MU-NLPC/Calc-aqua_rat huggingface dataset:
Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet?	Choose the correct choice from the following answers:
A) 70 minutes B) 80 minutes C) 85 minutes D) 90 minutes E) 95 minutes

Solution: Let us consider that speed of train , first man and second man are respectively t, f and s.   According to first given condition goods train crossed the first person moving in same direction in 20 sec.   so length of the will be 20(t-f)   similarly train crossed the second man in 18 sec.   so length of the train will be 18(t+s)   on comparing these two equations, we get 20(t-f) = 18(t+s)   or 2t = 20f + 18s   or t = 10f + 9s   now it is given that After 10 min the train crossed the other person who is coming in opposite direction so   if we consider this way of train as L then the next equation will be   L = 600t (here 600 is used for 10 minutes)   finally as asked in the question the time required to meet the two man after the train has passed will be given by   time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes}   = (600t-600f)/(f+s)   = [600(10f+9s)-600f]/(f+s)   = 600(10f+9s-f)/(f+s) = 600*9(f+s)/(f+s) = 600*9 seconds = 600*9/60= 
600*9/60 = 90
90 minutes   ANSWER:90 minutes
Answer: D
If Ramola ranks 14th in a class of 26, what is her rank from the last?	Choose the correct choice from the following answers.
A) 11th
B) 13th
C) 12th
D) 14th
E) 15th

Solution: when considered from last, 12 (i.e 26-14) students are ranked before her. so she is 13th rank from last.   ANSWER:13th
Answer: B
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Answers.
A) 2/3
B) 8/21
C) 3/7
D) 9/22
E) 10/21

Solution: Explanation:   Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 8/21.   Answer: Option 8/21
Answer: B
In a contest, a bowl contains 18 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
Select the correct option.
A) 1/18	B) 1/9	C) 5/36	D) 1/4	E) 3/71

Solution: P(not winning) = 17/18*16/17 = 8/9   P(winning) = 1 - 8/9 = 1/9   The answer is 1/9.
Answer: B
A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 7.2 kilometer long bridge, at the same speed?
Pick one:
A) 4 min	B) 2 min	C) 8 min	D) 9 min	E) 3 min

Solution: S = 600/40= 
600/40 = 15
15 mps   S=7200/15= 
7200/15 = 480
480 sec=8 min.Answer:8 min
Answer: C
A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $5.00 a pound. How many pounds of cashews must she use?  Choose the correct choice from the following choices:
A) 40 B) 45 C) 50 D) 55 E) 60

Solution: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y   From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:   $2.5 * (x + 100 - x) = $1.5x + $4(100 - x)   If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.   You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)   Answer is 45
Answer: B
The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 50 kms. what was the total distance traveled in 12 hours?  Options:	A) 252 kms	B) 152 kms	C) 732 kms	D) 752 kms	E) 152 kms

Solution: Explanation:   Total distance travelled in 12 hours =(50+52+54+.....upto 12 terms)   This is an A.P with first term, a=50, number of terms,   n= 12,d=2.   Required distance = 12/2[2 x 50+{12-1) x 2]   =6(122)   = 732 kms.   Answer: 732 kms
Answer: C
workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.15 lacs . How many workers were they? Choose the correct option:
A) 300
B) 230
C) 500
D) 560
E) 590

Solution: N * 50 = (315000 - 300000)= 
(315000 - 300000) = 15_000
15000   N= 15000 / 50= 
15000 / 50 = 300
300   300
Answer: A
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 60. He was allowed to drop his lowest score. After doing so, his average test score improved to 65. What is the lowest test score that was dropped? Choose the correct answer.
A) 20  B) 25  C) 45  D) 65  E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.   He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 60.   So the lowest score= 60 - 15= 
60 - 15 = 45
45   Answer (45)
Answer: C
Dhoni bought a 1-year, $40,000 certificate of deposit that paid interest at an annual rate of 6 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Pick one:
A) $2456 B) $2436 C) $2446 D) $2466 E) $2426

