MU-NLPC/Calc-aqua_rat huggingface dataset:
How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
Choose the correct choice from the following options:  A) 48.74 inches  B) 58.74 inches  C) 78.74 inches  D) 28.74 inches  E) 88.74 inches

Solution: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm   x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches   correct answer 78.74 inches
Answer: C
What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 4?	Choose the correct choice from the following options:
A) 123,750 B) 164,850 C) 164,749 D) 149,700 E) 156,720

Solution: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 4   Seeing the Options 123,750fter Dividing and Finding the Reminder of 2   My 123,750nswer was 123,750
Answer: A
A bag contains 3 white balls, 3 black balls & 2 red balls. One by one three balls are drawn out without replacement. What is the probability that the third ball is red? Pick one:
A) 0.25 B) 0.15 C) 0.35 D) 0.45 E) 0.4

Solution: Favorable outcomes :   WWR -> P(WWR)= 3/8 * 2/7 * 2/6 = 12/336   WRR -> P(WRR)= 3/8 * 2/7 * 1/6 = 6/336   RWR -> P(RWR)= 2/8 * 3/7 * 1/6 = 6/336   BBR -> P(BBR)= 3/8 * 2/7 * 2/6 = 12/336   BRR -> P(BRR)= 3/8 * 2/7 * 1/7 = 6/336   RBR -> P(RBR)= 2/8 * 3/7 * 1/6 = 6/336   WBR -> P(WBR)= 3/8 * 3/7 * 2/6 = 18/336   BWR -> P(BWR)= 3/8 * 3/7 * 2/6 = 18/336   So, P(Total) = 84/336 = 1/4= 
1/4 = 1/4 = around 0.25
0.25   0.25nswer is 0.25
Answer: A
If x is an integer such that 0 < x < 12, 1 < x < 15, 10 > x > 5, 11 > x > 8, and x + 2 < 12, then x is Select
A) 3
B) 5
C) 7
D) 9
E) 11

Solution: 0 < x < 12,   1 < x < 15,   -5 < x < 10   8< x < 11   x<10   From above: 8 < x < 10 --> x = 9.   Answer: 9.
Answer: D
At an elementary school, 60% of the faculty members are women and 60% of the faculty members are married. If 3/4 of the men are single, what fraction of the men are married?  Pick one.
A) 3/4  B) 2/5  C) 4/5  D) 2/3  E) 1/4

Solution: --------------------M------W--------Total   Marrried---------10-----50---------60   Not married-----30-----10---------40   Total-------------40-----60--------100   need married man/total man, so 10/40=1/4   1/4
Answer: E
If the Average of 10 consecutive integers is 24.5 then the 10th integer is :-  Choose the correct answer.
A) 15 B) 20 C) 23 D) 29 E) 25

Solution: The average falls between the 5th and 6th integers,   integer 5 = 24, integer 6 = 25.   Counting up to the tenth integer   we get 29.   ANSWER:29
Answer: D
In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 37. In the company, what is the maximum number of non-managers in a department that has 9 managers? Choose the correct choice from the following options:
A) 44
B) 45
C) 46
D) 47
E) 48

Solution: 9/7 * 37 = 47.6   The answer is 47.
Answer: D
A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?  Choose the correct choice from the following answers:
A) 75 and 80 B) 80 and 85 C) 74 and 74 D) 75 and 75 E) 70 and 80

Solution: Ans: C   Deviation means spreading of the numbers from one median point value..   as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.   so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value.   74 and 74
Answer: C
A cube has a volume of 125 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?	Choose the correct choice from the following answers:
A) 24
B) 48
C) 64
D) 80
E) 1000

Solution: Volume = 125 = side^3   i.e. Side of Cube = 5   New Cube has dimensions 10, 10, and 10 as all sides are twice of teh side of first cube   Volume = 10*10*10= 
10*10*10 = 1_000
1000 square feet   Answer: option 1000
Answer: E
If m is a positive integer greater than 1, what is the sum of the multiples of m from m to m^2, inclusive?  Select
A) m(m + 1)(m-1)
B) m^2(m + 1)/2
C) m^2(m-1)
D) (x^3 + 2x)/2
E) x(x-1)^2

