MU-NLPC/Calc-aqua_rat huggingface dataset:
If q=4p where p is a prime number greater than 2, how many different positive even divisors does q have, including q?
Choose the most appropriate option:
A) two	B) three	C) four	D) six	E) eight

Solution: q=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)   2   4 (because of 2*2)   2p (because of 2 * p)   4p (because of 2 * 2 * p)=four
Answer: C
If * stands for +, / stands for * and + stands for /, then which of the following equations is TRUE? Pick one:
A) 7*14/7+35-14=-4.2	B) 5+7*7-5/14=24	C) 14*5/7+35-14=-10.1	D) 5/7*7+35-14=4	E) None of these

Solution: 7*14/7+35-14 will become   7+14*7/35 - 14 = -7 + 14/5 = -21/5 = -4.2   7*14/7+35-14=-4.2NSWER:7*14/7+35-14=-4.2
Answer: A
A firm has 3 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (2 groups are considered different if at least one group member is different)	Pick one:  A) 64  B) 72  C) 84  D) 96  E) 120

Solution: The total number of ways to form a group of 3 is 9C3 = 84   The number of groups without a senior partner is 6C3 = 20   The number of groups which include a senior partner is  84-20= 
 84-20 = 64
64   The answer is 64.
Answer: A
Peter and Rhea lives some distance apart from each other, separated by a straight road. They both take out their cars and start driving at the same time with the same speed towards each other's home.
After some time, their cars meet at 500 miles away from Peter's house. They keep driving and reach at each other's home. Without stopping by, they turn back and start driving again. This time, they meet 300 miles away from each other's home.
What is the distance between their houses?	Answers
A) 1200 Miles. B) 110 Miles. C) 1300 Miles. D) 1400 Miles. E) 1500 Miles.

Solution: Solution:   Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.   When P and R meet for the first time, P has traveled 500 miles.   In that case, R has traveled (D - 500) miles.   => Speed of P / Speed of R = 500 / (D - 500) ...... (1)   When P and R meet for the second time, P has traveled (D - 500) + 300 miles   Now, R has traveled (500 + D - 300)   => Speed of P / Speed of R = 5 / (D - 5) ..... (2)   Equating (1) and (2)   500 / (D - 500) = (D - 2) / (D + 2)   D = 1200 Miles.   1200 Miles.nswer 1200 Miles.
Answer: A
A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 20 gallons of gasoline?  Choose the most appropriate option.
A) 190	B) 284.6	C) 300	D) 244	E) 312

Solution: so 12.2 * 20 = 244..   IMO option 244 is correct answer..
Answer: D
R-R-R-G-G-G-Y-Y-B-R-R-R-G-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
Choose the correct choice from the following choices
A) 62
B) 63
C) 64
D) 65
E) 66

Solution: The repeated pattern R-R-R-G-G-G-Y-Y-B has 9 beads.   But the missing section includes R-R-R-G-G-G-Y-Y at the end.   Thus the number of beads in the missing section has the form 9k + 8.   The answer is 62.
Answer: A
If 4 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture? Choices:
A) (4x + 2y)/5 B) (4x + 2y)/(x + y) C) (4x + 2y)/(xy) D) 5(4x + 2y) E) 4x + 2y

Solution: Total Cost = Weight(in pounds) * Price/pound;   To find Total cost/pound, Divide by total pounds.   Cost of Dried apricots = 4x;   Cost of prunes = 2y;   Cost per pound = (4x + 2y)/5;   (4x + 2y)/5ns is ((4x + 2y)/5).
Answer: A
Once I had been to the post office to buy five-rupee, two-rupee and one-rupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more one-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought ? Choose the correct option:	A) 10	B) 9	C) 12	D) 8	E) 4

Solution: Explanation :   At least two stamps of each type were ordered initially.   So, Rs.2 ( 5 + 2 + 1 ) = Rs.16 have been spent.   That leaves ( 20 – 16 ) = Rs.4.   In this Rs.4, three more stamps of one rupee were given, thus accounting for Rs.19 in all.   Since, one more rupee remains, it means that one more stamps of Rs.1 were bought initially.   So the total number of stamps is 2(of Rs.5) + 2(of Rs.2) + 6(of Rs.1). i.e 10.   10nswer : 10
Answer: A
Three unbiased coins are tossed. What is the probability of getting at most two heads?  Choices
A) 3/4
B) 1/4
C) 7/8
D) 3/8
E) 2/8

