MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent F of the distribution is less than m +d ?
Choose the correct choice
A) 16%	B) 32%	C) 48%	D) 84%	E) 92%

Solution: D   The prompt says that 68% of the population lies between m-d and m+d.   Thus, 32% of the population is less than m-d or greater than m+d.   Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.   Thus, F=(68+16)% or (100-16)% of the population is less than m+d.84%
Answer: D
Which of the following inequalities is equivalent to −6 < x < 8? Pick
A) |x - 1| < 7
B) |x + 2| < 6
C) |x + 3| < 5
D) |x - 2| < 6
E) None of the above

Solution: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -6 < x < 8, let's say by adding y to this inequality we will get into the above format   -6+y < x+y < 8+y   Now, to move this into the mod format, we need to have (-6+y) + (8+y) = 0 => y = -1   Thus, -7 < x-1 < 7 => |x-1| < 7.   Hence, answer is |x - 1| < 7
Answer: A
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Choose the correct choice from the following answers:  A) 298  B) 280  C) 279  D) 267  E) 297

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer:280
Answer: B
Of the 150 employees at company X, 60 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year? Choose the correct choice from the following options.
A) 20	B) 30	C) 50	D) 80	E) 100

Solution: Full time employee who have NOT worked for at least one year = a   Full time employee who have worked for at least one year = b   NON Full time employee who have worked for at least one year = c   NON Full time employee who have NOT worked for at least one year = d   a+b+c+d = 150   a+b = 80   i.e. c+d = 70   b+c = 100   i.e. a+d = 50   d = 20   i.e. c = 70-20= 
70-20 = 50
50   i.e. b= 100-50= 
100-50 = 50
50   i.e. a= 80-50= 
80-50 = 30
30   b= 80   Answer: Option 80
Answer: D
Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent?  Choose the correct choice from the following answers
A) Rs 634.76	B) Rs 554.76	C) Rs 654.76	D) Rs 664.76	E) none of these

Solution: Let the monthly rent be Rs X.   We have,   5.5% of 100000 = 12 (X - 12.5% of X) - 325   5500/12 = X - (X/8) - 325/12   5500/12 + 325/12 = 7/8 x X   X = 5825/12 x 8/7   Rs 554.76 per month   ANSWER:Rs 554.76
Answer: B
On dividing a number by 357, we get 41 as remainder.On dividing the same number by 17, what will be the remainder ?  Answers
A) 4  B) 5  C) 8  D) 7  E) 2

Solution: Let x be the number and y be the quotient.Then,   x=357*y+41   =(17*21*y)+(17*2)+7   =17*(21y+2)+7.   Required number =7.   Answer is 7
Answer: D
s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Y are in s(99)?  Select.
A) Y=350  B) Y=353  C) Y=354  D) Y=356  E) Y=357

Solution: Focus on the points where the number of digits in squares change:   1, 2, 3 - Single digit squares. First 2 digit number is 10.   4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.   10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.   32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.   So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272= 
3 + 12 + 66 + 272 = 353
353.Y=353
Answer: B
The digit at the ten’s place of a 2 digit no. is twice the digit at the unit’s place. If the sum of this no. and the no. formed by reversing the digits is 66. Find the no.
Choose the correct option:
A) 26 B) 28 C) 32 D) 42 E) 47

Solution: Let the unit place digit = x   Ten’s place digit = 2x   Number formed = 10(2x ) + x = 20 x + x = 21x   Reversing the digit :   Unit digit = 2x   Ten’s digit = x   New number formed = 10 (x) + 2x = 10x + 2x = 12x   As the sum of the number is 66.   21x + 12 x 10  + 2= 
10  + 2 = 12
12x   As the sum of the number is 66.   21x + 12 x= 66   33x = 66   X = 2   So unit digit = 2   Number = 21x = 21(2)   =42   42
Answer: D
Find the base K of the number system, if (524)8 = (664)K ?  Choose the correct choice:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: 5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0   320 + 16 + 4 = 6(K^2) + 6K + 4   340 = 6(K^2) + 6K + 4   6(K^2) + 6K + 4 - 340 = 0   6(K^2) + 6K - 336 = 0   dividing by 6;   (K^2) + K - 56 = 0   solving this quadratic equation we get, K=7 and K=-8   thus K=7   ANSWER:7
Answer: D
A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once? Choose the correct choice from the following options:
A) 1/3
B) 2/5
C) 1/6
D) 1/7
E) 2/5

Solution: Let E be the event that ‘number 4 appears at least once’ and F be   the event   that ‘the sum of the numbers appearing is 6’.   Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),   (5,4), (6,4)}   and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}   We have P(E) = 11/36   and P (F) = 5/36   Also EnF = {(2,4), (4,2)}   Therefore P(EnF) = 2/36   the required probability   P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.   2/5
Answer: B
Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number.	Choose the correct choice
A) 8  B) 9  C) 10  D) 12  E) 11

