MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains 15 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf? Options:	A) 2/35	B) 1/15	C) 6/35	D) 13/70	E) 1/5

Solution: We have 15 scarves: 1 red, 1 green and 13 other. We're asked for the probability of grabbing 3 scarves that include the 1 red but NOT the 1 green scarf.   Even though the question states that we are supposed to grab all 3 scarves simultaneously, we can still refer to them as 1st, 2nd and 3rd. There are 3 ways to get what we *want*   R = Red   O = Other   ROO   ORO   OOR   The probability of getting ROO = (1/15)(13/14)(12/13) = 2/35   The probability of getting ORO = (13/15)(1/14)(12/13) = 2/35   The probability of getting OOR = (13/15)(12/14)(1/13) = 2/35   Total ways = 2/35 + 2/35 + 2/35 = 6/35   ANSWER:6/35
Answer: C
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is	Choose the correct option:  A) 2/13  B) 4/13  C) 1/13  D) 1/52  E) None

Solution: Solution   Here, n(S) = 52.   There are 13 cards of diamond(including 1 king) and there are 3 more kings.   Let E = event of getting a diamond or a king.   Then, n(E) = (13+3)= 
(13+3) = 16
16.   Therefore, P(E)= n(E)/n(S)   = 16 / 52   = 4 / 13.   Answer 4/13
Answer: B
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? Choose the correct choice from the following:
A) 5  B) 6  C) 8  D) 4  E) 1

Solution: US = 25   DS = 35   M = (35 - 25)/2= 
(35 - 25)/2 = 5
5   5nswer: 5
Answer: A
the probability that I will sit next to Ann is 1/12.
the probability that I won't sit next to Alice is 11/12.
What is the probability that I will sit next to Alice and not next Ann? Choose the correct choice from the following answers:
A) 1/6 B) 11/12 C) 11/144 D) 1/12 E) 1/144

Solution: the probability that I won't sit next to Ann is 1-1/12=11/12.   the probability that I will sit next to Alice is 1-11/12 = 1/12.   Therefore the probability that I will sit next to Ann and Alice is 11/12*1/12=11/144   Answer:11/144
Answer: C
For any integer z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD(-15) completely? Choose the correct choice from the following options:  A) 3^8  B) 5^5  C) 7^3  D) Options B and C  E) Options A and C

Solution: Solution 1:   Given POOptions B and COptions B and C(Z) is product of all odd integers -Z to Z, so doesn't matter what the prime factors are, they will have even powers, So B and C WILL NOT divide POOptions B and COptions B and C(-15) completely(!!!!, when you say completely i hope you meant without any remainder)   Solution 2:   POOptions B and COptions B and C(-15) = (15.13.11.9.7.5.3)^2 and breaking down to prime factors (5.3.13.11.3.3.7.5.3)^2 = (13^2.11^2.7^2.5^4.3^8)   ANSWER:Options B and C
Answer: D
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother?  Choose one.
A) 25 B) 30 C) 35 D) 40 E) 45

Solution: Let present age of the mother =5x   Then, present age of the person =2x   5x+8=2(2x+8)5x+8=4x+16x=8present age of the mother =5x=40   Answer is 40.
Answer: D
There are 11 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?  Choose the correct choice from the following choices:  A) 3/17  B) 4/19  C) 5/21  D) 6/22  E) 7/23

Solution: P(first stamp is different) = 6/11   P(second stamp is different) = 5/10   P(both stamps are different) = 6/11*5/10 = 6/22   The answer is 6/22.
Answer: D
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 18% if no discount was offered?  Select:
A) 17608
B) 17606
C) 17604
D) 17600
E) 18880

Solution: Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000   The price at whichthe TV should be sold to get a profit of 18% if no discount was offered = 16000 * 118/100 = Rs. 18880.Answer: 18880
Answer: E
How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?  Pick:  A) 28 sec  B) 23 sec  C) 24 sec  D) 25 sec  E) 26 sec

Solution: 25 sec   25 sec   25 sec = 100 + 150= 
100 + 150 = 250
250   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 250/10= 
250/10 = 25
25 sec
Answer: D
If the S.P of Rs. 21 results in a 30% discount on the list price, What S.P would result in a 10% discount on the list price?  Choose the correct choice from the following answers
A) s. 23 B) s. 24 C) s. 25 D) s. 26 E) s. 27

