MU-NLPC/Calc-aqua_rat huggingface dataset:
A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
Pick:
A) 20
B) 22
C) 24
D) 26
E) 30

Solution: we have 3 places (---)to fill & we can use only digits 2, 4, 5   First place can be filled in 3 ways   2nd place can be filled in 3 ways because we can repeat the digits   3rd place can be filled in 3 ways because we can repeat the digits   Total no of codes = 3 x 3 x 3= 27   but one combination (555) will not be even so total no of even codes = 27 - 1= 
27 - 1 = 26
26   Answer 26
Answer: D
A set of numbers has the property that for any number x in the set, x+2 is also in the set. If -2 is in the set, which of the following must also be in the set
1. -4
2. 4
3. 0 Pick one.
A) 1 only	B) 2 only	C) 1 and 2 only	D) 1 and 3 only	E) 1,2 and 3

Solution: If X is in the set than X+ 2 is also in the set   If -2 in the set than    -2+2= 
 -2+2 = 0
0 is also in the set   Since + 2 is Present, 2 + 2= 4 Is also present in the set .   Therefore Ans 1 and 3 only
Answer: D
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ? Choose the correct choice from the following answers
A) 13	B) 21	C) 23	D) 24	E) 25

Solution: The reasoning is as follows:-   B) can't be answer because Y<x (23)="" 23="" 23)="" 3="" 4="" a)="" answer="" be="" because="" but="" can't="" correct="" d)="" digit="" e)="" equal="" give="" is="" it="" middle="" not="" number="" number.="" the="" thus="" to="" will="" wrong="" x="" xy="" y="" y.="" yx="">x & will give 3 digit number & middle digit is Y</x>
Answer: C
A man sells two articles for Rs.3600 each and he gains 48% on the first and loses 48% on the next. Find his total gain or loss?  Options:
A) 9% loss
B) 400
C) 4000
D) 324
E) 23.04%loss

Solution: (48*48)/100= 
(48*48)/100 = 576/25 = around 23.04
23.04%loss   ANSW23.04%lossR:23.04%loss
Answer: E
X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work? Answers.
A) 2	B) 3	C) 6	D) 7	E) 8

Solution: Work done by X in 1 day = 1/18   Work done by Y in 1 day = 1/15   Work done by Y in 10 days = 10/15 = 2/3   Remaining work = 1 – 2/3 = 1/3   Number of days in which X can finish the remaining work = (1/3) / (1/18)= 
(1/3) / (1/18) = 6
6   6
Answer: C
The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Pick.
A) 180
B) 787
C) 178
D) 179
E) 172

Solution: Let the five numbers be P, Q, R, S and T.   => P + Q + R + S + T = 655.   (P + Q)/2 = 85 and R = 125   P + Q = 170 and R = 125   P + Q + R = 295   S + T = 655 - (P + Q + R) = 360   Average of the last two numbers   = (S + T)/2 = 180.   180nswer:180
Answer: A
When a number is divided by 6 &then multiply by 12 the answer is 13 what is the no.?	Select the correct option:
A) 6.5  B) 5  C) 5.5  D) 5.8  E) 6

Solution: if $x$ is the number, x/6 * 12 = 13   => 2x = 13   => x = 6.5   6.5
Answer: A
A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6500?  Choose one.
A) Rs. 5870  B) Rs. 5991  C) Rs. 8870  D) Rs. 6850  E) None of these

Solution: Explanation:   Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130   Therefore, required sale = Rs. [(6500 * 6) – 30,130] = Rs. (39000 – 30,130) = Rs. 8870   ANSWER Rs. 8870
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good. Pick:
A) 20/68  B) 20/63  C) 20/69  D) 20/64  E) 20/62

Solution: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63.Answer: 20/63
Answer: B
A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A? Choose the correct choice from the following choices.
A) Rs.240 B) Rs.340 C) Rs.260 D) Rs.280 E) Rs.440

