MU-NLPC/Calc-aqua_rat huggingface dataset:
Seven years ago the average age of a family of 2 members was 26 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?  Choices.
A) 25years
B) 29years
C) 30years
D) 35years
E) 40years

Solution: Explanation:   Average of the family of two numbers   7 years ago = 26   = (26+ 7) * 2 = 40 years   Average age of the family of three members at present = 23 years   = 23 * 3= 
23 * 3 = 69
69 YEARS   Age of child= 69 - 40= 
69 - 40 = 29
29 years   Answer: Option 29years
Answer: B
Which of the following is a prime number ?
Choose the correct choice from the following
A) 90  B) 94  C) 96  D) 97  E) 98

Solution: Clearly, 97 is a prime number.   97
Answer: D
The total of the ages of Mahesh, Suresh, Ramesh is 138 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh? Choose the correct choice:
A) 32years
B) 58years
C) 42years
D) 35years
E) 30years

Solution: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x   2x+10 + 3x+10 +4x+10 = 138   x = 12   Ramesh present age = 4*12+10= 
4*12+10 = 58
58 years   Answer is 58years
Answer: B
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 50 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
Choose the correct option:
A) 40
B) 45
C) 50
D) 55
E) 60

Solution: Annie earned 40x + 10(2x) = 60x   Let H be the number of hours that Harry worked.   Harry earned 30x + 1.5x(H-30) = 60x   (1.5x)(H) = 75x   H = 50 hours   The answer is 50.
Answer: C
Suppose that this fresh fruit contains 80% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100kg of fresh fruit?	Choose the correct choice from the following.
A) A)32kg	B) B)40kg	C) C)25kg	D) D)80kg	E) E)100kg

Solution: Quantity of pulp in 100kg of fresh fruits = (100-80)% of 100kg = 20kg   Let the quantity of dry fruit obtained be x kg   then, (100-20)% of x = 20   (80/100)*x = 20   x = 25   correct option is 25kg
Answer: C
A circle graph shows how the budget of a certain company was spent: 20 percent for transportation, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for salaries. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent salaries? Options: A) 90° B) 135° C) 216° D) 240° E) 270°

Solution: The percent of the budget for salaries is 100 - (20+9+5+4+2)= 
100 - (20+9+5+4+2) = 60
60%   100% of the circle is 360 degrees.   Then (60%/100%)*360 = 216 degrees   The answer is 216°.  (60 /100 )*360= 
  (60 /100 )*360 = 216
216 degrees   The answer is 216°.
Answer: C
The current in a river is 4 mph. A boat can travel 18 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours? Pick one
A) 69 miles
B) 85.5 miles
C) 96 miles
D) 100 miles
E) 112 miles

Solution: Upstream Speed = 18-4= 
18-4 = 14
14 mph   Downstream Speed= 18+4= 
18+4 = 22
22 mph   D/14 + D/22= 10 hours   Solving for D we get D=85.5   Answer: 85.5 miles
Answer: B
It is required to seat 7 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?	Choose the correct option
A) 86,288 B) 86,214 C) 86,400 D) 86,328 E) 86,368

Solution: Total number of candidates = 6 + 5= 
6 + 5 = 11
11. In the row of 11 positions, the even places are 2nd, 4th, 6th,8th,10th.   Now, number of even places= 5.   Number of girls to occupy the even places = 5.   Even places can be filled = P (5, 5) ways.   Number of boys = 6.   The remaining 6 places can be filled by 6 boys = P (6, 6) ways   By the fundamental principle of counting:   The required number of seating arrangements   P(5, 5) x P(6, 6) = 5! x 6! = 120 x 720 = 86,400   ANSWER:86,400
Answer: C
For which of the following functions is f(e) = f(−e) for all values of e ? Choose the correct option
A) f(x) = x^3 + 3 B) f(x) = −x C) f(x) = 2x + 3 D) f(e) = −e^2 + 2 E) f(x) = 5x − 4

Solution: f(e) = f(−e)   The above is a property of an even function .   f(e) = f^(n)   f(e) = f(−e) will hold when n is an even integer .   The only case when e is even is option f(e) = −e^2 + 2   Answer f(e) = −e^2 + 2
Answer: D
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 46 kg more than the weight of the third boy, what is the weight of the lightest boy?
Choose one.
A) 87 kg  B) 36.8 kg  C) 98.8 kg  D) 65.8 kg  E) 87.8 kg

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 46   => 5k = 46 => k = 9.2   Therefore the weight of the lightest boy   = 4k = 4(9.2) = 36.8 kg.   Answer:36.8 kg
Answer: B
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? Answers.
A) 288	B) 150	C) 277	D) 269	E) 261

