MU-NLPC/Calc-aqua_rat huggingface dataset:
210 school students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?	Answers:
A) 25	B) 40	C) 50	D) 60	E) 75

Solution: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.   So, if we use your formula it should be: 210={Mac}+{Windows}-{40oth}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: B
A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is	Pick: A) 378 B) 278 C) 258 D) 287 E) 271

Solution: Explanation:   area of cross roads = 55*4 + 35*4 - 4*4= 
55*4 + 35*4 - 4*4 = 344
344sq m   cost of graveling= 344 * (75/100) = Rs. 258   Answer: 258) rs.258
Answer: C
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Choose the correct choice.
A) 67 sec
B) 89 sec
C) 36 sec
D) 87 sec
E) 45 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer: 36 sec
Answer: C
Two persons start at the same point, walk in opposite directions with 5 km/hr and 5.5 km/hr respectively.
What is the distance separated after 2 and half hrs? Options:
A) 26.250 km
B) 27.250 km
C) 28.250 km
D) 29.250 km
E) 25.250 km

Solution: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 5 + 5.5= 
5 + 5.5 = 10.5
10.5 km.   They will be separated in 2.5 hours= 10.5 * 2.5= 
10.5 * 2.5 = 26.25
26.250 km   26.250 kmNSWER:26.250 km
Answer: A
8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is ?  Choose the correct choice from the following answers:
A) 8/39 B) 15/39 C) 12/13 D) 11/13 E) None of these

Solution: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)   = 1 - [16C1x14C1x12C1x10C1/16C4] = 15/39   Answer is 15/39
Answer: B
38, 52, 22,79, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?  Options:
A) a- 56
B) b- 65.5
C) c- 69
D) d- 71
E) e- 73

Solution: Important:- Arrange the numbers in ascending order first.   13, 22, 31, 38, 47, 52, 79, 82   3/4th of the number list represents- 52 (6th number)   remaining 1/4th list represents 79 (7 th number)   65.5 fits in between above 2   Answer:- b- 65.5
Answer: B
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:  Select:
A) 2520  B) 2420  C) 2320  D) 2620  E) 2760

Solution: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.   Solving the two equations, we get: l = 63 and b = 40.   2520rea = (l x b) = (63 x 40) = 2520 sq.m   2520nswer: 2520
Answer: A
A bat is bought for Rs.400 and sold at a gain of 40% find its selling price  Choose the correct answer:  A) A)Rs.560/-  B) B)Rs.470/-  C) C)Rs.480/-  D) D)Rs.500/-  E) E)Rs.520/-

Solution: 100 % ------> 400 (100 * 4 = 400)   140 % ------> 560 (140 * 4 = 560)   Selling price = Rs.560/-   Rs.560/-nswer : Rs.560/-
Answer: A
The angles of a triangle are in the ratio 4:3:8. Find the measurement of the largest of three angles of triangle.  Options:
A) 96° B) 100° C) 120° D) 140° E) 160°

Solution: If the ratio of the three angles is 4:3:8, then the measures of these angles can be written as 4x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   4x + 3x + 8x = 180   Solve for x   15x = 180   x = 12   The measures of the three angles are   4x = 4 x 12° = 48   3x = 3 × 12 = 36°   8x = 8 × 12 = 96°   96°
Answer: A
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?  Options
A) 41 B) 30 C) 35 D) 48 E) 49

Solution: B   30   There is a meal for 200 children.   150 children have taken the meal.   Remaining meal is to be catered to 50 children.   Now, 200 children 120 men.   50 children = (120/200)x 50 = 30 men.
Answer: B
If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?  Choose the correct answer:
A) 8	B) 9	C) 12	D) 15	E) 27

Solution: umber of factors of (2^a)*(3^b)*(5^c) ... = (a+1)(b+1)(c+1) ...   If m, p and t are the distinct prime numbers, then the number is already represented in its prime factorization form   Number of factors = (3+1)(1+1)(1+1) = 16   Out of these, one factor would be 1.   Hence different positive factors greater than 1 = 15   Correct Option: 15
Answer: D
In a certain neighborhood, there are half as many beige houses as white houses, and 3 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
Answers:
A) 4:1  B) 3:5  C) 2:3  D) 1:3  E) 1:4