Solution: LCM = 180   Share of Rs.240 = (LCM/a x Total amount)/LCM/a + LCM/b + LCM/c   = (180/15)/(180/15 +180/20 + 180/45)   = (12/25) * 500   = Rs.240   Rs.240NSWER:Rs.240
Answer: A
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1/2 m board?
Choose the correct choice from the following answers:	A) 99	B) 18	C) 16	D) 10	E) 231

Solution: 70 * 33/2 = 5/2 * 2 * x => x   = 231   Answer:231
Answer: E
A train 300 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going? Choose the correct option:	A) 6 sec.	B) 7 sec.	C) 9 sec.	D) 18 sec.	E) None

Solution: Solution   Speed of the train relative to man	=( 68 - 8 )= 
( 68 - 8 ) = 60
60 Kmph= 60 x 5 / 18   =50/3 m/sec.   Time taken by it to cover 300 m at (50 /3)m/sec   = (300 x 3/50)sec   = 18 sec.   Answer 18 sec.
Answer: D
3,7,12,18,25..............10th terms Options:	A) 43	B) 53	C) 63	D) 65	E) 74

Solution: 3+4= 
3+4 = 7
7   7+5= 
7+5 = 12
12   12+6= 
12+6 = 18
18   18+7= 
18+7 = 25
25   25+8= 
25+8 = 33
33   33+9= 
33+9 = 42
42   42+10= 
42+10 = 52
52   52+11= 
52+11 = 63
63   63+11= 
63+11 = 74
74   ANSW74R:74
Answer: E
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Choose the correct choice from the following answers:
A) 120	B) 139	C) 140	D) 122	E) 178

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120rea of the triangle = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2   120nswer: Option 120
Answer: A
The grade point average of one third of the classroom is 54; the grade point average of the rest is 45. What is the grade point average of the whole class?
Choose one: A) 52 B) 54 C) 48 D) 58 E) 60

Solution: Let n=total students in class   total points for 1/3 class=54n/3=18n   total points for 2/3 class54 /3= 
54 /3 = 18
18n   total points for 2/3 class=45*2n/3=30n   total points for whole class45*2 /3= 
45*2 /3 = 30
30n   total points for whole class=18n+30n=48n   48n total class points/n total students18 +30= 
18 +30 = 48
48n   48n total class points/n total students=48 grade point average for total class   Answer : 48
Answer: C
Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:  Choose the correct choice from the following:
A) broke even	B) lost 10 cents	C) lost 4 cents	D) gained 10 cents	E) gained 4 cents

Solution: 20 % profit on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Similarly, 20 % loss on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.   Since both profit and loss amount is same so, it’s broke even.
Answer: A
The speed of a car is 98 km in the first hour and 60 km in the second hour. What is the average speed of the car?  Choose the correct choice from the following choices.
A) 76 kmph  B) 75 kmph  C) 87 kmph  D) 79 kmph  E) 86 kmph

Solution: S = (98 + 60)/2= 
(98 + 60)/2 = 79
79 kmph   Answer: 79 kmph
Answer: D
A test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232?
Select the correct option:	A) A)1.2	B) B)2.4	C) C)5	D) D)5.6	E) E)7

Solution: 1.2 test has a mean of 220 and a standard deviation of 10,   find the corresponding z score for:   a) a test score of 232,   z(232) = (232-220)/10 = 12/10= 
12/10 = 6/5 = around 1.2
1.2   Option 1.2
Answer: A
If x and y are integers and x + y = 7, which of the following must be true?
Choose the correct choice:  A) x and y are consecutive integers.  B) Both x and y are less than 5.  C) If x > 0, then y < 0.  D) Both x and y are even.  E) If x < 0, then y > 0.