Solution: 6 percent compounded semiannually --> 3% in 6 moths.   For the first 6 moths interest was 3% of $40,000, so $1200   For the next 6 moths interest was 3% of $41,200, so $1236   Total interest for 1 year was $1200+$1236=$2436   Answer : $2436  1200+ 1236= 
  1200+ 1236 = 2_436
$2436   Answer : $2436
Answer: B
A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in	Pick one
A) 40 days  B) 30 days  C) 60 days  D) 70 days  E) 50 days

Solution: Explanation:   12 = (15 * x)/(15 + x)   180+12x=15x   3x=180   X=60   Answer: Option 60 days
Answer: C
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?	Choose the correct choice from the following choices.
A) 6 days
B) 7 days
C) 8 days
D) 9 days
E) 10 days

Solution: Explanation:   1 woman's 1 day's work = 1/70   1 Child's 1 day's work = 1/140   5 Women and 10 children 1 day work =   (5/70+10/140)=1/7   So 5 women and 10 children will finish the work in 7 days   Option 7 days
Answer: B
Adding two non multiples of R always results in a multiple of R; which of the following must be the value of R ? Pick one: A) [A] two B) [B] three C) [C] five D) [D] ten E) [E] hundred

Solution: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.   so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..   [A] two
Answer: A
Ashish and Rahul started walking from same point E. Ashish walked at the speed of 15 kmph to the east, and Rahul walked 25 kmph to south, at what time they meet 10 miles apart? Select
A) 15 min B) 16 min C) 17 min D) 18 min E) 19 min

Solution: Consider 1 mile = 1.6 km   so 10 miles = 16 km   both are walking in at an angle 90 from same point so pythagorous theorem can be apply hence   (15x)^2 + (25x)^2 = 16^2   by solving and x hours are converted into min we got   approximate 18 min   ANSWER:18 min
Answer: D
Find the fourth proportional to 0.2,0.12 and 0.3?  Answers:
A) 0.18
B) 0.21
C) 0.22
D) 0.34
E) 0.45

Solution: Formula = Fourth propotional = (b × c)/a   0.18 = 0.2 , B = 0.12 and C = 0.3   (0.12 × 0.3)/0.2   0.036/0.2= 
0.036/0.2 = 0.18
0.18   0.18
Answer: A
Bottle R contains 100 capsules and costs $6.30. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
Choose the correct choice from the following choices.
A) $0.04
B) $0.12
C) $0.05
D) $0.03
E) $0.002

Solution: Cost per capsule in R is 6.30/100= 
6.30/100 = 0.063
0.063   Cost per capsule in T is  2.99/130= 
 2.99/130 = 0.023
0.023   The difference is 0.004   The answer is $0.04
Answer: A
Using all the letters of the word "NOKA", how many words can be formed, which begin with N and end with A?
Choose the correct choice from the following options:	A) 8	B) 2	C) 9	D) 3	E) 1

Solution: There are five letters in the given word.   Consider 4 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 2! ways.   The number of words = 2! = 2.   Answer:2
Answer: B
The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 16.56 years. What was the average age of five new men?
Choose the correct choice from the following options
A) 15.5	B) 15.4	C) 15.25	D) 20.4	E) 15.6

Solution: Total age of 20 men = 15.6 x 20 = 312   Now, total age of 25 men = 141.   Total age of five men added later = 414 - 312 = 202.   Hence, the total average of five men = 102/5= 
102/5 = 102/5 = around 20.4
20.4   ANSWER:20.4
Answer: D
If f(1, 1) = 5 and f(1, 5) = 26, what is the value of f(1, 10)?
Pick one:
A) 107 B) 101 C) 147 D) None of these E) Cannot be determined

