MU-NLPC/Calc-aqua_rat huggingface dataset:
In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is ?	Choose the correct choice from the following answers:
A) 11
B) 82
C) 10
D) 28
E) 23

Solution: Explanation:   Total employees = \inline \frac{(25-10)\times 20}{10}=30   Hence number of educated employees = 30-20= 
30-20 = 10
10   Answer: 10
Answer: C
Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48?	Choose the correct choice from the following:  A) 240/1576  B) 240/1542  C) 240/1547  D) 240/1528  E) 240/1529

Solution: P : 2/13 = 5/34 : 7/48   As the product of the means is equal to the product of the extremes.   P*7/48 = 2/13 * 5/34   P*7/48 = 10/442   P = 480/3094 => P = 240/1547   Answer: 240/1547
Answer: C
If the average of q, b, c, 14 and 15 is 12. What is the average value of q, b, c and 29
Pick
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: q+b+c+14+15 = 12*5= 
12*5 = 60
60=>q+b+c = 60-29= 
60-29 = 31
31   q+b+c+29= 31+29= 
31+29 = 60
60   Average= 60/4= 
60/4 = 15
15   Answer 15
Answer: D
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 5th shift? Choose the correct choice from the following answers
A) 1/27	B) 1/54	C) 1/81	D) 1/162	E) 1/216

Solution: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2   Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)   Fraction of area unpainted after SECON1/162 shift of Amit = (1/2)(2/3)(1/2)   Fraction of area unpainted after SECON1/162 shift of Ian = (2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after THIR1/162 shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after THIR1/162 shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)   Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=1/162   Answer: option 1/162
Answer: D
Average of first five multiples of 2 is Choose one: A) 9 B) 6 C) 13 D) 15 E) 16

Solution: Explanation:   Average=2(1+2+3+4+5)5=6   Answer: Option 6
Answer: B
The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?	Pick
A) 6
B) 8
C) 9
D) 10
E) 12

Solution: Let the number be xy.   Given xy – yx = 36.   This means the number is greater is than the number got on reversing the digits.   This shows that the ten’s digit x > unit digit y.   Also given ratio between digits is 1 : 2 => x = 2y   (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.   Hence, (x + y) – (x – y) = 3y – y = 2y = 8   8
Answer: B
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is? Pick one:
A) 227	B) 268	C) 245	D) 299	E) 271

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer:245:
Answer: C
A bag contains 15 purple jellybeans, 10 green jellybeans, and 10 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?	Choose the most appropriate option.
A) 15%	B) 29%	C) 25%	D) 30%	E) 35%

Solution: Probability of green beans = 10 / (15 + 10 + 10) = 10/35 = 29%   Answer is 29%
Answer: B
What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?	Pick:
A) Rs. 24800	B) Rs. 28400	C) Rs. 24400	D) Rs. 28800	E) None of these

Solution: Explanation:   Simple interest = (18000 * 4 * 15)/100 = Rs. 10800   Amount = P + I = 18000 + 10800 = Rs. 28800   ANSWER IS Rs. 28800
Answer: D
For the symbol, m”n=n^2−m for all values of m and n. What is the value of 3”3?  Choose the correct choice from the following options:
A) 6
B) 3
C) 2
D) 1
E) 0

Solution: 3”3= 9 - 3= 
9 - 3 = 6
6   6nswer: 6
Answer: A
In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is:	Choose the correct choice from the following.
A) 4	B) 5	C) 6	D) 7	E) 9

Solution: Explanation :   Let the required number of men be x.   Less days, More men (Indirect Proportion)   More working hrs per day, Less men (Indirect Proportion)   7ays 8 : 10   Working Hrs 15 : 9 :: 12 : x   => 12 x 15 x x = 10 x 8 x 12   => x = 10 x 9 x 12 / (12 x 15)   => x = 7   Answer : 7
Answer: D
Half of 1 percent written as decimal is
Choose the correct choice.
A) 5  B) 0.5  C) 0.05  D) 0.005  E) None of these

Solution: Explanation:   It will be 1/2(1%) = 1/2(1/100) = 1/200= 
1/200 = 1/200 = around 0.005
0.005   Option 0.005
Answer: D
If 20 typists can type 40 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?  Choose one
A) 63	B) 72	C) 144	D) 180	E) 400