Solution: In option C if x > 0,then y<0 means x is +ve and y is -ve   In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.   How option If x < 0, then y > 0. is right could you explain
Answer: E
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 140 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire? Choose the correct choice from the following choices: A) 90 B) 120 C) 160 D) 360 E) 560

Solution: If we exclude those cases and take the question at face value, then it seems straightforward.   Group #1 = (didn't like, didn't understand) = 120   Group #2 = (likeunderstood) = 3/4   (1/4)N = 560   N = 480   Answer =(560)
Answer: E
An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 1/2 %, then the amount invested at 11% was?
Select.
A) 23777
B) 25000
C) 29977
D) 26777
E) 19871

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,   (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 19/2 * 1/100)   (9x + 1100000 - 11x) = 950000   x =75000   Sum invested at 9% = Rs. 75000   Sum invested at 11% = Rs. (100000 - 75000) = Rs. 25000.   Answer: 25000
Answer: B
There are 100 fish in a pond. A fisherman put 20 more fish in the pond. How many fish are in the pond Choose the correct choice from the following answers
A) 0 B) 19 C) 178 D) 140 E) 120

Solution: If there are 100 fish and you put 20 more fish in the pond, you will have 120 fish     100+20= 
  100+20 = 120
120 120
Answer: E
A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
Choose the correct answer
A) 2.15 p.m.	B) 1.15 p.m.	C) 4.15 p.m.	D) 3.15 p.m.	E) 12.15 p.m.

Solution: Suppose they meet x hours after 10 a.m.   Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.   65x + 35(x-1) = 390 => 100x = 425 => x =	17/4   So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.   Option 2.15 p.m.
Answer: A
Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by  Select the correct option.
A) 6
B) 3 × 2^a
C) 2 × 3^(2a)
D) 6^a
E) 6^(2a)

Solution: Easiest method is to assume a value of a = 1   Given n is divisible by 2^2 ---> n = 2^1*p ---> n =2p   Also, n is also divisible by 3^(2a) ---> n = 3^(2a) * q = 3^2*q = 9q   Lets look at a few numbers that are multiples of both 2 and 9 are 18,36,72....   Thus looking at the options , A-D divide the numbers 18,36,72.... while E (=6^(2) = 36 ) does not divide 18. Thus 6^(2a) is the correct answer.
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 27 seconds. What is the length of the train? Choose the correct option:
A) 186 m B) 176 m C) 450 m D) 150 m E) 765 m

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train   = (Speed x Time) = (50/3 * 27)= 
(50/3 * 27) = 450
450 m.   Answer: 450 m
Answer: C
An alloy weighing 48 ounces is 25% gold. How many ounces of pure gold must be added to create an alloy that is 40% gold? Choose the correct choice from the following answers.
A) 15  B) 20  C) 12  D) 14  E) 7

Solution: An alloy of 48oz which is 25% gold means there is 12 oz of gold. To get to an alloy that is 40% gold, let's use this expression: (12 + x)/(48 + x) = 0.40 with x representing the amount of pure gold that must be added to get to 40%. The expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40% or 0.4. you will see that 12 is the correct answer, as  24/60= 
 24/60 = 2/5 = around 0.4
0.4   12hoose 12
Answer: C
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction R of time taken by the two wide pipes working together to fill the tank?  Choose the correct choice from the following choices:
A) 1/2 B) 2/3 C) 3/4 D) 3/7 E) 4/7

Solution: I always plug in for these questions.. I find them easier   Let 2 large pipes each work fill 10lts/hr   small ones = 1/2*10= 
1/2*10 = 5
5   total 5= 10+10+5+5+5= 
10+10+5+5+5 = 35
35 lts/hrs   now assume the total capacity= 140 lts ( LCM of 20,35)   Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank   all working together will take 140/35= 
140/35 = 4
4 hrs   two large pipes working will take   140/20= 
  140/20 = 7
7 hrs   hence ratio R= 4/7 = 4/7
Answer: E
Can you find the missing number in the sequence given below?
10 16 22 11 17 ? 12 18 24 13 19 25	Choose the most appropriate option:
A) 25
B) 23
C) 20
D) 18
E) 19

Solution: Let's break the given series as below:   10 16 22   11 17 ?   12 18 24   13 19 25   Now read the number from left hand side from top to bottom as :   So the number that will replace '?' is 23   Answer : 23
Answer: B
A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be A's share of the earnings?	Choose the correct option
A) $1100
B) $520
C) $1040
D) $1170
E) $630