Solution: Solution:   The function f(a, b) = a3 + b2   f(1, 2) therefore is = 1^3 + 2^2 = 1 + 4= 
1 + 4 = 5
5 and   f(1, 5)= 1^3 + 5^2 = 1 + 25= 
1 + 25 = 26
26   Therefore, f(1, 10)= 1^3 + 10^2 = 1 + 100= 
1 + 100 = 101
101   Answer 101
Answer: B
In a survey about potential presidential candidates A and B, 30% of the public likes A and 50% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither. Answers:
A) 70%
B) 55%
C) 60%
D) 65%
E) 50%

Solution: T=100   70%=30   B=50   Both=x   70% only=30-x   B only=50-x   N=Neither   Given:   70% only+B only=2*Both   30-x+50-x=2x   80=4x   x=20   T=70% only+B only+Both+Neither   100=30-20+20-20+20+N   100=30+N   N=100-30= 
100-30 = 70
70   70%ns:70%
Answer: A
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?  Choose the most appropriate option.
A) 14299  B) 27888  C) 26687  D) 14000  E) 62912

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000 .Answer: 14000
Answer: D
The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is	Choices
A) 338 B) 140 C) 287 D) 277 E) 136

Solution: Explanation:   distance covered in 1 revolution = {\color{140lue} 2\Pi r} = 2 *(22/7) *20 = 880/7 cm   required no of revolutions = 17600 *(7/880)= 
17600 *(7/880) = 140
140   Answer: 140) 140
Answer: B
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 65 sq. cm. Find the length of the rectangle.  Choose the correct choice from the following:
A) 12cm
B) 14cm
C) 16cm
D) 18cm
E) 20cm

Solution: Explanation:   Let breadth = x. Then, length = 2x. Then,   (2x - 5) (x + 5) - 2x * x = 65 => 5x - 25 = 65 => x = 16.   Length of the rectangle = 16 cm.   Answer: Option 16cm
Answer: C
The base of pyramid P is an isosceles right triangle whose leg is 3. If the height of P is 4, what is the volume of P? Choose the correct choice from the following answers:
A) 36
B) 18
C) 12
D) 8
E) 6

Solution: Volume of a pyramid is given by   V=1/3Ah, where A is the area of the triangular base and h is the height of the pyramid.   Area of triangular base = 1/2 * 3*3 = 9/2   So, V = 1/3 * 9/2 *4= 
1/3 * 9/2 *4 = 6
6   Option 6
Answer: E
Suppose you want to buy three loaves of bread that cost $1.00 each
and a jar of peanut butter that costs $5. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $16. How much money will you have left
over?  Choices.
A) $1.50	B) $6	C) $8	D) $7	E) $5.50

Solution: The jelly is extra information. 16.00 â€“ 3 x 1 â€“ 5.00 =   16.00 â€“ 3 â€“ 5.00 = 8   You have $8 left.   correct answer $8
Answer: C
30% people of a village in Sri Lanka died by bombardment, 25% of the remainder left the village on account of fear. If now the population is reduced to 6695, how much was it in the beginning? Choose the correct choice from the following options: A) 7000 B) 6700 C) 6695 D) 7645 E) 6575

Solution: X * (70/100) * (75/100) = 3515   X = 6695   Answer: 6695
Answer: C
A’s speed is 17/14 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?	Select:  A) 1/14  B) 1/17  C) 3/14  D) 3/17  E) 1/31

Solution: Let x be the fraction of the distance that B runs.   Let v be the speed at which B runs.   The time should be the same for both runners.   Time = D / (17v/14) = xD/v   (14/17)*D/v = x*D/v   x = 14/17   B should have a head start of 3/17 of the full distance.   The answer is 3/17.
Answer: D
Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5700. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
Choices
A) s.750, Rs.2250	B) s.2000, Rs.750	C) s.750, Rs.2000	D) s.850, Rs.2250	E) s.950, Rs.2850

Solution: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18   Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2   Minuâ€™s share = Rs.5700* 2/12 = Rs.950   Anuâ€™s share = Rs.5700* 6 /12= 
.5700* 6 /12 = 0.285
Rs.2850   ANSWs.950, Rs.2850R:s.950, Rs.2850
Answer: E
If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units?  Choices.
A) 50 hours B) 40 hours C) 25 hours D) 12 hours E) 8 hours

