MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio of the ages of Raja and David is 2 : 3. The total of their ages is 3.0 decades. The proportion of their ages after 0.5 decades will be
[1 Decade = 10 years]  Choose the most appropriate option.
A) 17 : 23  B) 3:4  C) 4:5  D) 7:9  E) 3:6

Solution: Let, Raja’s age = 217 : 23 and David’s age = 317 : 23   Then 217 : 23 + 317 : 23 = 30   17 : 23 = 6   Raja’s age = 12 years   and David’s age = 18 years   Proportion of their ages after 5 is = (12 + 5) : (18 + 5)   = 17 : 23   17 : 23nswer : 17 : 23
Answer: A
A chemist mixes one liter of pure water with x liters of a 30% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?  Choose the correct option
A) 1/4 B) 1/3 C) 1/2 D) 1 E) 2

Solution: Concentration of salt in pure solution = 0   Concentration of salt in salt solution = 30%   Concentration of salt in the mixed solution = 20%   The pure solution and the salt solution is mixed in the ratio of --> (30 - 20)/(20 - 0) = 1/2   1/x = 1/2   x = 2   Answer: 2
Answer: E
Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $4 million from its orange exports, how much money does it generate from its yearly total of exports? Choose the correct choice from the following options: A) $21.25m B) $25.5m C) $106.25m D) $120m E) $153m

Solution: 2/10*1/6*(total) = 4   1/30*(total) = 4   (total) = 4*30= 
4*30 = 120
120   Answer: $120m.
Answer: D
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?
Select
A) 20
B) 24
C) 28
D) 32
E) 36

Solution: 2 oxen = 3 buffaloes = 4 cows   Also: 15 buffaloes + 8 oxen + 24 cows   = 10 oxen + 8 oxen + 12 oxen = 30 oxen   There is enough fodder for 1 oxen for 30*48 days.   40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen   The new total is equal to 60 oxen instead of 30 oxen.   30*48 / 60= 
30*48 / 60 = 24
24 days   The answer is 24.
Answer: B
If it is possible to make only one meaningful English word with the second, the fourth, the fifth and seventh letters of the word COURTESY, using each letter only once in the word, which of the following will be the third letter of that word? If no such word can be formed, give 'N' as the answer and if more than one such word can be formed, give 'M' as the answer.
Choose the correct option
A) N  B) B  C) V  D) C  E) M

Solution: Answer: Option M
Answer: E
Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $10.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?  Pick.
A) a. $3.19  B) b. $3.75  C) c. $3.90  D) d. $4.08  E) e. $4.23

Solution: On Monday and Thursday, she spent $10.43total.   On Tuesday and Wednesday, she spent $3.54on each day.   On Friday, she spent $7.89 on lunch.   The average = (10.43 + 2*3.54 + 7.89)/5 = 4.08.   Answer: d. $4.08.
Answer: D
FOG + FOG + FOG + FOG = 1460.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?  Choose the correct choice from the following choices
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: given,FOG + FOG + FOG + FOG = 1460   4(FOG)=1460   =>FOG=365   Face value of F is:3   Face value of O is:6   Face value of G is:5   so F+O+G=3+6+5= 
3+6+5 = 14
14   ANSWER:14
Answer: D
Arrange the fractions in ascending order  Select the correct option:	A) 5/8 < 7/12 < 3/4< 13/16	B) 5/8 < 7/12 < 13/16 < 3/4	C) 5/8 < 3/4< 13/16 < 7/12	D) 7/12 < 5/8 < 3/4< 13/16	E) None of these

Solution: Explanation:   5/8= 
5/8 = 5/8 = around 0.625
.625, 7/12= .5833, 3/4 = .75, 13/16 = .8125   So order will be   7/12 < 5/8 < 3/4< 13/16   Option 7/12 < 5/8 < 3/4< 13/16
Answer: D
Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 4x + 2 = 0?	Choose one: A) 8 B) 10 C) 2 D) 16 E) 24

Solution: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab   = [(a + b)2 - 2ab]/ab   a + b = -4/1 = -4   ab = 2/1= 
2/1 = 2
2   Hence a/b + b/a= [(-4)2 - 2(2)]/2 = 4/2= 
4/2 = 2
2.   2)
Answer: C
What is the minimum number of square tiles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?	Answers
A) 187
B) 180
C) 190
D) 195
E) 197