Solution: Let the list price be Rs. X,   70/100*x = 21, x = 21*100/70= 
21*100/70 = 30
30   Required S.P= 90% of Rs. 30   = 90*30/100= 
90*30/100 = 27
27   ANSWs. 27R:s. 27
Answer: E
Look at this series: 544, 509, 474, 439,404, 369, 334, ... What number should come next?	Select the correct option
A) 206	B) 299	C) 306	D) 507	E) 404

Solution: 299   This is a simple subtraction series. Each number is 35 less than the previous number.   299
Answer: B
In how many ways can the letters of the word "SATURN" be arranged?	Choose one:
A) 560	B) 640	C) 720	D) 800	E) 880

Solution: The total ways of arranging the letters = 6! = 720   The answer is 720.
Answer: C
If TIER is written as 9163 and BRAIN is written as 23415, how is RENT coded ?  Pick one
A) 3653
B) 3657
C) 2977
D) 3659
E) 2711

Solution: Explanation:   Given :   Letter : T I E R B A N   Code : 9 1 6 3 2 4 5   Thus, the code for RENT is 3659.   ANSWER:3659
Answer: D
An investor bought N shares of company X at $15 per share and N shares of company Y at $20 per share. If a month later the investor sold all the shares at $20 per share and made a profit of $200, then what is the value N?
Choose the correct choice from the following options:  A) 35  B) 40  C) 50  D) 60  E) 75

Solution: The investor made a profit of (2∗N∗20)−(15N+20N)=200. This equation simplifies to 5N=200 from where N=40.   Answer: 40
Answer: B
Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)?
Choose one
A) 1/4  B) 1/7  C) 3/7  D) 4/9  E) 5/11

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 0.4/0.4= 
0.4/0.4 = 1
1   P(F|E)= P(EnF)/P(E) = 0.4/0.16 = 1/4.   1/4)
Answer: A
2,6,30,60,130,221...tell 8th digit in series?? Choose the correct choice from the following choices.
A) 458
B) 504
C) 524
D) 534
E) 621

Solution: in this series   T(n)=n^3+/- n   + for odd n and - for even n   n=1 T(n)=1+1= 
1+1 = 2
2   n=2 T(n)=8-2= 
8-2 = 6
6   n=3 T(n)=27+3   n=4 T(n)=64-4= 
64-4 = 60
60   n=5 T(n)=125+5= 
125+5 = 130
130   n=6 T(n)=216-6= 
216-6 = 210
210   n=7 T(n)=343+7= 
343+7 = 350
350   n=8 T(n)=512-8= 
512-8 = 504
504   ANSWER:504
Answer: B
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum? Choose the correct choice from the following choices:
A) Rs.647	B) Rs.640	C) Rs.621	D) Rs.619	E) Rs.612

Solution: (P*5*15)/100 - (P*3.5*15)/100 = 144   75P/100 – 52.5P/100 = 144   22.5P = 144 * 100   => P = Rs.640   Answer:Rs.640
Answer: B
A dog buys a boat for rs.132.44 and sells it for rs.263.59. Find her gain %. Choose the correct choice from the following choices:
A) 10%	B) 99.03%	C) 87%	D) 16%	E) 94.06%

Solution: sol. cp=rs 132.44, sp=rs 263.59   gain=rs(263.59 –132.44)=rs 131.15   so gain%={(131.15/132.44)*100}=99.03%   Answer is 99.03%.
Answer: B
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them? Choose the correct option.
A) 5/7
B) 5/3
C) 5/1
D) 5/6
E) 5/2

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)   = 5/6   Answer: 5/6
Answer: D
Evaluate 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 =?
Options
A) 3043
B) 5050
C) 5176
D) 9356
E) 4890

Solution: B   5050   You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.   n^2 – (n-1)^2 = n + (n – 1)   In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
Answer: B
The compound interest on $ 27,000 at 11% p.a is $ 11,000.Find out the period (in years) ? Choose the correct answer
A) 2.5  B) 3 1/4  C) 3  D) 2 3/4  E) 4

Solution: Amount = 27,000 + 11,000   = 38,000 ......... Now by using compound interest formula we get, 27,000 * (111/100)^n = 38000 ====> n == 3 1/4 years   Ans - 3 1/4
Answer: B
What is the units digit of (3^10)(4^13)?
Pick.
A) 2 B) 4 C) 6 D) 7 E) 8