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer: 150
Answer: B
Jon had an average score of 85 on his first five quizzes. He had an
average score of 83 on his first six quizzes. What score did he receive on
his sixth quiz?  Choose the correct option.
A) 55	B) 69	C) 75	D) 73	E) 80

Solution: The sum of Jon's first five scores is 5 Â· 85 and the sum of his first six scores is 6 Â· 83, so he received   6 Â· 83 âˆ’ 5 Â· 85 on his 6th quiz. You can do the arithmetic or note that the answer ends in a 3. The correct answer is 73.
Answer: D
After giving a discount of rs.45 the shopkeeper still gets a profit of 20%,if the cost price is rs.180.find the markup %?  Choose one:
A) 0.4
B) 0.55
C) 0.45
D) 0.48
E) 0.58

Solution: cost price=180   s.p=180*120/100= 
180*120/100 = 216
216   disc=45   so...mark price=216+45=261......   mark up%=261-180/180=81/180= 
81/180 = 9/20 = around 0.45
.45 or 45%   ANSWER:0.45
Answer: C
If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a50 is equal to ? Choose one.
A) a. 5*2^99-6	B) b. 5*2^99+6	C) c. 6*2^99+5	D) d. 6*2^99-5	E) e. 6*2^99-6

Solution: Here is my solution:   an+1=2an+5............(1)   lets ADD 5 to both sides....   so (an+1) + 5= 2 (an+5)....................taking 2 as common factor   now a1=1. so for n=1, an+5=6.......   putting n=1. we get both sides as,   a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)   a2= 2 *6 - 5   a2= 2 * 2 *3 - 5   a2= 2^2 *3 - 5................. so with same progression   a50= 2^50 * 3 - 5   a50=2 * 2^49 * 3 - 5   a50= 6*2^49 - 5   e. 6*2^99-6
Answer: E
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Choose the correct choice from the following: A) 24 kmph B) 22 kmph C) 21 kmph D) 28 kmph E) 29 kmph

Solution: 24 kmph   24 kmph   Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   24 kmphverage speed = 3x/(x/8) = 24 kmph
Answer: A
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 360 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?	Select the correct option: A) 90 B) 110 C) 120 D) 140 E) 220

Solution: Orchestra Seats - a   Balcony Seats - b   a+b = 360   and 12a + 8b = 3320   Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)   4a = 3320 - 8*360 = 3320 - 2880= 
3320 - 2880 = 440
440   i.e. a= 110   and b = 360-110= 
360-110 = 250
250   More seats in balcony than orchestra= b-a = 250 - 110= 
250 - 110 = 140
140   Answer: option 140
Answer: D
When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
Choose the most appropriate option
A) 97
B) 103
C) 99
D) 101
E) None of these

Solution: Let the number be x   x2 - 732 = 5280   x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9= 
5280 + 4900 + 420 + 9 = 10_609
10609= 10000 + 2(100)(3) + 32 = (100 + 3)2   x = 100 + 3= 
100 + 3 = 103
103.   ANSWER:103
Answer: B
Of the 20,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?  Choices:
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%

Solution: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.   If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.   What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 49.67%.   Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.   The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?   The correct answer is 2nd place.   Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.49.67%
Answer: E
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?	Choose the correct choice from the following choices.
A) 1/5  B) 1/4  C) 1/3  D) 2/3  E) 4/5

Solution: the successful events are when Sarah pulls 2 matching pair of socks out of 3 matching pairs of socks, which can be done in 3C2 ways as the order is not important   So,3C2 = 3 ways are:   RRBB   RRGG   BBGG   Now,the ways in which 4 socks can be pulled out of 6 socks (3 pairs) = 6C4 = 15   So, probability = 3/15 = 1/5   1/5ns: 1/5
Answer: A
Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper?	Choose the correct choice from the following answers:
A) A)1040	B) B)1045	C) C)1055	D) D)1190	E) E)1075

Solution: Cost of 8 kg apples= 70 × 8 = 560.   Cost of 9 kg of mangoes = 70 × 9 = 630.   Total cost he has to pay = 560 + 630= 
560 + 630 = 1_190
1190.   1190)
Answer: D
The ratio of income of Anand to that of Balu is 5 : 4 and the expenditure of Anand to that of Balu is 3: 2. If at the end of the year, each saves Rs, 800, the income of Anand is : Choose the correct choice from the following: A) Rs 1600 B) Rs 1800 C) Rs 2000 D) Rs 2200 E) None of these