Solution: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting at most two heads.   Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.   P(E) =	n(E)	=	7	.   n(S)	8   Answer : 7/8.
Answer: C
What number has a 5:1 ratio to the number 13?
Choose the correct choice
A) 22  B) 50  C) 88  D) 65  E) 12

Solution: 5:1 = x: 13   x = 65   Answer: 65
Answer: D
The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?	Choose the correct choice
A) 19 B) 20 C) 1 D) 0 E) 25

Solution: 19vg of 20 nos = 0   sum of 20 numbers/20 = 0   sum of 20 nos = 0   =>19 positive nos   19NSWER 19
Answer: A
In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?  Answers.
A) 20
B) 25
C) 30
D) Data inadequate
E) None of these

Solution: In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively.   say 3x and 2x respectively.   If the number of boys participating in the sports is 15,no of girls participating in sports = 10.   Total students participating out of 60 in class = 15+10= 
15+10 = 25
25   Total students not participating out of 60 in class= 60-25= 
60-25 = 35
35   The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports.   so out of 45 not participating in sports, 20 are girls and 15 are boys.   No of girls in class= 20+10= 
20+10 = 30
30   ANSWER:30
Answer: C
Lisa earns a profit of $3 on each ribbon that she sells, and $5 on each bracelet. If at the end of the day Lisa has earned $120 and she has sold at least 10 pieces of each item. At least how many bracelets she has sold?
Choices
A) 2  B) 5  C) 9  D) 12  E) 15

Solution: Since Lisa has sold at least 10 pieces for each item, let us say Lisa sells (10 + r) number of ribbons and (10 + b) number of bracelets, her profit for the day = 3(10 + r) + 5(10 + b)   => 3(10 + r) + 5(10 + b) = 120   => 30 + 3r + 50 + 5b = 120   => 3r + 5b = 120 - 30 - 50= 
120 - 30 - 50 = 40
40=> 5b = 40 - 3r   => b = 8 - (3/5)r   To minimize b, we need to maximize r and it will be a multiple of 5.   r = 5, b = 8 - (3/5)5 = 5   r = 10, b = 8 - (3/5)10 = 2   Beyond that b will become -ve. So Lisa has sold at least 10 + 2= 
10 + 2 = 12
12 bracelets.   Answer: 12
Answer: D
The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 14000, then find the annual income of A?
Choose the correct choice from the following answers.
A) Rs. 420000  B) Rs. 180000  C) Rs. 201600  D) Rs. 470400  E) None of these

Solution: B's monthly income = 14000 * 112/100 = Rs. 15680   B's monthly income = 2 parts ----> Rs. 15680   A's monthly income = 5 parts = 5/2 * 15680 = Rs. 39200   A's annual income = Rs. 39200 * 12 = Rs. 470400   ANSWER:Rs. 470400
Answer: D
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $61, how much does one shirt cost? Select
A) $9	B) $12	C) $13.20	D) $15	E) $16.80

Solution: 3J + 2S = 69   2J + 3S = 61   ----------------   5J + 5S = 130 ----(divide by 5)---> J + S = 26   3J + 2S = J + 2(J + S) = J + 52 = 69 ---> J = 17   3*17 + 2S = 69   51 + 2S = 69   2S = 18   S = 9   $9nswer: $9
Answer: A
Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 2/3 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors?	Select the correct option
A) 3/20 B) 1/3 C) 3/7 D) 2/7 E) 7/2

Solution: Let total number of juniors= J   total number of seniors =S   (2/3) J = (1/2) S   => S = 4/3 J   Total number of students = J+S = (7/3) J   Fraction of the students in the room are juniors = J/(J+S) = J/[(7/3) J]   =3/7   Answer 3/7
Answer: C
If x is a positive integer, which of the following must be odd?
Choose the correct choice from the following choices:
A) x+1	B) x^2+x	C) x^2+x+5	D) x^2−1	E) 3x^2−3