Solution: Length = width   ==>square = 5 m 78 cm and 3m 74   5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm   HCF of 578 and 374 = 34   square is 34   =578*374/34*34 == 17*11= 
17*11 = 187
187   187NSWER 187
Answer: A
What is the number of integers from 1 to 100 (inclusive) that are divisible by neither 5 nor by 6?	Select the correct option.
A) 35	B) 47	C) 58	D) 26	E) 34

Solution: In 100 consecutive numbers, number of multiples of 5 = 100/5= 
100/5 = 20
20 (Ignore decimals)   In 100 consecutive numbers, number of multiples of 6= 100/6 = 16   Number of multiples of 5*6 i.e. 30 = 100/30 = 3   Number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - (29 + 16 - 3) {Using the concept of sets here) = 58   Answer is 58
Answer: C
In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is single?
Choose the correct choice:
A) 2/7  B) 1/3  C) 1/2  D) 2/3  E) 5/7

Solution: Let the universal set be X = {all students in the graduate physics course}, such that n(X) = 100   It will contain 2 mutually exclusive sets; M (all male students) & F (all female students), where n(M) = 70, n(F) = 30   Now 2/7 of all male students are married, implying their number = 20.   However the total number of married students = 30, implying 10 married females.   Therefore 20 single females; = 2/3 of total females.   ANSWER:2/3
Answer: D
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 80% Vermouth by volume. How many ounces of Gin must he add?  Choose the correct choice from the following options:  A) n/6  B) n/3  C) 3n/5  D) 5n/6  E) 8n/5

Solution: 4 ounces is vermouth   6 ounces of gin...   Total volume 10.   To make vermouth account for 80% of total volume the new volume must be....   x*0.8=4   x=5 ounces....   So now you see that he must add 5 ounces of gin...   Plug in 6 for n in the answer choices and look for answer 5   5n/6
Answer: D
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back?  Choose the most appropriate option.
A) 7	B) 14	C) 10	D) 12	E) 9

Solution: Let son's present age be x years. Then,   (38−x)=x⇒2x=38⇒x=382=19   Son's age 5 years back =19−5=14   Answer is 14.
Answer: B
The tax on a commodity is diminished by 10% but its consumption is increased by 20%. Find the decrease percent in the revenue derived from it?  Select.
A) 18%
B) 4%
C) 32%
D) 12%
E) 52%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 120= 
80 * 120 = 9_600
9600   10000------- 400   100 ------- ?= 4%   Answer:4%
Answer: B
The greatest ratio out of 2:3, 5:1, 3:2, 8:9 and 8:5 is?
Select the correct option
A) 2:3	B) 3:2	C) 5:1	D) 8:5	E) 8:9

Solution: 2/3=0.666   5/1= 
5/1 = 5
5   3/2= 
3/2 = 3/2 = around 1.5
1.5   8/9=0.888   8/5= 
8/5 = 8/5 = around 1.6
1.6   ANSWER:5:1
Answer: C
Amber works 10 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?	Choose the correct choice from the following.
A) m/(20d) B) 10md/6 C) 10d D) 20d/m E) 20md

Solution: ANSWER: 10d The passage states that she works 10 days a month at d dollars per day, so 20 d is her monthly pay
Answer: C
Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?
Choose the correct choice from the following:
A) 85
B) 97
C) 109
D) 178
E) None

Solution: Explanation: This is an alternating division and addition series: First, divide by 2, and then add 8.   Answer: Option 178
Answer: D
The number of new words that can be formed by rearranging the letters of the word 'LOVE' is ? Choose the correct answer:  A) 25  B) 26  C) 23  D) 29  E) 10

Solution: Number of words which can be formed = 4! - 1   = 24 - 1= 
24 - 1 = 23
23.   Answer:23
Answer: C
A restaurant meal cost $50 and there was no tax. If the tip was more than 20 percent but less than 25 percent of the cost of the meal, then total amount paid must have been between:
Choose the correct option: A) $61 and $63 B) $60 and $61 C) $62 and 63 D) $59 and $63 E) $61 and $62.5

Solution: let tip=t   meal cost=50   range of tip = from 20% of 50 to 25% of 50 = 10 to 12.5   hence range of amount paid= 50+T= 60 to 62.5 i.e. $59 and $63
Answer: D
A man spends half of his salary on household expenses, 1/4th for rent, 1/5th for travel expenses, the man deposits the rest in a bank. If his monthly deposits in the bank amount 50, what is his monthly salary?  Select
A) Rs.500  B) Rs.1500  C) Rs.1000  D) Rs. 900  E) Rs. 800