Solution: 20 typists can type 40 letters, so 30 typists can type = 40*30/20   40*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 40*30*60/20*20= 180   180 is the answer
Answer: D
In a game of 60 points; A can give B 10 points and C 15 points. Then how many points B can give C in a game of 40 ? Pick:
A) can give C 1 points  B) can give C 4 points  C) can give C 2 points  D) can give C 6 points  E) can give C 8 points

Solution: A: B = 60 : 50, A : C = 60 : 45.   B/C = ( B/ A * A/C) = (50 / 60 * 60 / 45) = 10/9 = 40 /36   Therefore ,In a game of 40, B can give C 4 points.   Answer is can give C 4 points.
Answer: B
How many two letter words are formed using the letters of the word RAM?
Choose one.
A) 22
B) 6
C) 8
D) 10
E) 12

Solution: Explanation:   The number of letters in the given word is three.   The number of two letter words that can be formed using these four letters is Ã¢Â´PÃ¢â€šÆ’ = 3 * 2= 
3 * 2 = 6
6.   Answer: 6
Answer: B
Count each 7 which is not immediately preceded by 5 but is immediately followed by either 2 or 3.
How many such 7's are there ?
5 7 2 6 5 7 3 8 3 7 3 2 5 7 2 7 3 4 8 2 6 7 8	Pick.
A) 2  B) 4  C) 3  D) 5  E) None

Solution: Answer: A . 2
Answer: A
What is the 8th digit to the right of the decimal point in the decimal expansion of 1/37?
Pick one.
A) 0	B) 2	C) 4	D) 7	E) 9

Solution: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2,0,7, thus 8th digit to the right of the decimal point is 2.   Answer: 2.
Answer: B
If the average (arithmetic mean) of the four numbers K, 2K + 2, 3K – 5 and 5K + 1 is 63, what is the value of K?
Pick:
A) 11 B) 15 3/4 C) 22 D) 23 E) 23 1/11

Solution: K + 2K +2 + 3K - 5 + 5K +1 = 11K -2   (11K -2)/4 = 63   11K = 63 * 4 +2 = 252 +2= 
252 +2 = 254
254   K= 254 / 11 = 23 1/11   Answer 23 1/11.
Answer: E
In a series of consecutive odd numbers, 27 is the seventh smallest number and 25 is the tenth largest number. What is the range of the series?
Select.
A) 32  B) 30  C) 29  D) 28  E) 14

Solution: Imp:All are consecutive odd numbers.   27 is the 8th smallest ,there are 6 numbers smaller then 27 ,smallest number :  27-12= 
  27-12 = 15
15   25 is the 10th largest ,so there are 9 numbers larger then 25, largest number: 25+18= 
 25+18 = 43
43   Range:43-15= 
43-15 = 28
28   Ans : 28
Answer: D
Insert the missing number.
2, 4, 12, 48, 240, (....) Options
A) 3388 B) 1440 C) 398 D) 278 E) 2771

Solution: Explanation:   Go on multiplying the given numbers by 2, 3, 4, 5, 6.   So, the correct next number is 1440.   Answer: 1440) 1440
Answer: B
Bongani and Jane are friends. Bongani takes Jane's physics test paper and will not tell her what her mark is. He knows that Jane hates maths so he decides to tease her. Bongani says: “I have 2 marks more than you do and the sum of both our marks is equal to 14. What are our marks?”
Pick one
A) j=6,b=8  B) j=3,b=5  C) j=8,b=2  D) j=1,b=3  E) j=5,b=5

Solution: We have two unknown quantities, Bongani's mark and Jane's mark. Let Bongani's mark be b and Jane's mark be j.   Set up a system of equations   Bongani has 2 more marks than Jane.   b=j+2............(1)   Both marks add up to 14.   b+j=14............(2)   Use equation (1) to express b in terms of j   b=j+2   Substitute into equation (2)   b+j=14   (j+2)+j=14   Rearrange and solve for j   2j=14−2   =12   ∴j=6   Substitute the value for j back into equation (1) and solve for b   b=j+2   =6+2= 
6+2 = 8
8   Bongani got 8 for his test and Jane got 6.   j=6,b=8nswer is j=6,b=8.
Answer: A
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?  Choose the most appropriate option:
A) 20  B) 34  C) 38  D) 40  E) 46