Solution: -> The ones place of (~3)^n repeats after 4 times like 39713.   The ones place of (~4)^n repeats after 2 times like 464.   Then, 3^10=3^4*2+23^2.,   4^13=4^2*6+1=4^1=~4   which is (3^10)(4^13) (3^2)(~4)=(~9)(~4)=~6. Therefore, the answer is 6.
Answer: C
The sector of a circle has radius of 7 cm and central angle 135o. Find its perimeter?	Choose the correct choice from the following.
A) 91.5 cm B) 92.2 cm C) 28.9 cm D) 30.5 cm E) 98.2 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 7) + 2(7)   = 16.5 + 14= 
16.5 + 14 = 30.5
30.5 cm   Answer:30.5 cm
Answer: D
If Josh, Doug, and Brad have a total of $68 between them, and Josh has two times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?	Choose the correct choice from the following answers:
A) $10
B) $24
C) $26
D) $12
E) $36

Solution: Josh+Doug+Brad = 68 ; Josh = 2 Brad, Josh =3/4 Doug   Josh+1/2 Josh+ 4/3 Josh = 68 (substituted the given values)   Josh = 24. 24= 3/4 $12oug => $12oug =32   Josh+$12oug+Brad = 68   24 + 32 + Brad = 68   Brad = 12   Answer is $12.
Answer: D
WILLIAM has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If WILLIAM needs to pay exactly $128, what is the least number of bills he will need to use?
Pick one
A) 567 B) 11 C) 22 D) 46 E) 16

Solution: 128 is the total sum of money.   as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils   128-120= 
128-120 = 8
8   so now we need to get 8 from either 5 dollar bills or 1 dollar bills   8 - 5 (use only 1 5 dollar bill)= 3   so we can get 3 from using 3 $1 bills.   Hence 16 ( 12+1+3 )   ANSW16R IS 16
Answer: E
A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Select the correct option: A) 28 B) 50 C) 77 D) 22 E) 12

Solution: Speed of the train relative to man = (200/10) m/sec = (20) m/sec. [(20) * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72 ==> x   = 77 km/hr.Answer:77
Answer: C
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Select: A) 21 sec B) 16 sec C) 71 sec D) 18 sec E) 28 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   Answer: 16 sec
Answer: B
Lines y=4√5·x−2 and y=3√5·x−1 intersect at what height above the x axis?  Choices:  A) 0  B) 2√5  C) 2  D) 3√5  E) 12√5

Solution: Solve two equations for y   y=4√5·x−2   y=3√5·x−1   Set the two equations equal to each other and solve for x   4√5·x−2=3√5·x−1   √5·x = 1   x = 1/√5   Plug x = 1/√5 into any one of the original equations to find the y value (height above x axis) where the two lines intersect   y=4√5·x−2   y=4√5·(1/√5)−2   y=4·1 - 2   y = 4 - 2= 
4 - 2 = 2
2   Final answer:   2) 2
Answer: C
12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1â„4 of the same job. How many days will 10 men and 8 women together take to complete the same job? Select
A) 6  B) 13 1â„2  C) 18  D) Data inadequate  E) None of these

Solution: 12 M Ã— 18 = 12 W Ã— 18 Ã— 4â„1   \ w = 1/4 M   10M + 8W = 10M + 8 Ã— 1â„4M = 12 M   \12 men can complete the same work   in 12Ã—18/12=18days   Answer 18
Answer: C
find value for x from below equation?
x + 1 = -3  Options
A) -2 B) -4 C) -1 D) -5 E) 1

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = -3 - 1   2. Simplify both sides:   x = -4   -4
Answer: B
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is  Answers
A) 10/17 B) 10/19 C) 46/105 D) 11/15 E) Cannot be determined

Solution: There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.   ANSWCannot be determinedR:Cannot be determined
Answer: E
Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?  Choose the correct choice from the following.
A) 11
B) 15
C) 16
D) 28
E) 19

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   4 --------- ? è 28 m   Answer: 28
Answer: D
The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?  Choose the correct option
A) Rs.16500/-
B) Rs.17000/-
C) Rs.18000/-
D) Rs.19000/-
E) Rs.20000/-

