MU-NLPC/Calc-aqua_rat huggingface dataset:
If x-y=10, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
Choose the correct option
A) I only
B) II only
C) III only
D) I and II
E) II and III

Solution: The best way to approach such questions is to plug in values for x and y   Given: x-y=10   I. Both x and y are positive:   Let x=12 and y=2   x-y=10   But,   Let x=6 and y=-4   x-y=8   Therefore, NOT TRUE   III. If x is positive, y must be positive   Let x=12 and y=2   x-y=10   But,   Let x = 6 and y=-4   x-y=10   Therefore, NOT TRUE   II. If x is negative, y must be negative   If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!   Therefore, TRUE   Ans: 'II only'
Answer: B
If each side of a square is increased by 25%, find the percentage change in its area?
Choose the correct choice from the following:  A) 65.25  B) 56.25  C) 65  D) 56  E) 25

Solution: let each side of the square be a , then area = a x a   New side = 125a / 100 = 5a / 4   New area =(5a x 5a) / (4 x 4) = (25a²/16)   increased area== (25a²/16) - a²   Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%   Answer: 56.25
Answer: B
If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:	Choose the correct choice from the following options:
A) 12
B) 28
C) 160
D) 180
E) 18

Solution: Let the numbers be x and y.   Then, x + y = 20 and x - y = 8   x2 - y2 = (x + y)(x - y) = 20 * 8= 
20 * 8 = 160
160.   ANSWER:160
Answer: C
If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years? Choose the correct choice from the following:
A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00

Solution: ROI = 5% per annum compounded Monthly   Tenure, n = 10 years = 120 month   Principal = $500   5% per annum compounded monthly will be a little more than 5% at end of an year compounded anually = 6% per annum (approx)   in 10 years the among simple rate will increase by 60% but at coumpound rate the amount wil increase more by 60%   This question can only be solved by approximation   60% of $500 = $300   i.e. amount after 10 years will be a little more than  500+300= 
 500+300 = 800
$800   i.e. $823.50 option seems the closest possible answer   Answer: option $823.50
Answer: B
Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ?	Pick:
A) 7.5 l	B) 15 l	C) 22.5 l	D) It is impossible	E) none of these

Solution: In both jars concentration of milk is more than 50%.   Therefore, in jar three concentration of milk cannot be 50%.   Hence, we cannot decide the volumes   ANSWER:It is impossible
Answer: D
A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 5 p.m.?	Choose the correct choice from the following answers:	A) 30 min	B) 35 min	C) 45 min	D) 40 min	E) 55 min

Solution: there are 8 hours in between 9 a.m. to 5 p.m.   8*5= 
8*5 = 40
40 minutes.   ANSWER:40 min
Answer: D
At a Supermarket a certain item has increased from 72 cents per pound to 78 cents per pound. What is the % increase in the cost of item? Select:
A) 6.33%
B) 7.22%
C) 8.33%
D) 8%
E) 7%

Solution: Percent change = (New Value- Old Value )/ old value x 100   =((78-72)/72)x100   = (6/72)*100   = 8.33%   There was an 8.33% increase in the cost of item   answer -8.33% = 8.33%
Answer: C
How many positive 5-digit integers have the odd sum E of their digits?  Choose one:
A) 9*10^2  B) 9*10^3  C) 10^4  D) 45*10^3  E) 9*10^4

Solution: We are looking at numbers between 10000 and 99999 both inclusive.   There are 90000 numbers.   Now for   10000 : sum of digits is odd;   10001 :sum of digits is even;   10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.   (Exception for the above statement :   When it is 10009 the E sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd   and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)   This means exactly half of the numbers will have odd sum of their digits. i.e 45000   Answer :45*10^3
Answer: D
There are different 15 circles. What is the number of the greatest possible points with which the circles intersect?  Pick.
A) 390 B) 100 C) 110 D) 180 E) 210