Solution: Ans :- B=m^2(m + 1)/2   I substituted 3 in all answer choices.   Option B and C were both satisfying the condition.   So i substituted 4 instead of 3 in all answer choices,   Only m^2(m + 1)/2 option satisfied.
Answer: B
A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 6 days.In how many days B alone can do the work? Choose the correct choice from the following answers.
A) 5days
B) 7 days
C) 12 days
D) 9 days
E) 10 days

Solution: Explanation:   A’s 5 day work = 5*1/15=1/3   Remaining work = 1-1/3=2/3   B completes 2/3 work in 6 days   B alone can do in x days   2/3*x=6   X=9 days   Answer: Option 9 days
Answer: D
If f(b)=b^2 and b is a positive integer, which of the following CANNOT be the value of f(f(b))?  Choose the correct choice from the following answers:
A) 1
B) 81
C) 200
D) 256
E) 625

Solution: f(b)=b^2   f(f(b)) = (b^2)^2 = b^4   Therefore f(f(b)) will be numbers that are 4th power of other numbers.   Checking the options:   1 = 1^$   81 = 3^4   200. This cannot be written as the 4th power of any number   256 = 4^4   625 = 5^4   Answer: 200
Answer: C
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?
Select the correct option:
A) 12 mins
B) 10 mins
C) 19 mins
D) 15 mins
E) 20 mins

Solution: Let the distance be x km. Then,   ( Time taken to walk x km) + (time taken to ride x km) =37 min.   ( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min.   But, the time taken to walk 2x km = 55 min.   Time taken to ride 2x km = (74-55)= 
(74-55) = 19
19 min.   Ans: 19 mins
Answer: C
An investor receives a total combined return of 10% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?
Choose the most appropriate option:	A) 7.25%	B) 12%	C) 8%	D) 8.5%	E) 9%

Solution: 0.06 * 10000 + 20000x = 0.10(30000)   solving for x give x = 12%   option 12%
Answer: B
Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/2 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
Select
A) 2/3  B) 3/4  C) 4/5  D) 5/6  E) 7/8

Solution: (1/2)X = (1/4)Y   (1/4)Y + (1/2)Y = (3/4)Y   The answer is 3/4.
Answer: B
Thomas's age and Matt's age are in the ratio 2:3. Two years ago the ratio of their ages was 1:2. Find the ratio of their ages four years hence?	Pick
A) 1:2	B) 2:3	C) 3:4	D) 4:5	E) 5:6

Solution: Let ages of Thomas and Matt be x and y respectively.   x/y = 2/3 => x = 2/3 y   (x- 2)/(y - 2) = 1/2     ( - 2)/(  - 2)= 
  ( - 2)/(  - 2) = 1
1/2=> 2x - 4 = y - 2 => 2x = y + 2= 
+ 2 = 2
2/3 y   2 * 2/3 y= y + 2   4y = 3y + 6 => y = 6years   => x = 4 years   Ratio of their ages five years hence, (4 +4)/(6 + 4) = 8/10. => 4:5   Answer:4:5
Answer: D
The function f is defined for all positive integers u by the following rule. f(u) is the number of positive integers each of which is less than u and has no positive factor in common with u other than 1. If s is any prime, number then f(s)=  Select the correct option.
A) 2 B) s-2 C) (s+1)/2 D) (s-1)/2 E) S-1

Solution: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.   This question for instance basically asks: how many positive integers are less than given prime number s which have no common factor with s except 1.   Well as s is a prime, all positive numbers less than s have no common factors with s (except common factor 1). So there would be s-1 such numbers (as we are looking number of integers less than s).   For example: if s=4 how many numbers are less than 4 having no common factors with 4: 1, 2, 3, 4,--> 4-1=3.   Answer: S-1.
Answer: E
The charge for a single room at Hotel P is 30 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?  Choose the correct choice from the following choices:  A) 28%  B) 20%  C) 40%  D) 50%  E) 150%

Solution: Let rate in R = 100x   then P = 70x   G = 100y   P = 90y   Thus   70 x=90y   or x = 1.28 y   28%ns R = 128y   so increase = 28%   28%nswer: 28%
Answer: A
Two stations P and Q are 290 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?	Pick.
A) 10 am
B) 12 am
C) 10.30 am
D) 12.30 pm
E) 2 pm