Solution: Here, we're told that 5 machines can produce 20 units in 10 hours....   That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.   20 units/5 machines = 4 units are made by each machine every 10 hours   Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...   10 hours/4 units = 2.5 hours per unit when 1 machine is working.   The prompt asks us how long would it take 20 machines to produce 200 units.   If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME.   (2.5 hours)(10 times) = 25 hours   Final Answer:   [Reveal]Spoiler:   25 hours
Answer: C
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 correct choice from the following options.
A) 1/2 day	B) 1/8 day	C) 1/3 day	D) 8/2 day	E) 1/7 day

Solution: 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.   1/2 daynswer: 1/2 day
Answer: A
It is known that no more than 100 children will be attending a birthday. What is the smallest number of toffees that must be brought to the party so that each child receives the same number of toffees?
Choose the correct choice from the following answers:
A) 15
B) 320
C) 400
D) 150
E) 36

Solution: The number of children is not specified. We are just given that there are no more than 100 children.   If we assume that number of children is 75 then answer will be D.   If we assume that number of children is 100 then answer will be 400 because only 400 is divisible by 100.
Answer: C
A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?  Pick one: A) 2 1/2 % B) 4% C) 5% D) 6 2/3 % E) 6%

Solution: S.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1)= 
(100 * 40)/(800 * 1) = 5
5%   ANSWER:5%
Answer: C
A vehicle has an insurance of 4/5 of its original value. Premium on the vehicle at the rate of 1.3% amounts to 910 Rs. What is the original value of the vehicle?	Pick:  A) 87,508  B) 87,502  C) 87,500  D) 87,509  E) 87,5083

Solution: Explanation:   No explanation is available for this question!   ANSWER: 87,500
Answer: C
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 220 per month. What is his monthly salary?	Choose the correct choice from the following answers
A) 5500	B) 2999	C) 2878	D) 2990	E) 2771

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 220 => 5500   5500nswer: 5500
Answer: A
In how many ways can be 7 boys and 7 girls sit around circular table so that no two boys sit next to each other?	Choose the correct choice.
A) (5!)^2  B) (6!)^2  C) 6!7!  D) 11!  E) (5!)^2*6!

Solution: first fix one boy and place other 6 in alt seats so total ways is 6!   now place each girl between a pair of boys... total ways of seating arrangement of girls 7!   total is 6!*7!   ANS 6!7!
Answer: C
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#39?  Pick.
A) 17 B) 18 C) 19 D) 20 E) 21

Solution: First, let's translate the expression 21#39, using the definition given:   21#39 = 21×24×27×30×33×36×39   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#39 = 3^7(7×8×9×10×11×12×13)   Now let's replace each consecutive integer with its prime factorization:   21#39 = 3^7(7×2^3×3^2×(2×5)×11×(2^2×3)×13)   Let's group the prime bases:   21#39 = 2^6×3^10×5×7×11×13   The sum of the exponents is  6 + 10 + 1 + 1 + 1 + 1= 
 6 + 10 + 1 + 1 + 1 + 1 = 20
20   The answer is 20.
Answer: D
John bought an old Vehicle for $42000. He spent $13000 on repairs and sold it for $64900. What is his profit percent?	Choose the correct answer
A) 11%  B) 15%  C) 18%  D) 17%  E) 13%

Solution: C   18%   Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900   Profit(%) = (64900 - 55000)/55000 * 100= 
(64900 - 55000)/55000 * 100 = 18
18%
Answer: C
If (2x + 1) times (x + 2) is an odd integer, then x must be:  Choose the correct choice from the following answers
A) an odd integer B) an even integer C) a prime number D) a composite number E) a negative integer