Solution: Maximum points of intersection between n different circles = n*(n - 1) = 15*14= 
15*14 = 210
210   Answer: 210
Answer: E
B completes a work in 9 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?	Answers.
A) 3.75 days	B) 4.73 days	C) 5.75 days	D) 6.75 days	E) 7.73 days

Solution: 1/9 + 1/10 = 19/90   90/19 = 4.73 days   ANSWER: 4.73 days
Answer: B
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?  Choose the correct choice from the following options
A) 1/3	B) 1/4	C) 1/5	D) 1/7	E) 1/8

Solution: Explanation:   Suppose the vessel initially contains 8 litres of liquid.   Let x litres of this liquid be replaced with water.   Quantity of water in new mixture =(3-3x/8+x)litres   Quantity of syrup in new mixture =(5-5x/8)litres   (3 -	3x/8 +x)=(5 -	5x/8)   =>5x + 24 = 40 - 5x   =>10x = 16   =>x =	8/5   So, part of the mixture replaced =(8/5 x	1/8)=1/5.   ANSWER IS 1/5
Answer: C
A car is running at a speed of 96kmph. What distance will it cover in 14sec?  Choose the correct choice from the following: A) 378m B) 350m C) 380m D) 200m E) 250m

Solution: Speed = 96kmph = 96*5/18 = 27 m/s   Distance covered in 14sec = 27*14= 
27*14 = 378
378m   378mnswer is 378m
Answer: A
The average of 6 observations is 11. A new observation is included and the new average is decreased by 1. The seventh observation is?	Pick one:  A) 4  B) 3  C) 5  D) 6  E) 7

Solution: Let seventh observation = X.   Then, according to the question we have   => (66 + X) / 7 = 10   => X = 4.   Hence, the seventh observation is 4.   4NSWER:4
Answer: A
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is :	Choose the correct choice from the following choices.
A) 4.37%  B) 5%  C) 6%  D) 8.75%  E) None of these

Solution: Solution   Increase in 10 year= (262500 - 175000)= 
(262500 - 175000) = 87_500
87500.   Increase%=( f87500/175000x 100 )% = 50%   ∴ Required average = ( 50/10 )= 
( 50/10 ) = 5
5%   Answer 5%
Answer: B
If a + b = y and a - b = z , then 3ab =
can someone explain!	Pick one:	A) (3y^2 - 3z^2)/4	B) (3z^2 - 3y^2)/4	C) 3y+3z/2	D) 3y - 3z/2	E) 3y^2 - 3z^2/2

Solution: plugging numbers is quite fast in this case:   Let   a=1   b=2   Then; y= 1+2= 
1+2 = 3
> 3 and z= 1-2=> -1   Question asks 3ab=.........   As our number 3ab= 3*1*2= 
3*1*2 = 6
6   now plug the value of y and z in the answer choices. Option A gives 6 and that is the number we need.   Hence: (3y^2 - 3z^2)/4ns is (3y^2 - 3z^2)/4.
Answer: A
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Choose the correct choice from the following choices
A) 12	B) 18	C) 20	D) 24	E) 26

Solution: 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   20
Answer: C
A batsman in his 12th innings makes a score of 65 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?  Choose the correct choice from the following answers
A) 42	B) 43	C) 44	D) 45	E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 2) + 65   ∴ x = 43   Answer 43
Answer: B
In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder. The dividend is  Choose the most appropriate option:
A) 74	B) 78	C) 86	D) 92	E) 106

Solution: Divisor = (6 * 3) + 7= 
(6 * 3) + 7 = 25
25   5 * Quotient= 25   Quotient = 5.   Dividend = (Divisor * Quotient) + Remainder   Dividend = (20 * 5) + 6= 
(20 * 5) + 6 = 106
106.   106)
Answer: E
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person?
Answers
A) 70kg B) 75kg C) 80kg D) 85kg E) 90kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (55 + 20)= 
(55 + 20) = 75
75 kg.   75kg)
Answer: B
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?  Choose the correct option:
A) 10
B) 8
C) 6
D) 4
E) 2