Solution: Explanation:   Let the two digit number be xy.   4(x + y) +3 = 10x + y - - - (1)   10x + y + 18 = 10 y + x - - - (2)   Solving 1st equation,   4x + 4y + 3 = 10x + y   3y + 3 = 6x   6x – 3y   3  + 3= 
  3  + 3 = 6
6x   6x – 3y= 3   Therefore, 2x – y = 1 - - - (3)   Solving 2nd equation,   xy + 18 = yx   ⇒⇒ (10x + b) + 18 = 10y + x   ⇒⇒ 18 = 9y – 9x   ⇒⇒ 2 = y – x   we get y - x = 2 - - - (4)   adding 3 and 4, we get x = 3   By substituting in (4), we get y = 5   So the given number is 35. Sum of the digits = 8.   Correct option: 8
Answer: A
In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks B are made of cotton?  Choose the correct choice
A) 100
B) 80
C) 60
D) 50
E) 25

Solution: I'll prefer to solve this with plug n play method.   As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks B has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.   100 fits perfectly after relevant calculations. Hence answer 100.
Answer: A
Indu gave Bindu Rs.3125 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Choose the correct choice from the following:
A) s.10 B) s.2 C) s.5 D) s.3 E) s.4

Solution: 3125 = D(100/4)2   D = 5   ANSWER:s.5
Answer: C
A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 20% less than B, and C costs 25% less than A,and D costs 30% less than C what percent of B's cost is D?  Choose one:	A) 40%	B) 38%	C) 44%	D) 36%	E) 42%

Solution: Soln:-   B=100   A 20% less than B = 80   C 25% less than A = 60   D 30% less than C = 42   D is what percent of B = D/B * 100   = 42/100 * 100= 
42/100 * 100 = 42
42%   ANSW42%R:42%
Answer: E
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.	Pick.
A) 2 B) 3 C) 4 D) 6 E) 60/7

Solution: For 1 hour-   Machine A rate- 2000 envelopes   Machine B+C rate- 2400 envelopes   Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour.   Which makes machine B's rate as 1400 envelopes per hour.   Thus, it will take 8 hours to manufacture 12000 envelopes.   Answer:-60/7
Answer: E
There is a 70% chance that Flora will visit Ghana this year, while there is a 70% chance that she will visit France this year. What is the probability that Flora will visit either Ghana or France this year, but NOT both?
Choose the correct choice from the following answers:
A) 34%	B) 36%	C) 38%	D) 40%	E) 42%

Solution: P(Ghana but not France)=0.7*0.3= 
0.7*0.3 = 0.21
0.21   P(France but not Ghana)=0.7*0.3= 
0.7*0.3 = 0.21
0.21   P(Ghana or France but not both)=0.21+0.21= 
0.21+0.21 = 0.42
0.42   The answer is 42%.
Answer: E
P can do the work in 8 days and Q can do the same work in 12 days. If they work together for 4 days, what is the fraction of work that is left?  Choose the most appropriate option.
A) 2/15	B) 2/11	C) 1/4	D) 1/5	E) 1/6

Solution: 4/8 + 4/12 = 1/2 + 1/3 = 5/6 (completed work)   The work that is left is 1 - 5/6 = 1/6   The answer is 1/6.
Answer: E
If f(x) = 12 - x^2/2 and f(2k) = 7k, what is one possible value for k? Answers.
A) 2	B) 3	C) 4	D) 6	E) 7

Solution: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.   We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be  12 - 4/2= 
 12 - 4/2 = 10
10.   So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:   f(2k)= 12 - (2k)^2/2 = 12 - 2k^2.   Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.   12 - 2k^2 = 2k --> k = -3 or k = 7.   All the answers are positive, so we choose k = 2.   Answer = 7
Answer: E
A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?	Choose the correct choice from the following choices:
A) 7.78 days B) 7.88 days C) 7.38 days D) 7.38 days E) 7.36 days

Solution: A + B = 1/8   B + C = 1/12   C + A = 1/16   -------------------------------   2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48   A + B +C = 13/96   96/13 = 7.38 days   Answer: 7.38 days
Answer: D
A sock drawer contains four socks, each one a different solid color. The colors of the socks are green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
Answers
A) 2400  B) 240  C) 1,024  D) 2,520  E) 24

Solution: I see no condition for arrangement.   So 4! ways - IMO option 24 is correct answer..
Answer: E
Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 7 times as heavy as water?	Choices
A) 3:2  B) 1:2  C) 3:1  D) 5:2  E) 2:3