Solution: s-(1/2 s+ 1/4 s + 1/5 s) = 50   1/20 s =50   s=1000   ANSWER:Rs.1000
Answer: C
Little Roshini had $10.50. He spent some money on sweets and gave to his two friends $3.40 each. How much money was spent for sweets?
Choices.
A) $4.70 B) $4.80 C) $3.85 D) $3.80 E) $ 3.70

Solution: Roshini spent and gave to his two friends a total of   x + 3.40 + 3.40 = $3.65   Money spent for sweet=   10.50 - 6.80= 
10.50 - 6.80 = 3.7
$3.70   correct answer is $ 3.70) $ 3.70
Answer: E
In a simultaneous throw of two dice, what is the probability of getting a doublet?
Answers:
A) 1/6
B) 1/4
C) 2/3
D) 3/7
E) 1/2

Solution: In a simultaneous throw of two dice, n(S) = (6 x 6)= 36.   Let E = event of getting a doublet = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}.   Therefore, P(E) = n (E)/ n(S) = 6/36 = 1/6.   1/6NSWER:1/6
Answer: A
The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidateswho passed the examination is? Choose one:  A) 50  B) 90  C) 100  D) 120  E) 140

Solution: Let the number of candidate who passed = y   Then, 39y + 15(120 - y) =120 x 35   ⇒ 24y= 4200 -1800= 
4200 -1800 = 2_400
2400 / 24= 
2400 / 24 = 100
100   100
Answer: C
In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 29 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students play only cricket ?	Pick:
A) 36
B) 42
C) 39
D) 47
E) 37

Solution: PERSONS PLAY CRICKET ONLY=N(C)-N(42∩C)+N(C∩T)-2(N(42∩T∩C))   =75-30+29-(2*16)= 
75-30+29-(2*16) = 42
42   ANSWER:42
Answer: B
A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.  Choices
A) 18 days
B) 22 Â½ days
C) 24 days
D) 26 days
E) 28 days

Solution: Explanation :   If A completes a work in 1 day, 22 Â½ days completes the same work in 3 days   Hence, if the difference is 2 days, 22 Â½ days can complete the work in 3 days   => if the difference is 60 days, 22 Â½ days can complete the work in 90 days   => Amount of work 22 Â½ days can do in 1 day= 1/90   Amount of work A can do in 1 day = 3 Ã— (1/90) = 1/30   Amount of work A and 22 Â½ days can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45   => A and 22 Â½ days together can do the work in 45/2 days = 22 Â½ days   Answer IS 22 Â½ days
Answer: B
A invested $100 in a business after 6months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?	Options: A) $100 B) $75 C) $20 D) $120 E) $50

Solution: A:B = 100*12:200*6   A:B = 1:1   A's share = 100/2= 
100/2 = 50
$50   Answer is $50
Answer: E
A basket has 5 apples and 5 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
Choose the correct choice:
A) 1/2  B) 3/5  C) 3/8  D) 4/9  E) 7/10

Solution: The total possible choices are 10C3 = 120   The ways to choose 3 apples: 5C3 = 10   The ways to choose 2 apples: 5C2 * 5C1 = 50   P(at least 2 apples) = 60/120 = 1/2   The answer is 1/2.
Answer: A
30 men can do a work in 40 days. When should 12 men leave the work so that the entire work is completed in 40 days after they leave the work?  Choose the most appropriate option:
A) 18 days B) 10 days C) 55 days D) 44 days E) 22 days

Solution: Total work to be done = 30 * 40= 
30 * 40 = 1_200
1200   Let 12 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.   40P + (12 * 40)= 1200   40P = 720 => P = 18 days   18 daysnswer:18 days
Answer: A
Find the area of circle whose radius is 6m? Choose the correct answer: A) 113.14 B) 111.54 C) 117.27 D) 112.88 E) 112.98

Solution: 22/7 * 6 * 6   = 113.14   113.14nswer:113.14
Answer: A
2+2+2²+2³ ... +2^10  Pick
A) 2^9
B) 2^10
C) 2^11
D) 2^35
E) 2^37