Solution: Explanation:   Amy can travel clockwise or anticlockwise on the diagram.   Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.   Similarly, anticlockwise she has four different routes.   Total routes = 8   Answer: 8
Answer: B
Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 25 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B? Choose the correct answer:  A) 80 lakh  B) 50 lakh  C) 40 lakh  D) 60 lakh  E) None of these

Solution: Let the incomes of two companies A and B be 5x and 8x respectively.   From the question,   5x+25/8x=5/4 ⇒ 20x + 100 = 40x   ∴ x = 5   ∴ Income of company B = 8x = 40 lakh   Answer 40 lakh
Answer: C
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.	Answers:  A) 0 sq m  B) 2 sq m  C) 9 sq m  D) 20 sq m  E) 5 sq m

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists   0 sq mnswer: 0 sq m
Answer: A
P and Q started a business investing Rs. 85,000 and Rs. 30,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?	Choose one
A) 17:6
B) 17:0
C) 17:4
D) 17:2
E) 17:3

Solution: P:Q = 85000 : 30000   = 17:6.   17:6nswer: 17:6
Answer: A
A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111,222,333,444,555,666, 777,888 and 999?"
B immediately gave the desired answer. It was :-	Choose the correct choice from the following answers.
A) 3, 37 and 119  B) 3, 37 and 111  C) 9, 37 and 111  D) 3, 9 and 37  E) None

Solution: Explanation :   Each of the number can be written as a multiple of 111. And,   The factors of 111 are 3 and 37.   Thus, the desired answer is 3, 37 and 111.   Answer : 3, 37 and 111
Answer: B
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?	Choose the correct choice from the following options.
A) 277 Sec	B) 190 Sec	C) 187 Sec	D) 286 Sec	E) 215 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer:190 Sec
Answer: B
In how many different ways can the letters of the word ‘ARMOUM’ be arranged? Choose the correct choice from the following answers:
A) 200
B) 210
C) 230
D) 250
E) 360

Solution: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360   360
Answer: E
Which digits should come in place of @ and # if the number 62684@# is divisible by both 8 and 5?	Choose the correct choice from the following:	A) 4,0	B) 0,4	C) 4,4	D) 0,0	E) None

Solution: Explanation :   Since the given number is divisible by 5, so 0 or 5 must come in place of #.   But, a number ending with 5 is never divisible by 8.   So, 0 will replace #.   Now, the number formed by the last three digits is 4@0, which becomes divisible by 8, if @ is replaced by 4.   Hence, digits in place of @ and # are 4 and 0 respectively.   4,0nswer : 4,0
Answer: A
A train 125 m long passes a man, running at 1 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Answers
A) 65 km/hr	B) 17 km/hr	C) 76 km/hr	D) 50 km/hr	E) 46 km/hr

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 1) km/hr.   x - 1 = 45 => x = 46 km/hr.   Answer: 46 km/hr
Answer: E
A work which could be finished in 8 days was finished 3 days earlier after 10 more men joined. The number of men employed was?	Options:
A) 22	B) 30	C) 88	D) 71	E) 11

Solution: x ------- 8   (x + 10) ---- 6   x * 8 = (x + 10)6   x = 30   \Answer: 30
Answer: B
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H	Select: A) 153 B) 159 C) 137 D) 121 E) 89

Solution: let the number be x, now x is halved => x/2..the question asks what is x?   x(number) + x/2 (half of that number) = something   => 3x/2 = something   => x = 2 (something) / 3   so the answer choice must be divisible by 3   eliminate C, E right away   check the rest   B satisfies   3x/ 2 = 159   => x = 106   Verify. 106 + 53 = 159   Answer is 159
Answer: B
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: Choose the correct choice from the following.
A) 9	B) 2	C) 7	D) 8	E) 1