Solution: Assume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 290   => 20x + 25(x-1) = 290   => 45x = 315   => x= 7   Means, they meet after 7 hours after 7 am, ie, they meet at 2 pm   Answer is 2 pm.
Answer: E
In an exam, A scored 75 percent, B scored 25 percent and C scored 32 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three candidates?  Choose the correct choice:
A) 190
B) 200
C) 210
D) 220
E) 230

Solution: Average mark scored by all the three boys   = [75/100 (500) + 25/100 (500) + 32/100 (500)] / 3   = 220   Answer: 220
Answer: D
It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 300, 300, and 300 as the side’s lengths, what is the triangle’s area?
Choose the correct choice from the following.
A) 34,200
B) 36,200
C) 38,200
D) 42,200
E) 38,971

Solution: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),   when p=(a+b+c)/2,   -> P=(300+300+300)/2= 
(300+300+300)/2 = 450
450, area=√(450(450-300)(450-300)(450-300))=38,971. Therefore, the answer is 38,971.
Answer: E
In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?
Pick
A) 290 sec
B) 190 sec
C) 199 sec
D) 192 sec
E) 240 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/40= 
(1000 * 10)/40 = 250
250 sec.   Time taken by A= 250 - 10= 
250 - 10 = 240
240 sec.   Answer: 240 sec
Answer: E
A candidate appearing for an examination has to secure 52% marks to pass paper I. But he secured only 45 marks and failed by 35 marks. What is the maximum mark for paper I?  Choose the correct choice from the following options:
A) 110	B) 154	C) 130	D) 140	E) 150

Solution: he secured 45 marks nd fail by 35 marks so   total marks for pass the examinatn=80   let toal marks x   x*52/100=80   x=154   ANSWER:154
Answer: B
A certain kind of necklace is made from 9 green, 6 white, and 3 orange beads. What is the maximum number of these necklaces that can be made from 45 beads of each color ? Choose the correct answer:
A) 7	B) 8	C) 5	D) 6	E) 2

Solution: Atleast 9 green breads are needed to make a necklace, so irrespective of the combinations of white and orange beads, the number of necklaces that can be formed will be   45/9= 
45/9 = 5
5   Answer:- 5
Answer: C
A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 10 hours, 50 percent worked 40 hours, and the rest worked 50 hours?	Choose the correct option:
A) $180,000 B) $185,000 C) $170,000 D) $200,000 E) $205,000

Solution: 30% of 1000 = 300 worked for 20 hours   Payment @ 5/hr   Total Payment = 300*10*5= 
300*10*5 = 15_000
15000   50 % of 1000= 500 worked for 40 hours   Payment @ 5/hr   Total payment = 500*40*5= 
500*40*5 = 100_000
100000   Remaining 200 worked for 50 Hours   Payment for first 40 Hours @ 5 /hr   Payment= 200*40*5= 
200*40*5 = 40_000
40000   Payment for next 10 hr @ 7.5/hr   Payment= 200 * 10 * 7.5= 
200 * 10 * 7.5 = 15_000
15000   Total Payment= 15000+100000 + 40000 +15000= 
15000+100000 + 40000 +15000 = 170_000
170000   Hence , answer is $170,000
Answer: C
Pipes A and B can fill a tank in 2 and 3 hours. Pipe C can empty it in 15 hours. If all pipes are opened together, then the tank will be filled in?
Answers
A) 60/17 hr
B) 13/12 hr
C) 42/11 hr
D) 6 hr
E) 30/23 hr

Solution: Net part filled in 1 hour = 1/2 + 1/3 - 1/15 = 23/30   The tank will be full in 30/23 hr   Answer is 30/23 hr
Answer: E
The average of ten numbers is 7 .If each number is multiplied by 12 , then the average of new set of numbers is Choose the correct answer
A) 28	B) 236	C) 288	D) 84	E) 26

Solution: Explanation:   If each number is multiplied by K, then the new average increases by K times. So new average = 84   Answer:84
Answer: D
The closest approximation of (69.28 × 0.004)/0.03 is Pick:
A) 0.092	B) 0.92	C) 9.2	D) 92	E) 920