Solution: 2+2=2^2   2^2+2^2=(2^2)*(1+1)=2^3   2^3+2^3=(2^3)*(1+1)=2^4   so you can notice the pattern... in the end you will have 2^10+2^10, which will give you 2^11   Answer 2^11
Answer: C
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:  Choose the most appropriate option
A) 10 B) 11 C) 13 D) 15 E) 17

Solution: Let the three integers be x, x + 2 and x + 4.   Then, 3x = 2(x + 4) + 3 x = 11.   Third integer = x + 4 = 15.   ANSWER : 15
Answer: D
If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? Answers.
A) 24  B) 40  C) 50  D) 80  E) 120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6.   But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4.   Total # of ways: 4C2*2^2=24.   24nswer: 24
Answer: A
This year, MBB Consulting fired 10% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction? Choose the correct choice from the following answers:	A) 99%	B) 100.0%	C) 102.8%	D) 104.5%	E) 105.0%

Solution: 100 employees getting 1000$ avg, so total salary for 100 ppl = 100000   10% reduction in employees lead to 90 employees and a salary increase of 10% of previous avg salary   Thus the new avg salary is = 10%(1000)+1000 = 1100   so total salary of 90 employees is   90*1100= 
  90*1100 = 99_000
99000   Now the new salary is more than previous salary by x%. x= (99000/100000)*100= 
(99000/100000)*100 = 99
99%   So the 99%nswer is 99%
Answer: A
The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?	Choose one
A) 16 a.m  B) 10 a.m  C) 17 a.m  D) 15 a.m  E) 11 a.m

Solution: D = 110 – 20 = 90   RS = 20 + 25= 
20 + 25 = 45
45   T= 90/45= 
90/45 = 2
2 hours   8 a.m. + 2= 10 a.m.   Answer: 10 a.m
Answer: B
The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface? Select the correct option:
A) 18 πr2 B) 12πr2 C) 3 πr2 D) 6 πr2 E) 9 πr2

Solution: Explanation:   2 * π * 2r * 3r = 12πr2   Answer: 12πr2
Answer: B
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green? Choices.
A) 7/22	B) 7/25	C) 8/21	D) 8/23	E) 8/25

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 8/21.   8/21)
Answer: C
If xy represents a positive two digit number, where x and y are single digit integers, which of the following cannot be true?
Choose the correct choice from the following choices:
A) x+y =9  B) (x)(y)=9  C) x-y = 9  D) y-x= 9  E) x/y = 9

Solution: (A) xy = 45 or 63 or 27   (B) xy = 33 or 19   (C) 90   (D) impossible   (E) xy = 91   (D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).   ans y-x= 9
Answer: D
A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 oranges are used, how many limes are needed?
Choose the correct answer:
A) 200 B) 700 C) 1400 D) 2800 E) 7000

Solution: 10%= 200 fruit   100%=2000 fruit   70% of 2000 fruit=1400 fruit   1400 limes   ANSWER:1400
Answer: C
There is a 10% chance that Tigers will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?  Choices:
A) 55%
B) 60%
C) 70%
D) 72%
E) 80%

Solution: There is a 10% chance that Tigers will not win at all during the whole season   We can infer that there is 90% chance Tigers will win .   Similarly There is a 20% chance that Federer will not play at all in the whole season   We can also infer that there is 80% chance that Federer will play.   Answer 80%
Answer: E
A company has 600 employees, 40% of whom are employed part time. If it hires 60 new employees, 15% of whom are employed part time, what will be the percent increase in part time employees?	Answers: A) 1 2/3 % B) 2 2/3 % C) 4 % D) 3.61 % E) 9 %

Solution: Total employee = 600   Part time Empl = 600 * 40/100= 
600 * 40/100 = 240
240   New part time empl= 60 * (15/100)= 
60 * (15/100) = 9
9   Total new part time Emp= 9+240= 
9+240 = 249
249   Old part time Emp= 240   % increase = (new - old)*100/old   =9*100/249   = 3.61 %   Ans-3.61 %
Answer: D
A password for a computer uses six digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?	Choose the correct option.
A) 1/32 B) 1/64 C) 1/8 D) 2/5 E) 1/2

Solution: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for six digits is 10 x 10 × 10 × 10 × 10 × 10 = 1,000,000 possible combinations.   Prime numbers constitute 2, 3, 5, 7 and 11. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 6 x 6 × 6 × 6 × 6 × 6. So the probability is 1/2 x 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/64.   The right answer is choice (1/64).
Answer: B
The fourth proportional to 12, 16 and 18 is?  Choose the correct choice from the following options:  A) 24  B) 66  C) 55  D) 88  E) 61