Solution: Let the numbers 13a and 13b.   Then, 13a x 13b = 2028   =>ab = 12.   Now, the co-primes with product 12 are (1, 12) and (3, 4).   [Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]   So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).   Clearly, there are 2 such pairs.   Answer: 2
Answer: B
Renu can do a piece of work in 8 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone?	Select the correct option: A) 8 B) 12 C) 14 D) 15 E) 17

Solution: Renuâ€™s one dayâ€™s work = 1/8   Sumaâ€™s one dayâ€™s work = 1/4 - 1/8 = 1/8   Suma can do it alone in 8 days.   8NSWER:8
Answer: A
There are 4 people who has to cross a stretch of 300 km. They normally run at a speed of 10 kmph. One
of them has a bike that travels at 50 kmph. The bike first takes one person alone and crosses the
stretch while the other two keep running. Then he comes back without wasting time and picks up
another person from the way, drives him across the stretch, and does the same for the last person. How
long does this whole process take?	Choose the most appropriate option:
A) 24 hrs  B) 16 hrs  C) 56/3 hrs  D) 58/3 hrs  E) 18 hrs

Solution: Expl : Time taken to carry 2nd person = 300/50= 
300/50 = 6
6 hrs.   Time taken to meet 3rd person=(300-6*10)/(50+10)= 
(300-6*10)/(50+10) = 4
4 hrs   Time taken to carry 3rd person= 4 hours   Time taken to meet 4th person = (300 –140)/60 = 8/3   Total time = 6+4+4+8/3+8/3 = 58/3 hours   Answer :58/3 hrs
Answer: D
The security gate at a storage facility requires a Six-digit lock code. If the lock code must consist only of digits from 1 through 9, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?
Choose the correct choice from the following answers:
A) 120	B) 240	C) 360	D) 720	E) 16800

Solution: X-X-X-X-X --> there are 5 odd digits from 1 to 9, inclusive thus options for the first and the last X's are: 5-X-X-X-X-4. Other X's can take following values: 5-7-6-5-4-4 -> 5*7*6*5*4*4=16800.   Answer: 16800.
Answer: E
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?	Choose the most appropriate option:
A) 5% B) 10% C) 20% D) 30% E) 45%

Solution: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%   10%
Answer: B
If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour? Choose the correct choice from the following answers.
A) 451 times
B) 638 times
C) 838 times
D) 436 times
E) 435 times

Solution: There are 60 minutes in an hour.   In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.   In ¾ of an hour there are   (60 * 45)= 
  (60 * 45) = 2_700
2700 seconds.   Light flashed for every 6 seconds.   In 2700 seconds 2700/6= 
2700/6 = 450
450 times.   The count start after the first flash, the light will flashes 451 times in ¾ of an hour.   451 timesnswer:451 times
Answer: A
Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $40,000 higher than Store B's revenues. In the second month, Store A's revenues were $6,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? Answers.
A) $14,000 B) $40,000 C) $42,000 D) $46,000 E) $50,000

Solution: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +40 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +6 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T):   (40 + 6 + T)/3 = 2   46 + T = 6   T = -40   Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -40 represents a $40,000 advantage in favor of Store B. Choice ($40,000) is correct.
Answer: B
some digits were given like 0 2 2 3 3 4 4 then how many no will be there which is greater than 1 lac ,all numbers are distinct  Answers.
A) 530  B) 540  C) 550  D) 560  E) 570

Solution: ( 6*6*5*4*3*2)/(2! *2!*2!)= 540 ways   ANSWER:540( 6*6*5*4*3*2)/(2  *2 *2 )= 
( 6*6*5*4*3*2)/(2  *2 *2 ) = 540
540 ways   ANSWER:540
Answer: B
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:  Answers
A) 600 B) 698 C) 675 D) 688 E) 900