Solution: For 2 years = (1002D)/R2   = (1002 × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-   Rs.18000/-
Answer: C
Reena took a loan of Rs. 2000 with simple interest for as many years as the rate of interest. If she paid Rs. 720 as interest at the end of the loan period, what was the rate of interest? Choose the correct answer:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Let rate = R% and time = R years.   =(2000xRxR)/100 =720   =20Rsquare =720   R Square = 720/20= 
720/20 = 36
36   R= 6   6NSWER :6
Answer: A
How many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the correct choice.
A) 25
B) 30
C) 40
D) 45
E) 54

Solution: Relative speed of the train=63-3= 
63-3 = 60
60kmph=60*5/18=50/3 m/sec   t=900*3/50= 
900*3/50 = 54
54sec   ANSW54R:54
Answer: E
In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks :	Options.
A) 300
B) 350
C) 400
D) 450
E) 550

Solution: total marks:1500 for three exams   70% of 1500=1050   first exam marks=45% of 500=225   second exam marks=55% of 500=275   let X be the third exam marks   225 + 275 + X =1050   X=550   ANSW550R:550
Answer: E
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ? Choose the correct choice from the following options
A) 0 B) 12 C) 13 D) 20 E) 25

Solution: 12*35= 
12*35 = 420
420   420%21=20   ANSWER:20
Answer: D
A fruit seller had some Mangoes. He sells 50% oranges and still has 500 Mangoes. How many Mangoes he had originally?	Select the correct option:
A) 800
B) 850
C) 900
D) 1000
E) 1050

Solution: He sells 50% of oranges and still there are 500 oranges remaining.   = 50% of oranges = 500   Total oranges x (50/100)= 500   = Total oranges =500×100/50=1000   answer :1000
Answer: D
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1600, then what is the smallest possible value of n? Choose the correct choice from the following answers:  A) 6  B) 8  C) 10  D) 12  E) 15

Solution: 1600=2^6*5^2   2^6 means that n must be at least 8. That is, we need 2, 2*2, 6, and 2*2*2.   5^2 means that n must be at least 10. That is, We need 5 and 10.   The answer is 10.
Answer: C
Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
27	12	18
5	2	?  Options
A) 19  B) 23  C) 21  D) 22  E) 20

Solution: E   20 fits in place of question mark.   This is because (number in first column) / (number in second column) * 8 = number in third column.   Here (left number / middle number) * 8 = right number   E.g. (35 / 20) * 8 = (7/4) * 8 = 7 x 2 = 14   The same process can be used to find out the missing digit.
Answer: E
A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 50% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?	Choose the most appropriate option:
A) 2/5 B) 4/7 C) 10/19 D) 7/24 E) 7/10

Solution: Suppose there are 100 students   Group A : 40% = 40 students   50% drink beer = 20   30% mixed = 12   20% both = 8   Group B 60% = 60   30% beer= 18   30% mixed = 18   20% both= 12   now we need both ( beer + mixed = both)   probability = total beer drinker = 20+18= 
20+18 = 38
38 and both= 20   thus 20/38 = 10/19   Hence 10/19
Answer: C
From a bunch of eight keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?  Choose one:
A) 1/120  B) 1/180  C) 1/336  D) 1/480  E) 1/720

Solution: The probability is 1/8*1/7*1/6 = 1/336.   The answer is 1/336.
Answer: C
A warehouse had a square floor with area 10,000 sq.meters. A rectangular addition was built along one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many meters did the addition extend beyond the original buildings ?  Choices
A) 10	B) 20	C) 50	D) 100	E) 500

Solution: as L*B=10000 ie for square L=B=100m   THEN,   IF A RE50TANGULAR ADDITIONALLY WAS BUILT ALONG ONE ENTIRE SIDE IT ENSURES THAT ONE SIDE MUST BE REMAIN SAME AS THE SQUARE   HEN50E EQUATION BE50OMES   (100+X)100=10000+(1/2)*10000   (100+X)100=15000   X=50   ANSWER:50
Answer: C
A 425 meter long train crosses a platform in 55 seconds while it crosses a signal pole in 40 seconds. What is the length of the platform?
Choices:
A) 155.68 B) 160 C) 159.38 D) 180 E) 175