Solution: (69.28 × 0.004)/0.03   1. 0.004 = 4 × 10^(-3)   2. 0.03 = 3 × 10^(-2)   3. (a × b)/c = a × (b/c)   4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)   Therefore,   (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33   Now,   7 × 2 = 14   7 × 1 = 7   or better:   6.9 × 1 = 6.9   6.9 × 2 = 13.8   hence,   6.9 <6.928 × 1.33 < 13.8   9.2 is the only answer that satisfies this condition.   ANSWER:9.2
Answer: C
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum? Choose one:
A) 1888
B) 1640
C) 2768
D) 2976
E) 2691

Solution: (x*8*3)/100 = ((2665 - x)*3*5)/100   24x/100 = 39975/100 - 15x/100   39x = 39975 => x = 1025   Second sum = 2665 – 1025   = 1640   Answer: 1640
Answer: B
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?  Choices
A) 21 : 9	B) 11 : 9	C) 71 : 9	D) 91 : 9	E) 21 : 2

Solution: Explanation:   In the same time, they cover 110 km and 90 km respectively.   {\color{11 : 9lue} \therefore } Ratio of their speeds = 110 : 90 = 11 : 9   Answer: 11 : 9
Answer: B
If 0 < x ≤ 3, then which one of the following is the maximum value of (x – 1)^2 + x ?
Choose the correct choice from the following answers:
A) –2
B) –1
C) 7
D) 1
E) 2

Solution: the maximum value of (x – 1)^2 + x for 0 < x ≤ 3 is when x=3 --> (x – 1)^2 + x =7   Answer 7
Answer: C
If 42/330 = 0.1272, what is the 32nd digit to the right of the decimal point of the fraction?  Choose the correct choice from the following choices
A) 1	B) 4	C) 5	D) 7	E) 2

Solution: we are not concerned what 42/330 means..   we have to look at the decimal..   0..1272 means 0.1272727...   so leaving first digit to the right of decimal, all ODD numbered are 7 and all EVEn numbered are 2.   here 32 is 2V2N, so ans is 2   Answer is 2
Answer: E
In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/6 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?	Choose the correct answer:	A) 23/30	B) 11/15	C) 7/10	D) 1/6	E) 2/15

Solution: 1/5 -- cable TV (This includes some data from video cassette recorder)   1/10 -- video cassette recorder including 1/6(equiped with cable tv) i.e. 1/6(1/5) = 1/30   therefore only video cassette recorder = 1/10 - 1/30 = 1/15   Total = 1/5+1/15+neither cable tv nor videocassette recorders   1 = 4/15 + neither cable tv nor videocassette recorders   therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15   Hence 11/15.
Answer: B
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the six socks?
Choose the correct choice from the following choices
A) 12
B) 15
C) 21
D) 36
E) 30

Solution: It's a question of permutation since order matters here ....   It can be deduced to-   6P2 = 6!/4! = 6*5= 
6*5 = 30
30 .........Answer is - 30
Answer: E
In how many ways can a Chief Minister and a Vice Minister be elected from a team of 14 members?  Pick:
A) 132
B) 144
C) 158
D) 170
E) 182

Solution: There are 14 choices for the Chief Minister.   Then there are 13 choices for the Vice Minister.   The total number of ways is  14*13= 
 14*13 = 182
182.   The answer is 182.
Answer: E
A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room?	Choose the correct answer:
A) 10:00am B) 10:45am C) 12:00pm D) 12:30pm E) 1:30pm

Solution: In 6 hours the entrance door is opened to fill the room equal to 6*1/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5= 
15/5 = 3
3 hours.   Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours= 12:30pm.   Answer: 12:30pm.
Answer: D
The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books?
Choose one
A) 7	B) 12	C) 13	D) 5	E) 26

Solution: Surface area of each shelf= 2ab + 2ac + 2bc   848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c   848 = 32 + 2c + 32c   816 = 34c   c = 24 in. (i.e. the length of each shelf)   Each book is 4 in thick   24/4= 
24/4 = 6
6 books per shelf   26/6= 4.333=5 shelves   Answer is 5
Answer: D
From a Group of 8 People, Including Timo and Gary, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Timo but not Gary	Choose one:
A) 5/56	B) 9/56	C) 15/56	D) 21/56	E) 25/56