Solution: G = 10W   C = 5W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   10W+5Wx = x+1 * 7W   10+5x = 7(x+1)   x = 3/2   Ratio of gold with copper = 1:3/2 = 2:3   Answer is 2:3
Answer: E
Which of the following CANNOT be a product of two distinct positive integers p and q?
Select the correct option
A) p	B) q	C) 3q + 2p	D) q - p	E) qp

Solution: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with   take p = 1 and q = 2 and work with the options   pq = 2   A) p take p =2, q = 1   B) q take p = 1 q = 2   C) 3q + 2p Seems tricky, lets see other options and then come back to it.   D) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?   E)qp Always true   You don't even have to worry what C is !   ans q - p
Answer: D
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 1 a rupee. Find his net profit or loss percent?  Choose the correct choice:
A) 330 %  B) 390 %  C) 200 %  D) 250 %  E) 300%

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his CP = 1   He selling at 3 a rupee, his SP = 4   Profit = SP - CP = 4 - 1= 
4 - 1 = 3
3   Profit Percent= 3/1 * 100= 
3/1 * 100 = 300
300 %   Answer:300%
Answer: E
John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?	Choose the correct choice from the following choices: A) 8 B) 9 C) 8.5 D) 9.5 E) 10.5

Solution: In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work.   So 3/5 of the work should have been completed by the two of them together before Jane left.   Their combined rate of work is 1/20 + 1/12 = 8/60   Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days.   So total number of days taken to complete the work =9/2 + 4= 
9/2 + 4 = 17/2 = around 8.5
8.5 days.   8.5
Answer: C
The greatest number by which the product of two consecutive multiples of 3 is always divisible is  Choose the correct choice from the following options.
A) 54
B) 76
C) 18
D) 162
E) None of these

Solution: Solution   Required number	= Product of first three multiplies of 3   = (3 Ã— 6)= 18.   Answer 18
Answer: C
Seven female friendsseven male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?  Answers.
A) 50803200 B) 1680 C) 1152 D) 576 E) 70

Solution: now any of the alternate 8 places can be filled by 7 male or female in 7!   similarily,   other 7 alternate places can be filled in 7!   hence required probability= 2*7!*7!=5,08,03,200   hence 50803200
Answer: A
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?	Pick one:	A) 14,7	B) 64,4	C) 18,4	D) 14, 4	E) 12,4

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x   = 14, y = 4.   Answer:14, 4
Answer: D
What will be the cost of building to paint which area equal to 196 sq ft, if the price per foot of building is Rs. 15?
Pick one
A) 120
B) 240
C) 360
D) 380
E) 840

Solution: Let the side of the square plot be a ft.   a2 = 196 => a = 14   Length of the fence = Perimeter of the plot = 4a = 56 ft.   Cost of building the fence = 56 * 15   = Rs.840.   Answer: 840
Answer: E
A batsman makes a score of 85 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?  Choose the correct choice from the following choices:
A) 19  B) 29  C) 37  D) 49  E) 59

Solution: let the average after 17th inning =x   Then average after 16th inning=(x-3)   Therefore 16(x-3)+85=17x   Therefore x=37   ANSWER:37
Answer: C
The length of rectangle is thrice its breadth and its perimeter is 64 m, find the area of the rectangle?  Choose the correct choice from the following: A) 432 B) 376 C) 299 D) 276 E) 288

Solution: 2(3x + x) = 64   l = 36 b = 8   lb = 36 * 8= 
36 * 8 = 288
288   288
Answer: E
The ratio of the arithmetic mean of two numbers to one of the numbers is 5:9. What is the ratio of the smaller number to the larger number?  Choose the correct choice:
A) 1:5	B) 1:6	C) 1:7	D) 1:8	E) 1:9

Solution: For two numbers, the arithmetic mean is the middle of the two numbers.   The ratio of the mean to the larger number is 5:9, thus the smaller number must have a ratio of 1.   The ratio of the smaller number to the larger number is 1:9.   The answer is 1:9.
Answer: E
When x is multiplied by 3, the result is 20 more than the result of subtracting x from 20. What is the value of x?  Select the correct option:
A) 10
B) -2
C) 11
D) 13
E) 22

Solution: The equation that can be formed is:   3x-20=20-x   or, 4x=40   or, x=10.   10nswer : 10
Answer: A
$366 is divided amongst A,B and C so that A may get 1/2 as much as B and C together, B may get 2/3 as much as A and C together, then the share of A is  Pick one:
A) $122
B) $150
C) $176
D) $200
E) $250

Solution: $122:(B+C) = 1:2   $122's share = 366*1/3= 
366*1/3 = 122
$122   $122nswer is $122
Answer: A
Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 3 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 3 minute mark.)  Answers
A) 14	B) 15	C) 16	D) 17	E) 18