Solution: Explanatory Answer   A, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.   As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.   Similarly, B will complete 1/8th and C will complete 1/12th of the work.   So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12   Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.   We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.   i.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.   Hence, A's share will be  4*2340/9= 
 4*2340/9 = 1_040
1040   correct choice is ($1040)
Answer: C
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 4 to n, inclusive. If p is the smallest prime factor of h(100) +4, then p is?
Choose the most appropriate option:
A) 4	B) between 10 and 20	C) between 20 and 30	D) between 30 and 40	E) 2

Solution: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 100. So h(100)+4 will have 4 in the units digit so smallest prime factor is 4.   4nswer: 4
Answer: A
Two numbers differ by 5. If their product is 336, then sum of two number is  Choose the correct choice from the following options.
A) 33	B) 34	C) 36	D) 37	E) 38

Solution: Explanation:   Friends you remember,   =>(x+y)2=(x−y)2+4xy   =>(x+y)2=(5)2+4(336)   =>(x+y)=1369−−−−√=37   Option 37
Answer: D
Which of the following numbers is between 1⁄3 and 1⁄2?
Answers
A) .45	B) .32	C) .29	D) .22	E) .20

Solution: Isn't it .45?   1/3 = .33   1/2= 
1/2 = 1/2 = around 0.5
.50   The only answer between that is .45, .45.
Answer: A
A customer went to a shop and paid a total of $30, out of which 90 cents was for sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Pick.
A) $12.70  B) $13.20  C) $14.10  D) $15.60  E) $16.80

Solution: The total cost was $30.   The tax was $0.90   Let the original price of the taxable items = x   Given that tax rate = 6%   0.06x = 0.90   x = $15   The cost of the tax free items was $30 - $15 - $0.90 = $14.10   The answer is $14.10.30 -  15 -  0.90= 
30 -  15 -  0.90 = 14.1
$14.10   The answer is $14.10.
Answer: C
Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?	Pick one
A) 20% B) 17% C) 4.0% D) 3.3% E) 2.8%

Solution: 20/6 =3.33   Answer : 3.3%
Answer: D
Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
Choose the correct choice from the following answers:  A) 87 km/hr  B) 70 km/hr  C) 76 km/hr  D) 97 km/hr  E) 57 km/hr

Solution: Let their speed be x km/hr and y km/he respectively.   Then, 120/(x + y) = 1 => x + y = 120 --- (i)   Now, when they move in same direction:   (Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km   6x - 6y = 120 => x - y = 20 --- (ii)   Sloving (i) and (ii), we get x = 70, y = 50   P's speed = 70 km/hr.   Answer: 70 km/hr
Answer: B
How many prime numbers are between 28/3 and 86/6?
Choose the correct choice from the following options.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 28/3 = 9.xxx   86/6 = 14.xxx   So we need to find Prime numbers between 9 (Exclusive) - 13 (Inclusive)   There are 2 Prime numbers 1113   Hence answer will be (2) 2   2
Answer: B
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.1 , what is the value of n?  Select:
A) 9
B) 20
C) 55
D) 70
E) 81

Solution: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:   We're told that K and N are both INTEGERS.   Since K/N = 81.2, we can say that K = 81.2(N)   N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.   With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)   Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH   Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.   Final Answer:   81
Answer: E
A test of 10 questions is chosen from 10 hard questions and 20 easy questions. The salad must have at least 4 hard questions at least 3 easy questions. How many ways can this test be created?
Pick one:
A) 13500611
B) 13200688
C) 13200858
D) 895
E) 7289

Solution: Solution: We have four possibilities 4H 6E , 5H 5E, 6H 4E, 7H 3E   (10132008584)(20132008586)+(10132008585)(20132008585)+(10132008586)(20132008584)+(10132008587)(20132008583)=13200858   13200858) 13200858
Answer: C
On day one, a store sold 90 books. On each of the next d days, the company sold 62 books. If the average daily sales of books over this time period (including day one) is 66 books, what is the value of d? Options: A) 5 B) 6 C) 7 D) 8 E) 9