Solution: Number of ways of selecting 3 people out of 8 people = 8C3   In the three members Timo will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Gary cannot be there in the team. So 2 members have to be selected and the number of available members = 7 -Gary = 6   Number of ways to form a 3 member team that includes Timo and excludes Gary = 615/562   Probability = 615/562/815/563 = 15/56   Answer: 15/56
Answer: C
The price of a car and AC are in the ratio 3:2. If the scooter costs $500 more than the AC. then the price of the AC? Select: A) 1500 B) 200 C) 1700 D) 2000 E) 2500

Solution: Let the price of the Car and 1500C is 3x and 2x   3x-2x = 500   x = 500   Price of 1500C = 3*500= 
3*500 = 1_500
$1500   1500nswer is 1500
Answer: A
The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is :
Choose the correct answer:
A) 25 years
B) 35 years
C) 45 years
D) 55 years
E) 75 years

Solution: Solution   Let their ages be x year and (x + 10) years respectively.   Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25.   ∴ Present age of the elder person =(x + 10) =35 years. Answer 35 years
Answer: B
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 47. The corrected new mean is? Choose the most appropriate option.
A) 36.7  B) 36.1  C) 36.5  D) 36.02  E) 36.3

Solution: Correct sum   = (36 * 50 + 48 - 47)= 
(36 * 50 + 48 - 47) = 1_801
1801.   Correct mean= 1801/50= 
1801/50 = 1_801/50 = around 36.02
36.02   Answer:36.02
Answer: D
If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?  Choose the correct choice from the following options: A) 1 B) 10 C) 19 D) 20 E) 21

Solution: Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2   Here A = sum of even ints from 2 to 20, inclusive   number of even ints = 10,   first int + last int = 2+20= 
2+20 = 22
22   A= 10*22 / 2= 
10*22 / 2 = 110
110   B= sum of odd ints from 1 to 19, inclusive   number of odd ints = 10,   first int + last int = 1+19= 
1+19 = 20
20   A= 10*20 / 2= 
10*20 / 2 = 100
100   A-B= 110 - 100= 
110 - 100 = 10
10   ANSWER:19
Answer: C
The length of the longest tape in cm which can be used to measure exactly, the length 6m; 5m ; and 12m is: Choose the correct choice
A) 200
B) 100
C) 50
D) 1200
E) 500

Solution: The three lengths in cm are 600,500 & 1200.   HCF of 600, 500 & 1200 is 100   Hence, the answer is 100 cm.   ANSWER:100
Answer: B
Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21.	Choose the correct answer
A) 9, 6, 16	B) 9, 6, 19	C) 9, 6, 16	D) 9, 6, 12	E) 9, 6, 11

Solution: Let the numbers be a, b and c.   a:b:c = 3:2:4   Given, (a + b) + (c - b) = 21   => a + c = 21   => 3x + 4x = 21 => x = 3   a, b, c are 3x, 2x, 4x   a, b, c are 9, 6, 12.   Answer: 9, 6, 12
Answer: D
A rectangular cube has sides measuring 15 inches long by 12 inches wide by 2 inches high. If the surface area of the rectangle is the same as a cube, what do the sides/walls of the cube measure? Round to the nearest whole number. Choose the correct choice from the following choices
A) 7 B) 5 C) 9 D) 6 E) 4

Solution: First calculate the surface area of the rectangle by multiplying the length and width of the rectangle together, then multiply by 2 to get both sides of the rectangle. This calculates to 360 inches. Find the surface area of the sides of the rectangular cube. Multiply the height by the length of the rectangle. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 60 inches. Then multiply the width of the rectangle by the height. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 48 inches. Add the totals together to get the rectangular cube surface area of 468 inches. Since a square cube has 6 sides - divide the surface area by 6. This calculates to 78 inches as the surface area of each side of the cube. The square root of 78 is 8.831. Rounding to the nearest whole number that makes each side of the cube measuring 9 inches. The correct answer is (9).
Answer: C