Solution: The ratio of beige:white:brown = 3:6:2   The answer is 2:3.
Answer: C
S = { 1,2,4,5,6}
T = { 4,5,6,8,12,10,7,14 }
what is the probability that x chosen from S and y chosen from T will result x*y = odd	Choose the correct choice from the following choices.
A) 1/3 B) 21/32 C) 20/11 D) 58/20 E) 11/20

Solution: p: the probability that x*y is even, then p=1-p(x*y is odd)   p(x*y even)=p(x even)*p(y even)=3/5*6/8=9/20   And p=1-9/20=11/20   Option: 11/20
Answer: E
David purchased a Motor Bike and a mobile phone for Rs. 40000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 10 percent and the mobile phone at a profit of 10 percent. Overall he make a.  Select the correct option:  A) loss of Rs. 200  B) loss of Rs. 3200  C) profit of Rs. 100  D) profit of Rs. 200  E) None of these

Solution: Total C.P. = 40000+8000= 
40000+8000 = 48_000
48000   S.P. of motor bike= 40000/100*90= 
40000/100*90 = 36_000
36000   S.P. of Mobile= 8000/100*110= 
8000/100*110 = 8_800
8800   Total S.P.= 36000 + 8800= 
36000 + 8800 = 44_800
44800   Tota. C.P. - Total S.P.= 48000 - 44800= 
48000 - 44800 = 3_200
3200   Answer : loss of Rs. 3200
Answer: B
On the number line, the number p is twice as many units from -2 as -2 is from 2. If p is less than –2, what is the value of p ?
Choose the correct choice from the following:
A) –18	B) –10	C) –6	D) 10	E) 14

Solution: Distance between -2 and 2 = 4   Since number p is twice as many units from -2 as -2 is from 2   , therefore p can be -10 Since , p is less than -2 ,   the value of p = -10   Answer –10
Answer: B
Bob invested $2000 in fund A and $2000 in fund B. Over the next two years, the money in Fund A earned an annual interest of 30 percent for the two years and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund B was worth how much more than his investment in fund A? Answers:
A) 1. $180
B) 2. $550
C) 3. $300
D) 4. $200
E) 5. $220

Solution: interest on fund A will be 1200. rate of interest will be 30% per annum simple interest as 60% is for 2 year. this will make investment A 3200 at the end of 2nd year.   interest on fund B will be 1380 on 30% interest compounded annually. This will make investment B 3380 at the end of 2nd year.   Difference in investment 1. $180 and investment B=3380-3200= 
3380-3200 = 180
180   answer is 1. $180.
Answer: A
A, B and C have Rs.450 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Select the correct option: A) A)100 B) B)110 C) C)120 D) D)130 E) E)140

Solution: 100+B+C = 450   100+C = 200   B+C = 350   --------------   100+B+2C = 550   100+B+C = 450   ----------------   C = 100   100nswer:100
Answer: A
A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?  Choose the most appropriate option
A) 35 days  B) 25 days  C) 30 days  D) 27 days  E) 23 days

Solution: Work done by B in 1 day = 1/10 - 1/14 = (7-5)/70   =2/70=1/35   So, B alone can do the work in 35 days.   35 daysNSWER:35 days
Answer: A
M is the sum of the reciprocals of the consecutive integers from 101 to 200, inclusive. Which of the following is true?	Choose one.
A) 1/3 < M < 1/2  B) 1/5 < M < 1/3  C) 1/2 < M < 1  D) 1/9 < M < 1/7  E) 1/12 < M < 1/9