Solution: 90 + 62d = 66(d+1).   4d = 24.   d = 6.   The answer is 6.
Answer: B
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? Choose one.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: You need to primarily find the primes of 990:   2,3,3,5,11   The integer must contain all these primes   By knowing 11 is an prime, we know the answer can be B,C,D or E as these all contain 11.   11=1,2,3,4,5,6,7,8,9,10,11   11 contains the 2,3,5 and 11 explicitly and the second 3 comes from the 6 (2*3), therefore the answer is 11.   This is because we know a number that contains all the primes of 990 will be a multiple of 990.   ANSWER:11
Answer: B
A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?	Select: A) 2 months B) 3 months C) 5 months D) 4 months E) 1 months

Solution: Suppose B was there in the business for x months. Then   A : B =76000×12:57000×x   Therefore,   76000×12:57000×x=2:1   76×12:57x=2:1   76×12×1=57x×2   76×4=19x×2   4×4=(x)×2   x=8   Hence B was there in the business for 8 months, or joined after   12-8= 
  12-8 = 4
4 months   Answer is 4 months.
Answer: D
An article is bought for Rs.600 and sold for Rs.500, find the loss percent? Options.
A) 16 2/3%	B) 15 2/3%	C) 18 2/3%	D) 11 2/3%	E) 22 2/3%

Solution: 16 2/3%   16 2/3%   600 ---- 100   100 ---- ? => 16 2/3%
Answer: A
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Answers:
A) 1000
B) 2777
C) 289
D) 2779
E) 27871

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000.1000nswer: 1000
Answer: A
How much time will take for an amount of Rs. 200 to yield Rs. 81 as interest at 4.5% per annum of simple interest?  Options.
A) 7	B) 4	C) 5	D) 3	E) 9

Solution: Time = (100 * 81) / (200 * 4.5) = 4 years'   Answer:9
Answer: E
P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?	Options
A) 9(3/5) days B) 9(1/5) days C) 9(2/5) days D) 10 days E) 15 days

Solution: Explanation :   9(3/5) daysmount of work P can do in 1 day = 1/16   9(3/5) daysmount of work Q can do in 1 day = 1/12   9(3/5) daysmount of work P, Q and R can together do in 1 day = 1/4   9(3/5) daysmount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 â€“ 1/12 = 5/48   => Hence R can do the job on 48/5 days = 9 (3/5) days   9(3/5) daysNSWER IS 9(3/5) days
Answer: A
A contractor undertook to do a piece of work in 6 days. He employed certain number of laboures but 7 of them were absent from the very first day and the rest could finish the work in only 10 days. Find the number of men originally employed ?  Choose the correct choice from the following answers
A) 17.2 B) 16.5 C) 17.5 D) 17.9 E) 17.3

Solution: Let the number of men originally employed be x.   6x = 10(x â€“ 7)   or x = 17.5   Answer 17.5
Answer: C
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors Q?
Pick:
A) 2 B) 3 C) 5 D) 6 E) 8

Solution: I like to put the numbers in prime factors so it is easier and faster to visualize.   14*n/60   If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have   (2*7*n)/(2^2*3*5)   Simplifying   7*n/(2*3*5)   The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.   The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....   However to be less than 200 we can not add any prime number.   2*3*5 = 120   If we added the next prime factor 7, we would have Q=2*3*5*7 = 840   Thus, answer 3.
Answer: B
Today David, who is 40 years old, and his daughter, who is 12 years old, celebrate their birthdays. How many years will pass before David’s age is twice his daughter’s age?  Choose the correct choice.
A) 22  B) 20  C) 16  D) 18  E) 14

Solution: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.   After x years passes David’s age will be (40+x) years old, and his daughter’s age will be (12+x) years old. Since the David’s age is twice his daughter’s age (40+x)= 2 * (12+x) --->   40+x=24+2x ---> x= 16   The answer is (16).
Answer: C
9000 + 16 2/3 % of ? = 10500
Choose the most appropriate option
A) 1500
B) 1750
C) 9000
D) 7500
E) None of these

Solution: Explanation:   9000 + 16 2/3 % of ? = 10500 => 9000 + 50/3 % of ? = 10500   50/(3 * 100) of ? = 1500 => ? = 1500 * 6= 
1500 * 6 = 9_000
9000   ANSWER IS 9000
Answer: C