Solution: Explanation :   Let the income of Anand and Balu be 5x and 4x and. the expenditures of Anand and Balu be 3y and 2y.   Then, 5x3y = 800 and 4x 2y= 800.   On solving we get : x = 400. As income = 5x = Rs. 2000.   Answer : Rs 2000
Answer: C
The average runs of a cricket player of 10 innings was 20. How many runs must he make in his next innings so as to increase his average of runs by 4?	Select the correct option.
A) 22
B) 77
C) 64
D) 19
E) 17

Solution: Explanation:   Average after 11 innings = 24   Required number of runs = (24 * 11) – (20 * 10)   = 264 – 200 = 64   ANSWER: 64
Answer: C
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
Choose the correct choice.
A) 200	B) 100	C) 276	D) 280	E) 279

Solution: Profit on first article = 10% of 1000 = 100.   This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.   Answer: 100
Answer: B
On my sister's birthday, she was 126 cm in height, having grown 5% since the year before. How tall was she the previous year?  Choose one:
A) 124 cm	B) 120 cm	C) 116 cm	D) 112 cm	E) 110 cm

Solution: Let the previous year's height be x.   1.05x = 126   x = 120   The answer is 120 cm.
Answer: B
The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Choices.
A) 22 degrees	B) 64 degrees	C) 77 degrees	D) 26 degrees	E) 18 degrees

Solution: Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4)= 
(58 * 4) = 232
232 degrees ... (1)   Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4)= 240 degrees ....(2)   Subtracting (1) From (2), we get :   Temp, on 5th day - Temp on 1st day = 8 degrees.   Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.   Then, 8x - 7x = 8 or x = 8.   Temperature on the 5th day = 8x = 64 degrees.   Answer: 64 degrees
Answer: B
Mr. Kela purchased two steel factories, one in india and other one in Malaysia for total Rs. 72
crores. Later on he sold the india factory at 16% profit and malaysian factory at 24% profit.
Thus he gained a total profit of 19%. The selling price of Indian factory is:	Choose the correct choice from the following answers:  A) 52.2 crores  B) 56 crores  C) 55.5 crores  D) 59.3 crores  E) None of these

Solution: Explanation :   If price(in crore) of Indian factory=x and Malaysian factory=72-x, then   => x*(116/100) + (72-x)*(124/100) = 72*(119/100)   => 1.16x+89.28-1.24x = 85.68   => x = 45   So selling price of an Indian factory = 45*(116/100)= 
45*(116/100) = 261/5 = around 52.2
52.2   Hence (A) is correct answer.   52.2 croresnswer : 52.2 crores
Answer: A
There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess? Pick
A) Rs. 450 B) Rs. 320 C) Rs. 550 D) Rs. 420 E) None

Solution: Solution:   Let the original average expenditure be Rs.x then, 42(x - 1) - 35x = 42.   => 7x = 84   => x = 12   Therefore original expenditure,   = Rs.(35 × 12)=Rs.420.   Answer: Option Rs. 420
Answer: D
A container has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 3 times. Find how much spirit is left in the resulting mixture finally?	Pick one
A) 6(257/525) gallons	B) 6(346/625) gallons	C) 6.5 gallons	D) 6.25 gallons	E) None of these

Solution: There is a direct formula to calculate such repetition:   Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n   where n is number of times mixing done:   Left QTY / 20 = (20 -4)^3 / 20^3   Left QTY = 20 (16/20)^3   Left QTY = 20 ( 4/5 )^3   Left QTY = 10.24   Answer is None of these
Answer: E
If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c+a=b+a+1
II. abc is an even integer
III. (a+b+c)/3 is an integer	Pick:  A) I  B) II  C) I and II  D) II and III  E) all are true

Solution: 1. c+a=b+a+1 --> a, b, c are consequitive positive integers and a<b<c then c+a=b+a+1. So this statement is always true;   2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;   3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.   Answer: all are true.
Answer: E
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Options
A) 756  B) 730  C) 250  D) 600  E) 350

Solution: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).   Required number of ways	= 7C3*6C2 + 7C4*6C1 + 7C5=>756   756NSWER 756
Answer: A
Two trains 150 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Choose the correct answer
A) 10.16 sec	B) 18.8 sec	C) 14.8 sec	D) 10.8 sec	E) 11.16 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 150 + 160= 
150 + 160 = 310
310 m.   Required time= 310 * 9/250 = 279/25= 
279/25 = 279/25 = around 11.16
11.16 sec.   Answer: 11.16 sec
Answer: E
At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 32 liters of Fuchsia to change it to Mauve paint?  Choose the correct choice from the following answers.
A) 9	B) 13	C) 15	D) 16	E) 18

