MU-NLPC/Calc-aqua_rat huggingface dataset:
Seats for Mathematics,PhysicsandfBilogy in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Choose the correct choice from the following answers:
A) 2:3:4	B) 6:7:8	C) 6:8:9	D) 5:8:9	E) 2:4:6

Solution: Let the no.of seats Maths, physics and Biology be 5x, 7x and 8x   No.of increased seats are (140%5x), (150%7x) and (175%8x)   Required ration = (150%7x)= 7x:21x/2:2x = 2:3:4   2:3:4NSWER : 2:3:4 2:3:4
Answer: A
In 10 years,A will be 1.5 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :  Answers:
A) 17 Years
B) 29 Years
C) 39 Years
D) 49 Years
E) 59 Years

Solution: Solution   Let B's present age = x years.Then,A's present age =(x +9) years.   âˆ´ (x + 9)+ 10 = 1.5 (x - 10) â‡” x + 19 = 1.5x- 15 â‡” 0.5x = 34. x=1717 Yearsnswer 17 Years
Answer: A
The number of stamps that Kaye and Alberto had were in the ration of 6:4 respectively. After Kaye gave Alberto 5 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 8:6. As a result of the gift, Kaye had how many more stamps than Alberto ?	Choose the correct option
A) 22
B) 25
C) 15
D) 35
E) 30

Solution: K1 = 6x   A1 = 4x   K2 = 6x - 5   A2 = 4x + 5   K2/A2 = 8/6   (6x-5)/(4x+5) = 8/6   6*(6x-5) = 8*(4x+5)   36x - 30 = 32x + 40   4x = 70   x = 17.5   K2 = 6*17.5 -5= 
6*17.5 -5 = 100
100   A2= 4*17.5 + 5= 
4*17.5 + 5 = 75
75   K2 - A2= 100-75= 
100-75 = 25
25   Answer : 25
Answer: B
The area of a square is added to one of its sides, and the perimeter is then subtracted from this total, the result is 4. What is the length of one side?  Choose the correct choice:
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: The equation is; side + Area - Perimeter = s + A - P = s + s^2 - 4s = s(1 + s - 4).   By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.   Answer: 4
Answer: B
The ratio of the present age of Sandy to that of Molly is 9:2. Eight years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago? Pick:	A) 18	B) 21	C) 24	D) 27	E) 30

Solution: Let the present age of Sandy be 9x years and that of Molly be 2x years.   (9x + 8) / (2x + 8) = 5 / 2   8x = 24   x = 3   Six years ago, Sandy's age was 9(3) - 6 = 21   The answer is 21.
Answer: B
Tom wants to buy items costing $25.35, $90.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.	Answers.
A) 8 hours	B) 48 hours	C) 38 hours	D) 18 hours	E) 35 hours

Solution: $6.50 x .10 = $.65 is 10% of his hourly income   $  6.50 - .65= 
  6.50 - .65 = 5.85
$5.85 hourly amount available to spend   $25.35 + $90.69 + $85.96 = $202 total needed   $202 ÷ $5.85  25.35 +  90.69 +  85.96= 
 25.35 +  90.69 +  85.96 = 202
$202 total needed   $202 ÷ $5.85= 34.5... rounds to 35 hours   correct answer 35 hours
Answer: E
The ratio of the adjacent angles of a parallelogram is 5 : 10. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral? Choose the correct choice from the following answers:
A) 168°	B) 228°	C) 144°	D) 224°	E) None of these

Solution: The measures of the adjacent angles of a parallelogram add up to be 180°   Given   So, 5x + 10x = 180°   Or, 15x = 180°   Or, x = 12°   Hence the angles of the parallelogram are 60° and 120°   Further it is given   We know sum of all the four angles of a quadrilateral is 360°   So, 5y + 6y + 7y + 12 y = 360°   Or, 5y + 6y + 7y + 12 y = 360°   Or, 30y = 360°   Or, y = 12°   Hence the angles of the quadrilateral are 60° , 72, 84° and 144°   Will be 60° + 84° = 144°   Answer : 144°60  + 84= 
60  + 84 = 144
144°   Answer : 144°
Answer: C
Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 8, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42  Choose the correct option: A) I, II, III B) I, III, II C) II, I, III D) II, III, I E) II,III, I

Solution: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.   sequence II,III,I   II,III, I
Answer: E
One fourth of a solution that was 10 percent wheat by weight was replaced by a second solution resulting in a solution that was 16 percent wheat by weight. The second solution was what percent wheat by weight ?
Pick one.
A) 34%
B) 24%
C) 22%
D) 18%
E) 8.5%

Solution: EQ can be written as ...   let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of wheat in 2nd sol)=34%=34%
Answer: A
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/41 ?  Choose one.
A) 6	B) 3	C) 2	D) 1	E) 0