Solution: Speed = [425 / 40 m/sec = 42.5/4 m/sec.   Let the length of the platform be x meters.   Then, x + 425 / 55= 42.5/4   4(x + 425) = 2337.5 è x =159.38 m. Answer: 159.38
Answer: C
In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 85 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?	Choose the correct choice from the following answers
A) 50%
B) 59%
C) 54%
D) 55%
E) 57%

Solution: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.   60*0.85= 
60*0.85 = 51
51 Democrats are expected to vote for Candidate A;   40*0.20= 
40*0.20 = 8
8 Republicans are expected to vote for Candidate A.   Thus total of   51+8= 
  51+8 = 59
59 registered voters are expected to vote for Candidate A, which is 59% of the total number of registered voters.   Answer: 59%.
Answer: B
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1008?  Choose the correct answer:  A) 900  B) 2217  C) 2889  D) 2777  E) 2991

Solution: 1008 = P [1 + (5*12/5)/100]   P= 900   900nswer: 900
Answer: A
A textile manufacturing firm employees 56 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 56 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is: Choose the correct choice from the following choices
A) 13000	B) 6250	C) 10000	D) 5000	E) None of these

Solution: Explanation :   Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.   Since, such loom contributes equally to sales and manufacturing expenses.   But the monthly charges are fixed at Rs 75,000.   If one loan breaks down sales and expenses will decrease.   New profit :-   =>500000Ã—(55/56)âˆ’150000Ã—(55/56)âˆ’75000.   =>Rs 2,68,750   Decrease in profit   =>2,75,000âˆ’2,68,750   =>Rs. 6,250   Answer : 6250
Answer: B
Which of the following is closer to (3!+2!)-(3!-2!)?	Choose the correct choice:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: 3!+2!)-(3!-2!)=6+2-6+2= 
6+2-6+2 = 4
4   Answer: 4
Answer: E
A is twice as good a work man as B and together they finish a piece of work in 14 days.The number of days taken by A alone to finish the work is :	Choose the correct choice.
A) 11  B) 21  C) 28  D) 42  E) None of these

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.   (A + B)'s 1 day’s work = 1/14   Divide 1/14 in the ratio 2 : 1.   ∴ A’s 1 day’s work = (1/14 x2/3)= 1/21   Hence,A alone can finish the work in 21 days.   Answer 21
Answer: B
A certain machine produces 550 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 5 days?
Choose one.
A) 7,000  B) 24,000  C) 66,000  D) 100,000  E) 168,000

Solution: Since 5 days consist of 24*5 hours the total is 120 hours.   Since every hour the machine produces 550 units of product P the total product during 120 hours is 120*550=66,000.   66,000orrect Option : 66,000
Answer: C
If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+13 is divided by 41?  Pick
A) 3  B) 18  C) 6  D) 16  E) 5

Solution: X can be written as 82K + 5 or X = 5,87,169,etc.   X + 13 = 82K + 5+13= 82K +18 or X + 13 = 18,100, 182 etc.   When divided by 41, we will get the remainder 18.   18
Answer: B
If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time? Choose the correct choice from the following answers:
A) Rs. 52	B) Rs. 51.25	C) Rs. 54.25	D) Rs. 60	E) Rs. 70

Solution: Simple interest for 2 years = Rs.50 ie. For 1 years Rs. 25. . In the first year the S.I and C.I are   same ie.Rs. 25. So in the 2nd year in C.I calculated for 1 years interest also. So in second years for   Rs.25 interest is  25*5/100= 
 25*5/100 = 5/4 = around 1.25
1.25 . So total C.P= 51.25.   ANSWER:Rs. 51.25
Answer: B
If x^2 – 2y^2 = 2xy, then (x + y)^2 =
Choose one.
A) x^2	B) 2x^2-y^2	C) 4xy	D) 2y^2	E) – y^2

Solution: (x+y)^2 = x^2 + y^2 + 2xy = x^2 + y^2+ x^2-2y^2 = 2x^2-y^2   Correct option : 2x^2-y^2
Answer: B
Stalin gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Jose gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?	Pick one
A) 19	B) 28	C) 34	D) 32	E) 30

Solution: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?   40 floors/120 floors per minute=1/3 minutes     11+57/3= 
  11+57/3 = 30
30   51-63/3= 
51-63/3 = 30
30   Answer : 30
Answer: E