Solution: M = 1/101 + 1/102 + 1/103 + ...... + 1/200   If we replace the first 99 terms by 1/200, then we get a sum = 100/200 = 1/2. Since the actual terms are larger than 1/200, the sum is larger than 1/2.   If we replace the all the 100 terms by 1/100, we get a sum = 100/100= 
100/100 = 1
1. Since the actual terms are smaller than 1/100, the sum is less than 1.   Therefore 1/2 < M < 1   1/2 < M < 1hoice 1/2 < M < 1
Answer: C
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?	Choose the correct choice from the following choices:
A) 6%	B) 2%	C) 4%	D) 5%	E) 3%

Solution: 150 = (750*5*R)/100   R = 4%   Answer: 4%
Answer: C
The average (arithmetic mean) of four numbers is 7x + 5. If one of the numbers is x, what is the average of the other three numbers?	Choose the correct choice from the following choices:
A) x + 1
B) 3x + 3
C) 9x + 20/3
D) 5x + 4
E) 15x + 12

Solution: If the average of four numbers is 7x + 5, then the sum of all four numbers if 4 * (7x + 5) = 28x + 20. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 20 - x)/3 = (27x + 20)/3 = 9x + 20/3.   Answer is 9x + 20/3.
Answer: C
A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?	Choose the correct choice
A) 325	B) 350	C) 375	D) 400	E) 425

Solution: Speed=(90 x(5/18)m/sec	=(25)m/sec.   Length of the train = (Speed x Time).   Length of the train =	((25)x 15)m = 375 m   375
Answer: C
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 16 boys and 44 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?	Choose the most appropriate option.
A) 2  B) 4  C) 6  D) 8  E) 10

Solution: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.   Table method is shown above; here is how you will use logic:   There are 6 happy boys.   There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.   We have 6 happy boys and 6 sad boys. Total we have 16 boys. So  16 - 6 - 6= 
 16 - 6 - 6 = 4
4 boys must be neither happy nor sad.   Answer (4)
Answer: B
If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?  Answers
A) 141  B) 200  C) 606  D) 391  E) 412

Solution: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).   We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...   A + (A+2) + (A+4) = 3A + 6   We know that 3A + 6 COULD equal one of those five answers; we just have to find it...   Could 3A + 6 = 141   3A = 135   A = 45   This is NOT an EVEN INTEGER, so 141 is NOT the answer   Could 3A + 6 = 200   3A = 194   A = 64.6666   This is NOT an EVEN INTEGER, so 200 is NOT the answer   Could 3A + 6 = 606   3A = 600   A = 200   This IS an EVEN INTEGER! The numbers would be 200, 202 and 204. This IS the answer   Final Answer:   606
Answer: C
James invested a certain sum of money in a simple interest bond whose value grew to $700 at the end of 3 years and to $ 800 at the end of another 2 years. What was the rate of interest in which he invested his sum?  Choose the correct choice from the following:
A) 9.09%	B) 12.5%	C) 6.67%	D) 6.25%	E) 8.33%

Solution: Lets assume the Principal Amount (initial amount invested) to be P   rate of interest to beRand time as T. We need to find R   Now After a time of 3years the principal P amounts to $700 and after a time of 5years ( question says after another 2years so 3+2) P becomes $800.   Formulating the above data   9.09%mount (9.09%1) at end of 3years   9.09%1= P(1 + 3R/100) = 700   9.09%mount (9.09%2) at end of 5years   9.09%2 = P(1 + 5R/100) = 800   Dividing 9.09%2 by 9.09%1 we get   (1 + 5R/100)/(1 + 3R/100) = 8/7   after cross multiplication we are left with 11R =100 which gives R = 9.09%   Option: 9.09%
Answer: A
If 0.5% of A =65 paise, then the value of A is ?  Choose the correct choice from the following:
A) Rs. 130
B) Rs. 17
C) Rs. 1.70
D) Rs. 4.25
E) None

Solution: Answer   ∵ 0.5/100 of A = 65/100   ∴ A = Rs. (65 / 0.5) = Rs. 130   Correct Option: Rs. 130
Answer: A
A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?  Choose one.
A) 1/3
B) 2/5
C) 2/7
D) 3/7
E) 3/8

