from the following answers
A) 16 2/3 % B) 25 percent C) 33 1/3 % D) 50% E) 75%

Solution: 1986; 2/3   1988; 1/2   % decrease = change/ original*100   2/3−1/2 / 2/3∗100   1/6∗3/2∗100=14∗100 =25   Answer: "25 percent"
Answer: B
What will be the cost of house to decorate which area equal to 324 sq ft, if the price per foot of building is Rs. 10?  Select
A) 120 B) 240 C) 360 D) 720 E) 860

Solution: Let the side of the square plot be a ft.   a2 = 324 => a = 18   Length of the fence = Perimeter of the plot = 4a = 72 ft.   Cost of building the fence = 72 * 10   = Rs.720.   Answer: 720
Answer: D
In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?	Choose the correct option.
A) 20 min B) 15 min C) 10 min D) 5 min E) None of these

Solution: Explanation :   The ratios of the speed of the fastest and the slowest is 2 : 1. Hence, they should meet only at one point at the circumference i.e the starting point (As the difference in the ratios in reduced form is 1).   For the two of them to meet for the first time, the faster shuld have completed one complete round over the slower one. Since, the two of them meet for the first time after 5 min, the faster one should have completed 2 rounds (i.e 2000 m) and the slower one should have completed 1 round (1000 in this time).   Thus the faster one would complete the race ( i.e 4000 m) in 10 min.   Answer : 10 min
Answer: C
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 54, what is the total amount?	Select:
A) 166  B) 105  C) 178  D) 177  E) 210

Solution: x:y:z = 100:45:30   20:9:6   9 --- 54   35 --- ? => 210   Answer: 210
Answer: E
Two pipes A and B can fill a cistern in 15 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?  Choose the correct choice from the following options
A) 17 1/4 min	B) 28 1/7 min	C) 17 1/7 min	D) 13 3/7 min	E) 17 5/7 min

Solution: 1/15 + 1/30 - 1/40 = 9/120   120/9 = 13 3/7   Answer:13 3/7 min
Answer: D
A can do a job in 18 days and B can do it in 30 days. In how many days will they finish it together? Choose the correct choice from the following answers:
A) 1/9 B) 4/45 C) 2/7 D) 6/3 E) 5/2

Solution: Explanation:   1/18 + 1/30 = 8/90 = 4/45   So, both together will finish the work in 4/45 days.   Answer:4/45
Answer: B
A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 4 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)  Choose the correct choice.
A) 5,500,000
B) 2,400,000
C) 55,000
D) 28,000
E) 280

Solution: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3   2,400,000y volume   40% is X = 400,000 cm^3   60% is Y = 600,000 cm^3   2,400,000y weight,   In 1 cm^3, X is 4 gms   In 400,000 cm^3 , X = 4 * 400,000 = 1,600,000 grams   In 1 cm^3, Y is 3 gms   In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms   Total gms in 1 m^3 = 1,600,000 + 1,800,000 = 2,400,000   ANSWER:2,400,000
Answer: B
In the fifth grade at Parkway elementary school there are 470 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?	Choose one.
A) 69.
B) 135.
C) 81.
D) 91.
E) 108.

Solution: Total students = 470   Boys = 300, Girls = 170   Total playing soccer = 250   86%of 250 = 215 are boys who play soccer.   Girls who play soccer = 35.   Total girls who do not play soccer = 170 - 35= 
170 - 35 = 135
135.   Correct option: 135.
Answer: B
Two negative numbers are multiplied to give a product of 48. If the lesser number is 10 less than thrice the greater number, what is the greater number? Choose the correct choice from the following options
A) -6  B) -8  C) -5  D) -9  E) -10

Solution: Test the options. The options give you the greater number.   (A) - 6   Triple of -6 is -18 and 10 less is -8.   -8 * -6= 
-8 * -6 = 48
48 (Correct)   Correct   -6nswer (-6)
Answer: A
A and B invests Rs.2500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?	Select:
A) 11:5  B) 15:16  C) 15:2  D) 9:9  E) 11:1

Solution: (2.5*6 + 5*6): (4*12)   45:48 =>   15:16   Answer:15:16
Answer: B
A number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e. What is the greatest two digit prime saturated integer ?	Choose the correct answer:
A) 99 B) 98 C) 97 D) 96 E) 95

Solution: e=96 = 3 * 32 = 3 * 2^5   Answer is 96.
Answer: D
A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10 days and left the job. In how many days A alone can finish the
remaining work?	Choose the correct choice from the following answers:
A) 5
B) 6
C) 3
D) 2
E) 1

Solution: B's 10 day's work=10/15=2/3   Remaining work=(1-(2/3))=1/3   Now, 1/18 work is done by A in 1 day.   Therefore 1/3 work is done by A in  18*(1/3)= 
 18*(1/3) = 6
6 days.   ANSWER 6
Answer: B
A basket has 4 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is	Choices:
A) 19/70	B) 17/70	C) 21/70	D) 23/70	E) 25/71

Solution: Total fruits = 8Since there must be at least 3 apples,(4C3 * 4C1)/8C4 + 4C4/8C4 = 17/70.Answer:17/70
Answer: B