Solution: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.   So, we start with   a=1, we get b as -ve. out   a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)   a=3, we get b as 3. Yes (Now we have 3 possible solutions)   a=4, we get b as fraction. Out   a=5, we get b again as some fraction. Out   a=6 already taken.   We have A,B options left. C,D,E are out.   A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.   When a=b, we have only 1 solution = 1. So, one more solution, where a=b is not possible.   So, answer will be 1.
Answer: D
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike? Answers:
A) 55 kg B) 55.5 kg C) 59.5 kg D) 66.5 kg E) 70.5 kg

Solution: Let Mike's weight be X kg.   According to Mike, 65 < X < 72.   According to Mike's brother, 60 < X < 70.   According to Mike's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   66.5 kg
Answer: D
How many ways are there to select a subcommittee of 12 members from among a committee of 17?	Select:
A) 22888	B) 19448	C) 28791	D) 27711	E) 6188

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,12)= 6188   Answer: 6188
Answer: E
A contractor undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that he needed to increase 5 additional men every 2 days to complete the work in the time the client wanted it:
If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the client. Select the correct option.
A) 1 day  B) 2 days  C) 5 days  D) None of these  E) Cannot be determined

Solution: Explanation:   Total work = 100+50= 
100+50 = 150
150man-days   In 8 days 100 man-days work has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days   Answer: 2 days
Answer: B
If the integer q is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when q is rounded to the nearest ten. which of the following is a possible value of q?  Choose the correct choice from the following.
A) 64  B) 67  C) 99  D) 133  E) 147

Solution: We have to check options 1 by 1.   64 rounded to nearest hundred = 100   64 rounded to nearest ten = 60   now difference = 40   the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.   therefore 40/60)*100 = 66 2/3 ==>this is the answer.   99 rounded to nearest ten = 100   133 rounded to nearest ten = 130   133 rounded to nearest hundred so q= 100=64
Answer: A
Two men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?
Choose the most appropriate option:
A) 1/2 day  B) 2 1/2 days  C) 1 1/2 days  D) 3 1/2 days  E) 2 days

Solution: A   1/2 day   Two men take four days to complete the work four men would take   (2 * 4)/4= 
  (2 * 4)/4 = 2
2 days to complete it.   Similarly four women would take two days to complete it and 20 children would take one day to complete it.   All the three groups working togerther will complete   1/2 + 1/2 + 1/1= 
  1/2 + 1/2 + 1/1 = 2
2 times the unit work in a day.   They will take 1/2 a day to complete it working together.
Answer: A
A city council will select 2 of 7 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?  Options.
A) 36 B) 72 C) 144 D) 216 E) 126

Solution: OA D   7C2 * 6C1   using the combination formula to choose 2 from 9 and 1 from 6   126
Answer: E
Angela has 13 pairs of matched socks. If she loses 7 individual socks, which of the following is NOT a possible number of matched pairs she has left?  Select:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: I think if Angela loses 7 individual socks,then she is bound to have lost minimum of 3 pairs and 1 individual sock,in this way she is left with only 9 pairs of socks (13-(3+1)).   Hence,10 cannot be the answer as maximum is 9.   Hence, option (10)
Answer: C
A store sells a certain product at a fixed price per unit. At the product's current price, e units cost a total of exactly $300. If the price were lowered by $5 from its current value, then e + 2n units would cost exactly $300; if the price were raised by $5, then e – n units would cost exactly $300. What is the value of e?  Choose the most appropriate option.
A) 10
B) 15
C) 20
D) 25
E) 30

Solution: It got too complicated when I used algebra. Using plugging in, it was quite fast.   Price Quantity total value   p e pe = 300   p-5 e+2n (p-5)(e+2n) = 300   p+5 e-n (p+5)(e-n) = 300   Solving three equations for three unknowns. Tough!!   Plugging in, I always start with C. 20 was the answer here, so saved calculation!   Putting values in above equations:   Price Quantity total value   15 20 300   10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5   20 15 300   So e = 20 satisfies all equations!!
Answer: C
A train of length 240 metres takes 60 seconds to cross a tunnel of length 450 metres. What is the speed of the train in km/hr?
Choose the most appropriate option:
A) 10 km/hr.
B) 20 km/hr.
C) 30 km/hr.
D) 40 km/hr.
E) None

Solution: Sol.   Speed = [240 + 450 / 60] m/sec = [690/ 60 * 18/5] km/hr = 41.4 km/hr.   Answer None
Answer: E
All of the students of Music High School are in the band, the orchestra, or both. 50 percent of the students are in only one group. There are 140 students in the band. If 20 percent of the students are in the band only, how many students are in the orchestra only? Choose the most appropriate option.
A) 60  B) 70  C) 50  D) 80  E) 40