Solution: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)   = = 2/5   2/5
Answer: B
If the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?
Choose the correct choice from the following answers: A) 1/8 B) 1/4 C) 1/3 D) 1/7 E) 1/9

Solution: The length of cube Q = 1;   The length of cube P = 2;   The ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8.   1/8nswer: 1/8
Answer: A
For which of the following functions does f(−y)=−f(y) for all real number values of x?
Choose the correct choice from the following answers
A) y^8−y^4	B) y^2−y^6	C) y^5/y^7	D) y^9/(y^5+1)	E) -32/5 putting y=2 on y^5/(y^2+1)

Solution: all even root cannot be matched eliminated   put y=2   f(−y)=(−2)^5/(−2^)2+1=−32/5, and   −f(y)=−2^5/2^2+1=−32/5, for a match.   y^8−y^4NSWER: y^8−y^4
Answer: A
The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 12. What is the radius of circle O?	Choose the correct choice from the following answers
A) –2/pi
B) 2
C) 3
D) 4
E) 6

Solution: pi*r^2 + 2r -2*pi*r = 12   Simplifying the equation: pi*r(r-2)+2r=12   Without much algebraic: We can Test the answers quickly, then 6 is the only possible answer that will eliminate pi from equation.   Answer is 6
Answer: E
A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 100 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
Choose the correct choice from the following answers:
A) 1	B) 2	C) 3	D) 5	E) 7

Solution: The distance between the nest and the ditch is 100 meters.   15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.   So the distance is  30 * 100= 
 30 * 100 = 3_000
3000.   5= ST   3000/1.5 = T , I think we can take 3000 meters as 3 km, then only we get T = 2.( 1000 meters = 1 km)   5)
Answer: D
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is  Options
A) 7/12  B) 5/9  C) 1/36  D) 5/12  E) 8/9

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   ANSWER:5/9
Answer: B
What is the greatest positive integer x such that 3^x is a factor of 9^5? Choose the most appropriate option:
A) 5 B) 9 C) 10 D) 20 E) 30

Solution: What is the greatest positive integer x such that 3^x is a factor of 9^5?   9^5 = (3^2)^5 = 3^10   C. 10
Answer: C
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: Choose the correct option:
A) 33  B) 38  C) 42  D) 12  E) 17

Solution: Explanation:   After 10 days : 150 men had food for 35 days.   Suppose 125 men had food for x days.   Now, Less men, More days (Indirect Proportion)   \inline {\color{Blue} \therefore } 125 : 150 :: 35 : x 125 x x = 150 x 35   => x=   => x= 42   Answer: 42
Answer: C
What is the smallest positive integer x, such that 2160 x is a perfect cube? Pick one.
A) 100
B) 6
C) 8
D) 12
E) 18

Solution: Take out the factors of 2160 that will come 6^3*10. for perfect cube you need every no. raise to the power 3. for 2160 to be a perfect cube, you need two 2 and two 5 that means 100   100 is the answer.
Answer: A
A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,800 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?  Choices:
A) 54,000  B) 64000  C) 62000  D) 60000  E) 68000

Solution: 80% parts used of subsidary company, so 20% parts used of other companies.   Now, 20% parts = 10,800 computers   So, 1% parts = 10,800/20   Or, 100% parts = 54,000 computers.   Hence answer is (54,000)
Answer: A
A takes twice as much time as B or thrice as much time to finish a piece of work.Working together they can finish the work in 2 days.B can do the work alone in:
Choose the correct answer:
A) 5 hours
B) 6 hours
C) 7 hours
D) 8 hours
E) 4 hours

Solution: Let 6 hours takes =x hours   A takes=x/2   1/x + 1/(x/2)=1/2   3/x=1/2   x = 6 hours   ANSWER:6 hours
Answer: B
The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?  Pick:
A) A)17 B) B)18 C) C)19 D) D)22 E) E)24

Solution: Explanation:   10 * 16 + 36 – 26=170 => 170/10= 
170/10 = 17
17   17)
Answer: A
Two numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is? Choose the correct choice from the following
A) 77%  B) 78%  C) 79%  D) 80%  E) 81%