Solution: 3 minutes is 180 seconds.   Lamp A and Lamp B will flash together every 24 seconds.   180/24=7 plus remainder.   In the time period, Lamp A and Lamp B will flash together 7 times.   Lamp A and Lamp C will flash together every 30 seconds.   180/30= 
180/30 = 6
6.   In the time period, Lamp A and Lamp C will flash together 6 times.   Lamp B and Lamp C will flash together every 40 seconds.   180/40=4 plus remainder.   In the time period, Lamp B and Lamp C will flash together 4 times.   All three lights will flash together every  2*2*2*3*5= 
 2*2*2*3*5 = 120
120 seconds.   180/120=1 plus remainder.   We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.   The number of times that exactly two lights flash together is   7+6+4-3= 
  7+6+4-3 = 14
14 times.   The answer is 14.
Answer: A
Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 90 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?	Select the correct option
A) 46 B) 42 C) 56 D) 32 E) 40

Solution: I'm going in on this one.   So let's say that we have the following   So we know that L1 = 90 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is  200 - 90= 
 200 - 90 = 110
110. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 60= 
100 - 60 = 40
40.   Thus 40 is the correct answer choice
Answer: E
A set consist of 2p-1 element. What is the number of subsets of this set which contain at most p-1 elements?	Select
A) 2^(2p-2)  B) 2^(2p) - 2  C) 2^(2p) -1  D) 2^(2p)  E) 2^(2p-1)

Solution: I used p=3, so then we have   5!/2!3! + 5!/4!1! + 5!/0!5!    10 + 5 + 1= 
 10 + 5 + 1 = 16
16   So our target is 16   Now replace in answer choices   2^(2p-2) gives us 2^4= 16   Hence 2^(2p-2) is the correct option   Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes   2^(2p-2)void 2 since you will get 1 arrangement (p-1) and may be risky since 1 is a number with certain unique properties
Answer: A
The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?  Pick:  A) 7:6  B) 7:3  C) 7:9  D) 7:1  E) 7:8

Solution: Let P's age and Q's age be 6x and 7x years respectively.   Then, 7x - 6x = 4 => x = 4   Required ratio = (6x + 4) : (7x + 4)   28 : 32 = 7:8   Answer: 7:8
Answer: E
Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. When will they meet each other?	Pick one
A) 12 miles away from A	B) 12 miles away from B	C) after 6 hours from start	D) after 9 hours from start	E) after 12 hours from start

Solution: Since the question is asking when A and B will meet each other, the answer will be one involving time elapsed.   In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.   Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of   36/2= 
  36/2 = 18
18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.   B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...   and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.   Since 2 is actually right in the middle of the 9 speeds, this implies both A and B will have the same average speed.   So the correct answer is (D): A and B will meet after 9 hours (midway between A and B.)   Had it been determined that B's average speed was more than 2 then that would indicate A and B would meet closer to point A and will take less than 9 hours and so on...   The correct answer is (after 9 hours from start).
Answer: D
At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?	Choose the correct choice from the following answers.
A) 11 points  B) 12 points  C) 15 points  D) 10 points  E) 12 points

Solution: "A can give 15 points to B in 60".   => In a game of 60, A starts with 0 points where B starts with 15 points   "A can give 20 points to C in 60".   => In a game of 60, A starts with 0 points where C starts with 20 points   ie, in a game of 60-15-45, B can give C   20-15= 
  20-15 = 5
5 points=> ie, in a game of 90, B can give C 5×2=10 points   Answer is 10 points
Answer: D
If 4x = 8^y, which of the following expresses x in terms of y? Choose one
A) 2^(y-2)
B) 2^(y-1)
C) 2^(3y-2)
D) 2^(2y-3)
E) 2^y

Solution: By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: 2^(3y-2)
Answer: C
Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $58 of gas?
Choose the correct answer.
A) 242
B) 353
C) 464
D) 575
E) 686

Solution: 58/4= 
58/4 = 29/2 = around 14.5
14.5 gallons     14.5*32= 
  14.5*32 = 464
464 miles   The answer is 464.
Answer: C
Present ages of X and Y are in the ratio 6:8 respectively. Ten years hence this ratio will become 8:10 respectively. What is X's present age in years?
Answers.
A) 35	B) 36	C) 37	D) 39	E) 30

Solution: Let the present ages of X and Y be 6x and 8x years respectively.   Then, (6x + 10)/(8x + 10) = 8/10   10(6x + 10) = 8(8x + 10) => 60x+100 = 64x+80 => 4x =20 => x =5   X's present age = 6x = 6*5= 
6*5 = 30
30   ANSW30R: 30
Answer: E