Solution: We have that X/24 - (60-X)/2R = 40   Also X/R - (60-X)/2R = 120   So we get that 2x - 60 = 80R   3x - 60 = 240R   Get rid of R   120 = 3x   x = 40   Hence answer is 40
Answer: D
Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?	Choices
A) 8
B) 12
C) 15
D) 48
E) 24

Solution: x rate = k/6   y rate = k/12   k/6 + k/12 = 12k / T   solving T = 48   Answer 48
Answer: D
Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 200 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 4 of the days were hot, then what was the price of 1 cup on a hot day?	Choose one
A) $ 1.56 B) $ 1.88 C) $ 2.25 D) $ 2.50 E) $ 3.25

Solution: 6 regular days --> sales = 6*32*x = 192x;   4 hot days --> sales = 4*32*(1.25x) = 160x;   Total sales 4*32*(1.25 )= 
4*32*(1.25 ) = 160
160x;   Total sales= 192x+160x = 352x.   Total cost 192 +160= 
192 +160 = 352
352x.   Total cost= 10*32*0.75= 
10*32*0.75 = 240
240.   Profit= 352x - 240 = 200 --> x=1.25.   1.25x=~1.56.   $ 1.56nswer: $ 1.56.
Answer: A
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?  Select the correct option.
A) 2!  B) 8!  C) 9!  D) 10!  E) 15!

Solution: Ans.(B)   Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
A basketball player practices 2 hours a day Monday through Friday. How many hours must he practice Saturday and Sunday combined if he wants to practice an average (arithmetic mean) of 3 hours a day for the seven day week?	Choose the correct choice from the following answers
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Total number of hours practiced Mon through Fri: 5*2= 
5*2 = 10
10   Total number of hours that will be practiced in a 7 day week considering 3 hours a day average:  7*3= 
 7*3 = 21
21   thus   21-10= 
  21-10 = 11
11 hours still need to be practiced (on Sat and Sun combined)   11
Answer: D
In how many ways can you walk up a stairway with 6 steps if you
can take one or two steps at a time? (For example, you can walk up
a stairway with 3 steps in three dierent ways: (i) Take three single
steps. (ii) Take one step and then two steps. (iii) Take two steps and
then one step.)
Select:	A) 9	B) 10	C) 11	D) 12	E) 13

Solution: Let fn denote the number of ways one can get to the nth step. Given the example   in the problem, we see then that f3 = 3. It is easy to see f1 = 1 and f2 = 2 (the latterfollows since one can take one step twice or two steps at a time to get to the second step).   To determine the value of fn for any n >/3, think about the previous step a person would   have to be on before getting to the nth step. Since only one or two steps are allowed at a   time, the person would have to be either on the (n-1)st step or the (n-2)nd step there are by definition fn-1 ways someone can get to the (n - 1)st step and fn􀀀-2 ways a   person can get to the (n - 2)nd step, there must be fn-1 + fn-2 ways of getting to the   nth step (by first going to the (n- 1)st step in one of fn-1 ways and then taking a single   step or by first going to the (n-2)nd step in one of fn-2 ways and then taking two steps   at once). In other words, fn = fn-1 +fn-2. This allows us to easily compute fn for n>/3   successively. Specifically,   f3 = f2 + f1 = 2+1= 
2+1 = 3
3 (as we knew); f4= f3 + f2 = 3+2= 
3+2 = 5
5;   f5= f4 +f3 = 5+3= 
5+3 = 8
8; and f6= f5 + f4 = 8+5= 
8+5 = 13
13:   Therefore, the answer is 13.   correct answer is 13
Answer: E
Two numbers N and 24 have LCM = 48 and GCF = 8. Find N.
Select the correct option:	A) 16	B) 56	C) 76	D) 87	E) 24