Solution: A. X+1 = can be odd or even. Since O + O =E or E + O = O   B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]   C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 5 = ODD   Hence x^2+x+5.
Answer: C
log3 N+log9 N what is 3 digit number N that will be whole number	Choose the most appropriate option:
A) 629
B) 729
C) 829
D) 929
E) 727

Solution: No of values N can take is 1   9^3=729   ANSWER:729
Answer: B
What least number must be added to 3000 to obtain a number exactly divisible by 19 ? Answers
A) 2
B) 19
C) 9
D) 4
E) 8

Solution: On dividing 3000 by 19, we get 17 as remainder.   Number to be added = (19 - 17)= 
(19 - 17) = 2
2.   2NSWER 2 2
Answer: A
The speed of a boat in upstream is 20 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose the correct choice from the following answers
A) 30 kmph	B) 13 kmph	C) 65 kmph	D) 55 kmph	E) 14 kmph

Solution: Speed of the boat in still water   = (20+80)/2= 
(20+80)/2 = 50
50 kmph. Speed of the stream= (80-20)/2= 
(80-20)/2 = 30
30 kmph.   30 kmphnswer: 30 kmph
Answer: A
The cost of 2 chairs and 3 tables is Rs.1800. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
Choose the correct choice from the following choices:
A) 228  B) 287  C) 277  D) 188  E) 600

Solution: 600xplanation:   2C + 3T = 1800 --- (1)   3C + 3T = 1200 --- (2)   Subtracting 2nd from 1st, we get   -C + T = 600 => T - C = 600   Answer:600
Answer: E
If 3^a - 3^(a-1) = 162 then a(a-1) = Choose one:
A) 12
B) 16
C) 20
D) 30
E) 81

Solution: It seems like you were really close but you solved for a - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of a(a -1), e.g. (3)(4) = 12. Even then, had you figured a has to be a little bigger (plugging in 4 for a gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (a - 1) exponent place.   Again, a quick plugging in should get you (20) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: C
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Choose the correct choice
A) 1/3 B) 1/5 C) 1/7 D) 1/9 E) 2/3

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1/3)
Answer: A
A certain company’s profit in 1996 was 17 percent greater than its profit in 1995, and its profit in 1997 was 25 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? Choose the correct choice from the following answers.
A) 5%
B) 18%
C) 33%
D) 35%
E) 46.25%

Solution: Profit in 1995 - 100   Profit in 1996 - 117   %increae Profit in 1997 in comparison to 1995 = 17 + 117*25%= 46.25   Correct Option : 46.25%
Answer: E
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 5, 12 and 13?
Choices.
A) 2.5
B) 6.5
C) 5
D) 6.0
E) 7

Solution: Some of pyhtagron triplets we need to keep it in mind.   Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).   So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.   The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 13 / 2= 
13 / 2 = 13/2 = around 6.5
6.5   Ans. 6.5
Answer: B
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-5)(x+4)(2X+5) = 0? Answers.
A) a) 1/12 B) b) 1/6 C) c) 1/4 D) d) 1/3 E) e) 1/2

Solution: x = -1   Prob = 1/12   a) 1/12nswer - a) 1/12
Answer: A
One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?	Choices:  A) 1.00 minutes  B) 1.20 minutes  C) 1.50 minutes  D) 1.85 minutes  E) 2.00 minutes

Solution: By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore, answer 1.85 minutes will be correct. Answer-1.85 minutes
Answer: D
How many integers from 101 to 700, inclusive, remains the value unchanged when the digits were reversed?
Choose the correct choice:
A) 50
B) 60
C) 70
D) 80
E) 90

Solution: question is asking for palindrome   first digit possibilities - 1 through 6 = 6   7 is not possible here because it would result in a number greater than 7 (i.e 707 , 717..)   second digit possibilities - 0 though 9 = 10   third digit is same as first digit   =>total possible number meeting the given conditions = 6*10= 
6*10 = 60
60   Answer is 60.
Answer: B
A restaurant meal cost $55 and there was no tax. If the tip was more than 20 percent but less than 30 percent of the cost of the meal, then total amount paid must have been between: Choose the correct choice from the following options.
A) $65 and $72  B) $66 and $71  C) $64 and $71  D) $63 and $70  E) $67 and $73