Solution: 1 year = Rs. (854 - 815) = Rs. 39.   3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698   ANSWER 698
Answer: B
Each of the following equations has at least one solution EXCEPT D. Is it true?	Pick:
A) -2*-a = 2a
B) 2*a = (–2)*-a
C) -4*a = -3-a
D) -3*a = -3-a
E) (–2)-a = –2-a

Solution: If we put a= 1 then   A. 2   B. 2   C. -4   E. -3   D. -3=-4 Not true
Answer: D
10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. Select:
A) 1628.4
B) 1534
C) 1492
D) 240
E) None of these

Solution: Solution: Let average expenditure of 10 people be x.   then,   10x = 20*5+5*(x+4);   Or, 10x = 20*5+5x+20;   Or, x = 24;   So, total money spent = 24*10 = Rs. 240.   Answer: Option 240
Answer: D
If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ? Pick one:
A) 30	B) 34	C) 36	D) 37	E) 39

Solution: It basically asks for the number of 5s in 150!   150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37   Answer: 37.
Answer: D
Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product M?  Choose the correct choice from the following.
A) 328 units  B) 368 units  C) 392 units  D) 616 units  E) None of the above

Solution: The final product is obtained by mixing 864 units of product M with water.   In 864 units of Product M, amount of B = 864×77/108 = 616   In the final mixture, concentration of B is 50%.   Therefore, the total quantity of final mixture = 616 × 2 = 1232   Water added = 1232 – 864 = 368   The correct answer is Choice 368 units.
Answer: B
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many Z different victory circles are possible?
Pick one.
A) 24 B) 52 C) 96 D) 144 E) 648

Solution: Possible scenarios are:   1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;   2. Gold/Gold/Silver/No medal - 4!/2!=12;   3. Gold/Silver/Silver/No medal - 4!/2!=12;   4. Gold/Gold/Gold/No medal - 4!/3!=4.   Total Z: 24+12+12+4= 
24+12+12+4 = 52
52   Answer: 52.
Answer: B
X completes a work in 20 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be?	Choose the correct choice:
A) 10 days. B) 12 days. C) 14 days. D) 8 days. E) 20 days.

Solution: If X can complete a work in x days and Y can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 20Ã— 30/ 50 = 12 days.   12 days.)
Answer: B
A chair is bought for Rs.300/- and sold at Rs.420/- find gain or loss percentage
Choose the correct choice from the following choices.
A) 15% loss	B) 40% gain	C) 25% gain	D) 30% gain	E) 35% gain

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (450- 300)/300= 40% gain   40% gain
Answer: B
What is the least number to be subtracted from 696 to make it a perfect square? Choose the correct choice from the following answers
A) 1
B) 16
C) 20
D) 71
E) 60

Solution: The numbers less than 696 and are squares of certain numbers are 676, 625.   The least number that should be subtracted from 696 to make it perfect square = 696 - 676= 
696 - 676 = 20
20.   ANSWER:20
Answer: C
There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 3 books from this shelf include at least one paperback?  Choose the correct choice from the following answers
A) a) 40  B) b) 45  C) c) 36  D) d) 55  E) e) 60

Solution: approach 1   at-least 1 paper back = total - no paper back   8c3-6c3 = 36   approach 2   at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back   = 2c1*6c2+2c2*6c1 = 36   Answer is c) 36
Answer: C
If a sum of money doubles itself in 20 years at simple interest, the ratepercent per annum is
Choose the correct choice from the following choices
A) 12	B) 12.5	C) 13	D) 5	E) 14

Solution: Explanation:   Let sum = x then Simple Interest = x   Rate = (100 * x) / (x * 20) = 5   Option 5
Answer: D
Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW ?
Choose one
A) EF  B) GH  C) EV  D) DW  E) KN

Solution: C   EV   The first letter moves one step forward. The second letter moves one step backward.   Answer is EV
Answer: C