Solution: % of students in one group only = 50%   % of students in both groups = 100 - 50= 
100 - 50 = 50
50%   % of students in the band only= 20%   Number of students who are in band = 140   50% + 20% = 70% 50  + 20= 
50  + 20 = 70
70%= 140 Students   Finding total students:   x = (140 x 100)/70   x = 200   60nswer:60
Answer: A
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 50 years now, the son's age 10 years back was: Choose the correct option.
A) 14 years
B) 19 years
C) 33 years
D) 15 years
E) 39years

Solution: Let the son's present age be x years. Then, (50 - x) = x   2x = 50   x = 25   Son's age 5 years back (25 - 10)= 
(25 - 10) = 15
15 years.   Answer: 15 years
Answer: D
A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 50% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
Choose the correct choice from the following choices:
A) 40%
B) 45%
C) 50%
D) 60%
E) 70%

Solution: 1st year Income= I   1st year savings= S   1st year Expense= E1   2nd year Income = 1.5I   2nd year savings= 2S (100% increase)   2nd Year expense= E2   E1+ E2= 2E1   E2=E1   That means Expenses are same during both years. With increase of 50% income the savings increased by 100%.   or S= .5I   or S= 50% of Income   50% is the answer
Answer: C
Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 10.0 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?  Choose the most appropriate option:
A) 12.0
B) 12.1
C) 10.0
D) 12.3
E) 12.4

Solution: let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =10.0 => x^2 =1.00 or x = 1.0 => @4PM quantity = 10x =10*1.0= 
10*1.0 = 10
10.   Answer 10.0
Answer: C
The ratio 10:20 expressed as percent equals to
Choose the correct choice:  A) 50 %  B) 80 %  C) 40 %  D) 90 %  E) 100%

Solution: Explanation:   50 %ctually it means 10 is what percent of 20, which can be calculated as,   (10/20)*100 = 10 * 5= 
10 * 5 = 50
50   50 %nswer: Option 50 %
Answer: A
Jonathan can type a 20 page document in 50 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?	Select:	A) 5 minutes	B) 11 minutes	C) 15 minutes	D) 18 minutes	E) 20 minutes

Solution: You may set up common equation like this:   job/A+job/B+job/C=job/x   Memorize this universal formula, you will need it definitely for GMAT.   and find x from this equation   In this specific case, the equation will look like this:   20/50+20/30+20/24=20/x   If you solve this equation, you get the same answer 11 minutes (11)
Answer: B
How many integers are between 3 and 86/7, inclusive?	Choose the correct choice
A) 8 B) 9 C) 10 D) 11 E) 12

Solution: 86/7 = 12.xx   We are not concerned about the exact value of 86/7 as we just need the integers.   Since the values are small, we can write down the integers.   The different integers between 3 and 86/7 would be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12   Total number of integers = 10   Option 10   If we need to find the number of integers between two numbers n and m, where m > n   The number of integers = m - n + 1   In the given question, the number of integers = 12 - 3 + 1= 
12 - 3 + 1 = 10
10   ANSWER:10
Answer: C
A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?
Choices
A) 166.69%  B) 166.66%  C) 166.76%  D) 136.66%  E) 566.66%

Solution: Let the cost price of 1 litre pure milk be Re.1, then   \inline \begin{166.66%matrix} 6 & litres(milk) & \rightarrow & CP=Rs.6\\ 2 & litres(water) & \rightarrow & CP=Rs.0 \end{166.66%matrix}\rightarrow CP=Rs.6 only   and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16   Profit %= %   Answer: 166.66%
Answer: B
what is the unit digit in the product (3^68 x 6^59 x 7^71) ?	Choose the correct answer: A) 1 B) 2 C) 4 D) 6 E) None of them

Solution: Unit digit in 3^4=1=>Unit digit in (3^4)^16=1   therefore, Unit digit in 3^65=Unit digit in [(3^4)^16x3]=(1x3)=3   Unit digit in 6^59=6   Unit digit in 7^4=1=>Unit digit in (7^4)^17 is 1   Unit digit in 7^71=Unit digit in [(7^4)^17 x 7^3]=((1x3)=3   Therefore, Required digit=Unit digit in (3x6x3)=4   Answer is 4
Answer: C
Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 10% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?	Choose the correct choice from the following.
A) $1600	B) $6000	C) $6050	D) $7050	E) $8000

Solution: Let T be the tier price, P be total price = 14000   Per the given conditions:   0.10T + 0.08(P-T) = 1440 ----> T= 1600. $1600 is the correct answer.
Answer: A
9 points are marked on a straight line and another 8 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points? Choose the correct answer.
A) 540
B) 105
C) 196
D) 21
E) 14

Solution: getting the answer 540 which is not in the choices, what is the source of the problem?   9C2* 8C1 + 8C2* 9C1 =540   540
Answer: A
A pair of articles was bought for Rs. 37.40 at a discount of 15%. What must be the marked price of each of the articles ?
Options:  A) Rs15  B) Rs 20  C) Rs 22  D) Rs 25  E) Rs 26