Solution: let tip=t   meal cost=55   range of tip = from 20% of 55 to 30% of 55 = 11 to 16.5   hence range of amount paid= 55+T= 66 to 71.5 i.e. $65 and $72
Answer: A
A train 180 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?  Choices
A) 7 B) 10 C) 8 D) 2 E) 4

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 180 * 3/55   = 10 sec.   Answer 10
Answer: B
Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes. Choose the correct choice from the following options:
A) 15343 B) 16423 C) 17576 D) 17809 E) 18790

Solution: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.   Having chosen this, the second letter can be chosen in 26 ways   The first two letters can chosen in 26 x 26 = 676 ways   Having chosen the first two letters, the third letter can be chosen in 26 ways.   All the three letters can be chosen in 676 x 26 =17576 ways.   It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.   17576
Answer: C
Look at this series: (1/9), (1/3), 1, ____ , 9, ... What number should fill the blank?  Choose the correct choice from the following answers:	A) 3	B) 4	C) 1	D) 6	E) 9

Solution: 3   3   This is a multiplication series; each number is 3 times the previous number.
Answer: A
A pipe takes a hours to fill the tank. But because of a leakage it took 4 times of its original time. Find the time taken by the leakage to empty the tank
Choose the correct choice.
A) 50 min  B) 60 min  C) 90 min  D) 80 min  E) 70 min

Solution: pipe a can do a work 60 min.   lets leakage time is x;   then   1/60 -1/x=1/240   x=80 min   ANSWER:80 min
Answer: D
The G.C.D. of 1.08, 0.36 and 0.5 is:	Choose the correct answer:
A) 0.02
B) 0.9
C) 0.18
D) 0.108
E) 0.118

Solution: Given numbers are 1.08, 0.36 and 0.50. H.C.F. of 108, 36 and 50 is 18,   H.C.F. of given numbers = 0.02.   0.02nswer: Option 0.02
Answer: A
The average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is	Choose the correct choice from the following choices:  A) 22  B) 30  C) 99  D) 38  E) 32

Solution: total age increased = (10 * 2)= 
(10 * 2) = 20
20 years.   Sum of ages of two new men= (21 + 23 + 20)= 
(21 + 23 + 20) = 64
64 years   Average age of two new men= (64/2)= 
(64/2) = 32
32 years.   Answer: 32
Answer: E
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs.1760 in all from both of them as interest. The rate of interest per annum is? Choose the correct choice from the following choices
A) 16%
B) 12%
C) 74%
D) 10%
E) 8%

Solution: Let the rate be R% p.a. Then,   (5000 * R * 2)/100 + (3000 * R * 4)/100 = 1760   100 R + 120 R = 1760   R = 8%   Answer:8%
Answer: E
(17)5.5 x (17)? = 178	Options: A) 2.29 B) 2.75 C) 4.25 D) 4.5 E) None of these

Solution: Solution   let (17)5.5 * (17)x = 178. then, (17)5.5 + x = (17)8.   ∴ 5.5 + x = 8 ⇔ x = (8 - 5.5)= 
(8 - 5.5) = 2.5
2.5   Answer None of these
Answer: E
A man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is: Answers.
A) 70%	B) 80%	C) 90%	D) 20%	E) 10%

Solution: Explanation:   Let the article be worth Rs. x.   C.P. 90% of Rs. x = Rs. 9x/10   S.P. = 110% of Rs. x = Rs. 11x/10   Gain = (11x/10 - 9x/10) = Rs. x/5   Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%   Answer:20%
Answer: D
A can do a piece of work in 16 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?  Choose the correct choice from the following options:  A) 3 days  B) 4 days  C) 6 days  D) 7 days  E) 11 days

Solution: B's 9 day's work = 9 x (1/12) = 3/4   Remaining work = (1 - 3/4) = 1/4   1/4 work is done by A in = 16 x (1/4) = 4 days.   answer : 4 days
Answer: B
Find the sub-triplicate ratio of 27:125 Choose the correct choice from the following options.
A) 3:5	B) 3:9	C) 3:6	D) 3:1	E) 3:2

Solution: The sub-triplicate ration of 27 : 125 = 3:5   3:5nswer:3:5
Answer: A
the profit of certain article is 25 percent.had it been bought at 10 percent discount and sold for 20 percent more than the earliest cost,the profit would have been rs600.what is the cost price of the article.	Choose the correct choice
A) 1800  B) 2000  C) 2200  D) 2400  E) 2600