Solution: Solution:   (2x + 1) times (x + 2) means (2x + 1)(x + 2)   (2x + 1)(x + 2) = 2x^2+5x+2   For 2x^2+5x+2 to be odd, 5x+2 must be odd since 2x^2 is always even.   So 5x must be odd, hence x must be odd.   Therefore x is an odd integer.   an odd integernswer: an odd integer
Answer: A
What is the speed of the stream if a canoe rows upstream at 9 km/hr and downstream at 12km/hr
Choose the correct choice from the following answers
A) 1 kmph  B) 4 kmph  C) 3 kmph  D) 2 kmph  E) 1.5 kmph

Solution: Sol.   Speed of stream = 1/2(12 -9) kmph = 1.5 kmph.   Answer 1.5 kmph
Answer: E
A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)? Choose the correct answer
A) 40	B) 42	C) 46	D) 48	E) 49

Solution: LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49   a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1   49
Answer: E
How many positive integers less than 100 are neither multiples of 5 or 6.	Options
A) a)30	B) b)31	C) c)32	D) d)33	E) e)67

Solution: To answer this Q we require to know   1) multiples of 5 till 100 = 100/5= 
100/5 = 20
20   2) Multiples of 6 till 100= 100/6 = 16.66= 16   add the two 20+16= 
20+16 = 36
36 ; subtract common terms that are multiple of both 5 and 6..   LCM of 5 and 6= 30   Multiples of 30 till 100 = 100/30 = 3.3 = 3   so total multiples of 2 and 3 = 36-3= 
36-3 = 33
33   ans= 100-33= 
100-33 = 67
67   e)67
Answer: E
Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?	Pick one:
A) 10.77 a.m
B) 10.85 a.m
C) 10.27 a.m
D) 10.25 a.m
E) 20.25 a.m

Solution: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4= 
80 * 9/4 = 180
180 hrs.   Time taken to cover remaining distance= (350 - 180)/60 = 17/6 hrs   = 2 5/6 = 2 hrs 50 min   Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.   So, Anna reached city A at 10.25 a.m.   Answer:10.25 a.m
Answer: D
How many different positive integers exist between 10^7 and 10^8, the sum of whose digits is equal to 2? Answers.
A) 6	B) 7	C) 5	D) 8	E) 18

Solution: So, the numbers should be from 10,000,000 to 100,000,000   The following two cases are possible for the sum of the digits to be 2:   1. Two 1's and the rest are 0's:   10,000,001   10,000,010   10,000,100   10,001,000   10,010,000   10,100,000   11,000,000   7 numbers.   2. One 2 and the rest are 0's:   20,000,000   1 number.   Total = 8 numbers.   Answer: 8
Answer: D
0.0005?=0.01  Answers:	A) 5	B) 0.05	C) 0.5	D) 50	E) None of these

Solution: Explanation :   Required Answer = 0.0005/0.01= 
0.0005/0.01 = 0.05
0.05/1= 0.05. Answer : Option 0.05
Answer: B
A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?	Choose the correct choice from the following answers:	A) $5.60	B) $7.20	C) $8.80	D) $9.60	E) $15.20

Solution: The lowest price would have to be calculated by finding the price of the $16 product after the initial 40% reduction, then the final price after 25% was taken off of the already-discounted price. So:   A 40% discount on a $16 product would = 60% of the original $16 price: $16 x .60 = $9.6   Next you have to find the price after an additional 25% had been discounted from the $9.6, which would be 75% of the $9.6: $9.6 x .75 = $7.20   The answer is $7.20
Answer: B
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ?	Choose the correct choice from the following options:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.   If this is hard to see let’s try it with a sample number, say 24. We can say the following:   24 = (2 x 10) + 4   24 = 20 + 4   24 = 24   Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 63. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.   10B + A = reversed integer   Since we know the resulting integer differs from the original by 63 we can say:   10B + A – (10A + B) = 63   10B + A – 10A – B =63   9B – 9A = 63   B – A = 7   Since B is the tens digit and A is the units digit, we can say that the digits differ by 7.   The answer is 7.
Answer: E