Solution: Solution: As question states that rate was of pair of articles, So rate of One article = 37.40/2 = Rs. 18.70 Let Marked price = Rs X then 85% of X = 18.70 => X = 1870/85= 
1870/85 = 22
22   Answer: Rs 22
Answer: C
Five persons - A, B, C, D and E are being compared in weight and height. The second heaviest person. D is the shortest. A is the 2nd tallest and shorter than E, The heaviest person is the third tallest person. There is only one person shorter than B, who is lighter than E and A respectively.
Who is the heaviest person?
Choose the correct choice from the following answers
A) A
B) B
C) C
D) D
E) E

Solution: Explanation:   A is the second tallest person. There is only one person shorter than B. So, B is the fourth tallest person. D is the shortest and second heaviest.   Weight Height   1   2 D A   3   4   B   5   D   A is shorter than E. So, the third tallest person is C. Who is the heaviest person. B is lighter than E and A respectively. So, the final arrangement is as follows.   Weight Height   1. C E   2. D A   3. E C   4. A B   5. B D   C is heaviest person.   ANSWER IS C
Answer: C
There are 600 military people in a division of the army. There is one Officer for every 29 soldiers in that division. Now the question is how many officers are in the division?	Choose the correct choice from the following choices.
A) 22	B) 35	C) 37	D) 20	E) 75

Solution: D   20   29 soldiers + 1 officer makes a group of 30 people. Now number of such groups = 600/30= 
600/30 = 20
20.
Answer: D
If the average (arithmetic mean) of a and b is 80, and the average of b and c is 180, what is the value of a − c?	Choose one:
A) −220 B) −200 C) 100 D) 135 E) It cannot be determined from the information given

Solution: a+b = 160   b+c = 360   a-c = -200.   IMO option −200.
Answer: B
An bus covers a certain distance at aspeed of 320 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?  Choose one:
A) 560 km/h
B) 960 km/h
C) 779 km/h
D) 723 km/h
E) 720 km/h

Solution: Distance = (320 x 5) = 1600 km.   Speed = Distance/Time   Speed = 1600/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1600 x 3/5 km/hr = 960 km/hr.   960 km/h
Answer: B
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
Select
A) 21000  B) 21009  C) 21029  D) 21298  E) 21098

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x)   = 35000 + 32/100 (35000)   x = 28000   35000 - x = 7000   Difference in the cost prices of televisions   = Rs.21000   21000nswer:21000
Answer: A
A train 120 m in length crosses a telegraph post in 16 seconds. The speed of the train is?	Options.
A) 16 kmph	B) 88 kmph	C) 54 kmph	D) 18 kmph	E) 27 kmph

Solution: S = 120/16 * 18/5= 
120/16 * 18/5 = 27
27 kmph   Answer: 27 kmph
Answer: E
Current age of Bruce and Tomy are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Tomy 's present age in years?  Select.
A) 18 years	B) 20 years	C) 24 years	D) 25 years	E) 26 years

Solution: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.   Then,	5x + 3	=	11   4x + 3	9   9(5x + 3) = 11(4x + 3)   45x + 27 = 44x + 33   45x - 44x = 33 - 27= 
33 - 27 = 6
6.   Anand's present age= 4x = 24 years.   24 years
Answer: C
A box contains four dime coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.	Answers:
A) 3/4
B) 1/5
C) 2/5
D) 3/5
E) 4/5

Solution: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)   How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)   Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)   = 4/5   4/5
Answer: E
On Monday, a certain animal shelter housed 50 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?	Choose the correct answer.
A) 12 B) 14 C) 16 D) 18 E) 20

Solution: To maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/4 > 1/5.   The greatest multiple of 4 less than 50 is 40 (such that the remaining number is divisible by 5), so let's assume there were 40 dogs and 10 cats.   Then the maximum number of adopted pets is 1/4*(40) + 1/5*(10) = 10 + 2= 
10 + 2 = 12
12.   The answer is 12.
Answer: A
A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?  Choose the correct choice from the following.
A) 12	B) 5	C) 7	D) 9	E) 10

Solution: Explanation:   3+11+7+9+15+13+8+19+17+21+14+x/12 =12   ⇒137+x12=12   ⇒137+x=144   ⇒x=144−137=7   Answer: Option 7
Answer: C
What is the ratio A of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Choose the correct choice from the following choices
A) 1/4  B) 3/8  C) 1/2  D) 3/5  E) 2

Solution: One side surface area of a cube = x*x = x^2   Total 6 sides = 6x^2   As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.   L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2   W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2   Total 6 sides = 8x^2 + 2x^2 = 10x^2   Ratio of cube area to rectangular area A= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (3/5)
Answer: D