Solution: The product of two integers is equal to the product of their LCM and GCF. Hence.   24* N = 48 * 8   N = 48*8 / 24= 
48*8 / 24 = 16
16 correct answer 16
Answer: A
Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 3 and the product of the given number and the sum of its digits is equal to 175.
Choose the correct choice from the following answers:  A) 25  B) 36  C) 47  D) 52  E) 63

Solution: Using the elimination method the option that fits this description is 25   5-2= 
5-2 = 3
3 (unit's digit that exceeds its ten's digit by 3)   25*7= 
25*7 = 175
175 (the product of the given number and the sum of its digits is equal to 175)   answer :25
Answer: A
If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.	Choose the correct choice:	A) 6 km	B) 8 km	C) 5 km	D) 3 km	E) 2 km

Solution: Let the required distance be x km   Difference in the time taken at two speeds=1 min =1/2 hr   Hence x/5-x/6=1/5<=>6x-5x=6   x=6   Hence, the required distance is 6 km   Ans: 8 km
Answer: B
Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 12 inches on a side and costs $10, and a large pizza that measures 18 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone? Pick one
A) 5 square inches  B) 36 square inches  C) 15 square inches  D) 25 square inches  E) 350 square inches

Solution: In the first case each can buy one pizza of $10 and one pizza of $20.   In square inches that would be (12*12=144) for the small pizza and (18*18=324) for the large pizza. In total sq inches that would be  (144+324)*2= 
 (144+324)*2 = 936
936 sq inches.   In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be   3*324= 
  3*324 = 972
972 sq inches.   Hence, the difference is 36 square inches more (972-936).   The correct answer is 36 square inches
Answer: B
A water tank is two-third full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Pick
A) 6 min. to empty B) 6 min. to full C) 10 min. to empty D) 9 min. to full E) 8 min. to full

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/3   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/3 :: 1 : x   x = (2/3 * 1 * 15)= 
(2/3 * 1 * 15) = 10
10 min.   So, the tank will be emptied in 10 min.   ANSWER:10 min. to empty
Answer: C
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 3, and 7, if the digits are allowed to repeat within a number? Pick:
A) 8,434  B) 9,656  C) 10,989  D) 11,323  E) 12,878

Solution: The number of these 3-digit numbers is   3*3*3= 
  3*3*3 = 27
27   Each digit 1, 3, and 7 will appear in the ones, tens, and hundreds place 9 times each.   The sum equals 9(111) + 9(333) + 9(777)= 10,989   The answer is 10,989.
Answer: C
When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?	Choose the correct option.
A) 3 : 4
B) 4 : 3
C) 3 : 2
D) Data inadequate
E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 30% of x = 140% of y   or, y + 0.3x = 1.4y   or, 0.3x = 0.4y   ∴ x : y = 0.4 : 0.3 = 4 : 3   Answer 4 : 3
Answer: B
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)
Answers: A) 0 B) 4 C) 6 D) 7 E) 13

Solution: explanations   We have the function f(x) = 3x – 5, and we want to some sophisticated algebra with it. Let’s look at the two sides of the prompt equation separately. The left side says: 2*[f(x)] – 1 —- this is saying: take f(x), which is equal to its equation, and multiply that by 2 and then subtract 1.   2*[f(x)] – 1 = 2*(3x – 5) – 1 = 6x – 10 – 1 = 6x – 11   The right side says f(3x – 6) — this means, take the algebraic expression (3x – 6) and plug it into the function, as discussed above in the section “How a mathematician things about a function.” This algebraic expression, (3x – 6), must take the place of x on both sides of the function equation.   f(3x – 6)= 3*[3x – 6] – 5 = 9x – 18 – 5 = 9x – 23   Now, set those two equal and solve for x:   9x – 23 = 6x – 11   9x = 6x – 11 + 23   9x = 6x + 12   9x – 6x = 12   3x = 12   x = 4   Answer = 4
Answer: B
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?	Choose the correct choice from the following answers: A) 65 sec B) 55 sec C) 48 sec D) 33 sec E) 60 sec

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 1.4= 
1.10 + 1.4 = 2.5
2.5 km= 2500 m.   Required time = 2500 * 3/125= 
2500 * 3/125 = 60
60 sec.   Answer:60 sec
Answer: E
Tickets numbered from 1 to 22 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?	Choose the correct choice from the following choices.
A) 1/5	B) 2/5	C) 3/10	D) 3/7	E) 7/22