Solution: Let CP be x   Gain% = 25%   Then SP = x*125/100   SP = 5x/4   If it had been bought at 10% discount   Then CP = x*90/100   CP = 9x/10   sold at 20% more that the earliest cost... [earliest cost means x]   Then SP = x*120/100 = 600+9x/10   6x/5 = 6000+9x/10   12x = 6000+9x   3x = 6000   x = 2000   ANSWER:2000
Answer: B
A dishonest shopkeeper deceives by 15% at the time of purchase of article and also 15% at the time of sale.Find out the profit percentage
Profit% Select
A) 32.25%. B) 32 C) 42.25% D) 42 E) 50

Solution: Solution   =15+15+(15*15 / 100)=30 + 225/100 =30+2.25= 
30+2.25 = 32.25
32.25%.   32.25%.nswer 32.25%.
Answer: A
If a certain number is divisible by 14 and 20, it is NOT necessarily divisible by which of the following?
Choose the correct choice from the following options
A) 2  B) 5  C) 7  D) 10  E) 15

Solution: If a certain number is divisible by 14 and 20, it is NOT necessarily divisible by which of the following?   let the certain number be 140, which is both divisible by 14 and 20.   140/15 = 28/3   E. 15
Answer: E
A shop owner sells 56 apples and gains SP of 16 apples. Find the gain %?
Choose the correct choice from the following options:
A) 30%	B) 40%	C) 50%	D) 56%	E) 78%

Solution: Gain=16 applesTotal 56 applesCP   56-16= 
  56-16 = 40
40(16/40)*100=40%Ans 40%
Answer: B
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 16 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?	Choose the correct choice:	A) 13	B) 13.5	C) 14.4	D) 14.5	E) 15

Solution: Ans is 14.4   Given d_ab = 2*d_bc   let d_ab = d and d_bc = x so d=2x   for average miles per gallon = (d+x)/((d/12)+(x/16)) = 14.4 (formula avg speed = total distance/ total time)
Answer: C
The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 45, find the other?  Choices
A) 100  B) 160  C) 120  D) 200  E) 150

Solution: Other number = 12*600/45= 
12*600/45 = 160
160   Answer is 160
Answer: B
Which of the following numbers is divisible by 9?  Answers:  A) 23274  B) 25181  C) 31001  D) 50123  E) 11251

Solution: 23274. This is the only option with last two digits divisible by 9   23274nswer:23274
Answer: A
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15%, in 2006 there is a decrement of 35% and in 2007 there is an increment of 45%, then find the population of city at theend of the year 2007	Choose the correct choice from the following options.
A) 2456789
B) 3458009
C) 3890043
D) 3455048
E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?	Choose the correct choice from the following options:	A) 975	B) 753	C) 642	D) 684	E) None of these

Solution: Let the three digit numbers be 100a + 10b + c   a = b + 2   c = b - 2   a + b + c = 3b = 18 => b = 6   So a = 8 and b = 4   Hence the three digit number is: 864   ANSWNone of theseR:None of these
Answer: E
If C.P. of 25 books is equal to S.P of 30 books , then your gain or loss is ? Choose the correct answer:
A) 23 1/3 gain %  B) 30 10/23 loss %  C) 16.7% loss %  D) 30 1/3 loss %  E) 40 1/3 loss %

Solution: Say the cost price of 25 books is $25 so $1 for a book.   The cost of 30 books would be $30, and the selling price of 30 books would be 25$, hence the loss = ($30 - $25)/$30 = ~16.7%.   Answer: 16.7% loss %.
Answer: C
At what rate of interest is an amount doubled in two years, when compounded annually?
Choose one.
A) 41.4%	B) 41.7%	C) 41.4%	D) 42.4%	E) 21.4%

Solution: Let the rate of interest be r. The amount gets doubled in two years   => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1   = 0.414 => r = 100(0.414)   = 41.4%   Answer:41.7%
Answer: B
John has on his shelf two books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
Choose the most appropriate option:	A) 1/2	B) 2/5	C) 3/10	D) 2/7	E) 8/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/8*2/7 + 2/8*4/7 = 2/7.   Answer: 2/7
Answer: D