Solution: in 32 liters, Red = 5/8 * 32= 
5/8 * 32 = 20
20 and 13lue= 12   so, 20/(12+x) = 4/5   or, x = 13 (Answer 13)
Answer: B
What is the principal sum?
I. The sum amounts to Rs. 690 at S.I.
II. Total year is 8 years.
III. The rate of interest is 5% p.a.	Choose one.
A) I and III only
B) II and III only
C) I and II only
D) Any two of the three
E) All I, II and III

Solution: All I, II and IIIxplanation:   Clearly, all the three statements are needed to solve this question   Answer: All I, II and III
Answer: E
If 'a' and 'b' are non-zero numbers such that their sum is seven times the product, what is the value of 1/a + 1/b?  Choices:
A) 6
B) 7
C) 8
D) 14
E) 21

Solution: a+b = 7ab   1/a + 1/b = (b + a)/(ab) = 7.   The answer is 7.
Answer: B
The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is: Choices:
A) 1/289	B) 289/290	C) 290/289	D) 289	E) 300

Solution: Explanation:   Let the numbers be a and b. Then,   ab = 17, a = 1 and b = 17   So, 1/a2 + 1/b2 = (a2 + b2)/a2 b2   = (12 + 172)/(1 * 17)2 = 290/289   ANSWER IS 290/289
Answer: C
The average of five consecutive even numbers A, B, C, D and E is 20. What percent of E is D? Choose the correct option.
A) 90.1
B) 91.7
C) 97.1
D) 101.1
E) 107.1

Solution: Explanation :   In such a case the middle number (C) is the average   ∴ C = 20 and D = 22 and E = 24   Required percentage = 22/24 x 100 = 91.7   Answer : Option 91.7
Answer: B
Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have? Choose the correct choice from the following answers
A) 5  B) 10  C) 30  D) 40  E) 50

Solution: Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)*100= 
(4.5/7.5)*100 = 60
60%   Now by Alligation Rule:   A . ......... B   20% . . . 80%   . . 60% . .   (80-60) . (60-20)=20 : =40   Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration)   So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%)   So as per above ration Qty B mixed will be 50 gallons.   Qty of water in mixture B = 20% of 50 = 10 gallons.   ANSWER:10
Answer: B
A jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Select the correct option:
A) 3.6 sec  B) 18 sec  C) 35 sec  D) 72 sec  E) None of these

Solution: Speed of train relative to jogger   = (45 – 9) km/h = 36 km/h   = (36 × 5⁄18) m/sec = 10 m/sec   Distance to be covered = (230 + 120)= 
(230 + 120) = 350
350 m.   ∴ Time taken= (350⁄10) sec = 35 sec.   Answer 35 sec
Answer: C
The simple interest on Rs. 8 for 12 months at the rate of 5 paise per rupeeper month is	Pick one
A) 1.2
B) 4.8
C) 4.4
D) 3.21
E) None

Solution: Sol.   S.I. = Rs. [8 * 5/100 * 12] = Rs. 4.8   Answer 4.8
Answer: B
Two commodities have cost per kg is 4.75Rs & 3.20Rswere mixed in a certain
ratio so as to make cost price of mixture as 17.75 Rs. Find the ratio
Select:	A) 14.55:13	B) 15.55:13	C) 16.55:13	D) 17.55:13	E) 18.55:13

Solution: mixture17.75-3.20= 
17.75-3.20 = 14.55
14.55   mixture   17.75-4.75= 
  17.75-4.75 = 13
13   14.55:13   14.55:13NSWER:14.55:13
Answer: A
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1800. What is their H.C.F.?
Choose the correct choice from the following choices.
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: Let the numbers be 3x, 4x and 5x.   Then, their L.C.M. = 60x   60x = 1800   x = 30   The numbers are (3 x 30), (4 x 30) and (5 x 30).   The H.C.F. is 30.   The answer is 30.
Answer: C
There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure q in inches of the width of the foil covered prism? Pick:	A) 4	B) 6	C) 8	D) 9	E) 10

Solution: If the width is w, then length and height would be w/2.   So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)   => w = 2*4= 
2*4 = 8
8 in.   Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes= 8 +2 =q=10   Ans 10.
Answer: E
Find the highest value of 'a' so that 365a16 is divisible by 8.	Choose the correct answer:
A) 9 B) 8 C) 0 D) 2 E) 1

Solution: Explanation:   Given, number is divisible by 8 only if 'a16' is divisible by 8.   .: highest value of a is '8'.   Answer: Option 8
Answer: B
A certain machine produces 780 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 4 days?	Choose the correct choice:
A) 7,000	B) 24,000	C) 74,880	D) 100,000	E) 168,000

Solution: Since 7 days consist of 24*4 hours the total is 96 hours.   Since every hour the machine produces 780 units of product P the total product during 96 hours is 96*780=74,880.   Correct Option : 100,000
Answer: D