Solution: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22]   Let 7/22 = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21]   P (7/22) = n (7/22) / n (S) = 7 / 22   The answer is 7/22.
Answer: E
How many minutes does it take John to type z words if he types at the rate of x words per minute?
Pick:
A) x/y	B) z/x	C) xy	D) 60x/y	E) y/(60x)

Solution: time*rate=job --> time*x=z --> time=z/x.   Answer: z/x.
Answer: B
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Choose the correct choice from the following choices:	A) 6 months	B) 8 months	C) 9 months	D) 10 months	E) 12 months

Solution: T10 months=Amt*R*T/(100+RT)   given T10 months=160,Amt=1760,R=12,T=?   by substituting the values we get,   160=(1760*12T)/(100+12T)   160(100+12T)=1760*12T   100+12T=(1760*12T)/160   100+12T=132T   120T=100   t=100/120=5/6yrs i.e (5/6)*12=10months   ANSWER:10 months
Answer: D
The average of first 20 even numbers is? Choose the correct option:
A) 19
B) 18
C) 16
D) 11
E) 21

Solution: Sum of 20 even numbers = 20 * 21= 
20 * 21 = 420
420   Average=420/20= 
420/20 = 21
21   Answer:21
Answer: E
A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, 4, 5, 6, and 7, how many palindromes are possible? Answers:  A) 35  B) 49  C) 105  D) 255  E) 343

Solution: There are 7 choices for each of the first three digits.   The number of possible palindromes is 7^3=343.   The answer is 343.
Answer: E
3,7,12,18,25,..............6th terms	Choose the most appropriate option:	A) 43	B) 53	C) 63	D) 33	E) 78

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   ANSWER:33
Answer: D
A sequence contains y numbers of alternating positive and negative numbers, If the first number is postive and y is an even number, how many negative numbers are in it?  Choose the correct choice from the following choices
A) (y+1)/2 B) (y-1)/2 C) y/(2+1) D) y/(2-1) E) y/2

Solution: Lets put values for y, say y=8 since it's even   and first number is positive so sequence will be {pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 4 negative terms   so putting y=8 in the options,   option y/2 = y/2 => 8/2= 
8/2 = 4
4 , the number of negative integers   So, y/2 is the answer
Answer: E
In how many ways 8 different tickets T can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.  Choose one:
A) From 2 to 6 inclusive.	B) From 98 to 102 inclusive.	C) From 122 to 126 inclusive.	D) From 128 to 132 inclusive.	E) From 196 to 200 inclusive.

Solution: Possibilities   J 8 6 4 2 0   B 0 2 4 6 8   # of ways 8C8 8C6 8C4 8C2 8C0   T=1+28+70+28+1= 
1+28+70+28+1 = 128
128 Answer is From 128 to 132 inclusive..
Answer: D
Company A has 13 employees, 8 of whom belong to the union. If 4 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift? Pick one.
A) 56 B) 231 C) 336 D) 350 E) 406

Solution: Looks easy: -- 8C4*4C1 + 8C5 --350 (350).
Answer: D
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 844 in 4 years. The sum is:  Answers:  A) s. 650  B) s. 690  C) s. 698  D) s. 728  E) s. 760

Solution: S.I. for 1 year = Rs. (844 - 815) = Rs. 29.   S.I. for 3 years = Rs.(29 x 3) = Rs. 87.   Principal = Rs. (815 - 87) = Rs. 728.   Answer: Option s. 728
Answer: D
The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 12, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.) Choose one:	A) 36	B) 47	C) 58	D) 55	E) 72

Solution: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.   Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.   As given that N = P + 12, then N=2*N/2.54+12 --> N=~55.   Answer: 55.
Answer: D
John draws a card from a pack of cards. What is the probability that the card drawn is a card of black suit?
Choose the correct choice from the following answers:
A) 1/2
B) 1/4
C) 1/3
D) 1/13
E) 1/15

Solution: Tot no of cards n(S) = 52   Tot no of black cards = 26   =>26/52=1/2   1/2NSWER 1/2
Answer: A