Solution: (15*18)/12   = 24   24nswer:24
Answer: A
A side of beef lost 30 percent of its weight in processing. If the side of beef weighed 500 pounds after processing, how many pounds did it weigh before processing?
Choose one
A) 714.28
B) 712
C) 714.88
D) 714.25
E) 714

Solution: Let weight of side of beef before processing = x   (70/100)*x = 500   => x = (500 * 100)/70 = 714.28   714.28nswer 714.28
Answer: A
Find a sum for first 5 prime number'ss?
Choose the correct choice:
A) 22
B) 28
C) 29
D) 32
E) 34

Solution: Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28   Note: 1 is not a prime number   Option 28
Answer: B
A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet? Choose the correct choice from the following answers:
A) 111 B) 771 C) 200 D) 873 E) 811

Solution: When the second train leaves Mumbai the first train covers 40 * 1= 
40 * 1 = 40
40 km   So, the distance between first train and second train is 40 km at 10.00am   Time taken by the trains to meet= Distance / relative speed = 40 / (50 -40)= 
40 / (50 -40) = 4
4 hours   So, the two trains meet at 2 p.m. The two trains meet 4 * 50= 
4 * 50 = 200
200 km away from Mumbai.   Answer: 200
Answer: C
A school has 4 section of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student. Choose the correct choice
A) 50.25	B) 52.25	C) 51.25	D) 53.25	E) None of the above

Solution: Required average marks   = 40×50+35×60+45×55+42×45/40+35+45+42   = 2000+2100+2475+1890/162   = 8465⁄162 = 52.25   Answer 52.25
Answer: B
How many integers are divisible by 3 between 10! and 10! + 40 inclusive?	Pick:
A) 6  B) 7  C) 8  D) 13  E) 10

Solution: D - 7   10! is divisible by 3   There are 12 numbers between 10! and 10!+40 that are divisible by 3.   Hence 13
Answer: D
A scuba diver descends at a rate of 35 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3500feet below the sea level..how long will he take to reach the ship?  Choose the correct choice from the following answers:
A) 160 minutes  B) 120 minutes  C) 100 minutes  D) 76 minutes  E) 77 minutes

Solution: Time taken to reach = 3500/35= 
3500/35 = 100
100 minutes   ANSWER:100 minutes
Answer: C
The sum of three integers is 24. The largest integer is 3 times the middle integer, and the smallest integer is 11 less than the largest integer. What is the product of the three integers? Choose the most appropriate option.
A) 200  B) 225  C) 250  D) 275  E) 300

Solution: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 11.   3x - 11 + x + 3x = 24   x = 5   The three integers are 4, 5, and 15.   The product is 4*5*15= 
4*5*15 = 300
300   The answer is 300.
Answer: E
In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−4, −4)?
Choose the correct choice from the following options:
A) 4  B) 2  C) 0  D) −2  E) −4

Solution: slope = rise/run = 7/14 = 1/2   The equation of the line is y = (1/2)x + b   3 = (1/2)(10) + b   b = -2   The equation of the line is y = (1/2)x - 2   To find the x-intercept, let y = 0:   0 = (1/2)x - 2   x = 4   The answer is 4.
Answer: A
A sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest. What is the rate of interest? Options:
A) 2% B) 3% C) 6% D) 5% E) 8%

Solution: B   3%   S.I. = (13500 - 11500)= 
(13500 - 11500) = 2_000
2000.   Rate= (100 x 2000)/(11500x5)% = 3%
Answer: B
If two balls are randomly selected from a green urn containing 8 black and 8 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?  Choose the correct choice from the following options:
A) A.2/9	B) B.4/9	C) C.5/9	D) D.7/30	E) E.1/9

Solution: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.   Probability (first ball is white) = 8/16   Probability(second ball is white) = 7/15   Probability (both balls are white) = (8/16)*(7/15) = 7/30   Answer D.7/30
Answer: D
A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Choose the correct choice from the following answers.
A) A)300	B) B)350	C) C)450	D) D)470	E) E)500

Solution: Explanation:   10 * 150= 
10 * 150 = 1_500
1500   4 * 100 + 5 * 150= 
4 * 100 + 5 * 150 = 1_150
1150   1500 – 1150=350   350
Answer: B