Solution: I II III   120 150 100   150----------120   100-----------? => 80%   Answer:80%
Answer: D
Joe's current weekly caloric intake is 20,000 calories. His physician has advised Joe to reduce the number of calories he consumes weekly to 14,000. By what percent does Joe need to reduce his weekly caloric intake?  Choose the correct choice from the following:  A) 20%  B) 30%  C) 50%  D) 60%  E) 70%

Solution: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.   Here, we're told that the original amount of calories is 20,000 and that the reduced amount of calories is 14,000. We're asked what PERCENT should the original amount of calories be REDUCED BY?   Original Calories= 20,000   Reduced Calories = 14,000   The percent of reduced calories is relative to the original calories as shown:   14,000/20,000 = 7/10 = 70%. So, 14,000 calories is 70% of 20,000 calories (100%). But the question is BY what PERCENT should the original amount of calories be REDUCED. 100% - 70% = 30%.   30%
Answer: B
A certain sum amounts to Rs.675 in 3 years and Rs.850 in 6 years. Find the rate % per annum? Choose the correct answer:
A) 10%  B) 8%  C) 11%  D) 9%  E) 7%

Solution: 3 --- 675   6 --- 850   --------------   3 --- 175   N = 1 I = 55 R = ?   P = 675 - 175= 
675 - 175 = 500
500   55= (500*1*R)/100   R = 11%   Answer: 11%
Answer: C
If (a – b) is 7 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:	Choose the correct choice from the following options:	A) 6	B) 2	C) 3	D) 4	E) 5

Solution: (a – b) – (c + d) = 7 and (c – d) – (a + b) = 3   => (a – c) – (b + d) = 7 and (c – a) – (b + d) = 3   => (b + d) = (a – c) – 7 and (b + d) = (c – a) – 3   => (a – c) – 7 = (c – a) – 3 => 2(a – c) = 4 => (a – c) = 2   ANSWER:2
Answer: B
Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use? Choose the correct choice from the following answers:
A) 14  B) 47  C) 54  D) 180  E) 64

Solution: Area = Length x Breadth   480 = 40 x Breadth   So, Breadth = 12 Units   Fencing required is -   Breadth + Breadth + Length    12 + 12 + 40= 
 12 + 12 + 40 = 64
> 64 feet   Answer must be (64) 64
Answer: E
A man buys 12 lts of liquid which contains 10% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
Select the correct option.
A) 80.91	B) 76.45	C) 77.45	D) 74.45	E) 73.45

Solution: 10% in 12 lts is 1.2. So water = 12-1.2= 
12-1.2 = 10.8
10.8 lts. 30% of 10 lts= 3. So water in 2nd mixture = 10-3= 
10-3 = 7
7 lts. Now total quantity= 12 + 10= 
12 + 10 = 22
22 lts. Total water in it will be 10.8 + 7= 
10.8 + 7 = 17.8
17.8 lts. % of water= (100*17.8)/22 = 80.91. 80.91nswer:80.91
Answer: A
If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
Choose the correct choice:	A) 500	B) 1000	C) 900	D) 800	E) 700

Solution: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x   1 = 1/10 * 1/10 * 1/10 * x => x = 1000   ANSWER:1000
Answer: B
If a and b are each greater than x and y, which of the following must be true?
I. a + b < x + y
II. ab > xy
III.a + b > x + y	Choose the correct choice from the following options:
A) I only
B) II only
C) I and II
D) III only
E) I, II and III

Solution: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.   II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.   III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.   Answer: III only.
Answer: D
A rummy( card game) player has 13 cards in his hand with 2 Aces, one of spades and other of hearts. All other cards are unique. How many ways can he hold the 13 cards? Options:  A) 14!  B) 11!  C) 12!  D) 10!  E) 13!

Solution: Even though the player has 2 Aces, both of them are of different colour and sign. So we can't consider them as a single object. Ace (spade)Ace(heart) is different to Ace(heart)Ace(spades). So there are 13! Ways to arrange the cards. Answer is E. 13!.
Answer: E