MU-NLPC/Calc-aqua_rat huggingface dataset:
If the cost price of 58 articles is equal to the selling price of 50 articles, then what is the percent profit?  Choose the correct choice from the following answers:
A) 12%
B) 16%
C) 20%
D) 24%
E) 28%

Solution: Let x be the cost price of one article.   Let y be the selling price of one article.   50y = 58x   y = 1.16x   The answer is 16%.
Answer: B
When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 727 more than 4times the middle integer. Find the numbers?
Choose the correct choice from the following choices
A) 650
B) 678
C) 727
D) 710
E) 729

Solution: x + 4 (x + 4) = 727 + 4 (x + 2)   Solve for x and find all three numbers   x + 4 x + 16 = 727 + 4 x + 8   x = 719   x + 2 = 721   x + 4 = 723   727heck: the smallest is added to four times the largest     719 + 4 * 723= 
  719 + 4 * 723 = 3_611
3611   four times the middle   4 * 721= 
4 * 721 = 2_884
2884   3611 is more than 2884 by   3611 - 2884= 
3611 - 2884 = 727
727   727
Answer: C
Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction? Choose the most appropriate option.
A) 90 sec  B) 30 sec  C) 10 sec  D) 70 sec  E) 30 sec

Solution: Let the length of each train be x m.   (x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)= 
(750 * 18) / (30 * 5) = 90
90 sec.   90 secnswer:90 sec
Answer: A
For a certain article, if discount is 25%, the profit is 25%. If the discount is 10%, then the profit is  Choose the correct choice from the following options
A) 10%
B) 20%
C) 35%
D) 50%
E) None of these

Solution: For same article, 100−d1/100−d2=100+g1/100+g2   ⇒ 100−25/100−10=100+25/100+g2 ⇒75/90=125/100+g2   ⇒ 100 + g2 = 90×125/75 =150 ⇒ g2 = 50%   Answer 50%
Answer: D
The sum of first five prime numbers is?	Options: A) 11 B) 18 C) 26 D) 28 E) None

Solution: Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28.   Note: 1 is not a prime number.   Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.   11)
Answer: A
If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 45000 sheets of xerox paper? Choices:
A) $1250	B) $1060	C) $1350	D) $900	E) $2100

Solution: 30 sec approach - solve it using approximation   45000 sheet at full price, 5 cent = 2250   45000 sheet at max discount price, 4 cent = 2000   Your ans got to be between these two.   Ans $2100 it is.
Answer: E
The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x? Options
A) 248
B) 240
C) 228
D) 236
E) 246

Solution: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)   Their sum = 10x = 440   x = 44 => 2(x - 2) = 84   Second least number of the other set = 2(84) - 121 = 47   This set has its least number as 46.   Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50   = 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240   ANSWER:240
Answer: B
A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 6, what is the smallest possible total number of tokens in the jar?
Pick
A) 9
B) 12
C) 15
D) 18
E) 21

Solution: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)   i.e. Red*White = Blue*Total Coins   Let, Red = 3a   White = 3b   Blue = 3c   Total Coins = 3(a+b+c)   i.e. 3a * 3b = 3c*3(a+b+c)   i.e. a*b = c*(a+b+c)   For smallest values of a, b and c   2*3 = 1*(1+2+3)   i.e. Minimum Total Coins = 3*(1+2+3) = 21   Answer: Option 21
Answer: E
A coin is tossed seven times. What is the probability that there is at the least one tail?  Select the correct option:
A) 127/128
B) 31/138
C) 31/167
D) 31/117
E) 31/128

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed seven times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/128 ; P(T) = 1 - 1/128   = 127/128   127/128nswer: 127/128
Answer: A
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed.	Choose the correct choice.
A) 10 m/sec
B) 15 m/sec
C) 18 m/sec
D) 19 m/sec
E) 25 m/sec

Solution: If length of train is l and speed of train is s, then   l/s = 10   (l+180)/s = 20   (l+180)/l = 20/10= 
20/10 = 2
2   l+180=2l   l= 180   l=180 mtrs   s= l/10 = 180/8 = 10 m/sec   10 m/secNSWER:10 m/sec
Answer: A
If m and n are whole numbers such that
mn=121
, the value of
(m−1)n+1 is Choose the correct choice from the following options.
A) 1 B) 10 C) 100 D) 1000 E) None of these

Solution: Explanation:   We know that   (11)2=121   So, putting values in said equation we get,   (11−1)2+1=(10)3=1000   Option 1000
Answer: D
In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what A percentage of those asked favoured more than one of the 3 proposals. Choose the correct answer:  A) 10  B) 12  C) 17  D) 22  E) 30

Solution: Bunuel, my answer for exactly 2 people was 17 and this was my approach:   100%=(A+B+17)-(AnB+An17+Bn17)-5%+22% which leads me to   A=100%=(50+30+20)-(at least 2 people)-5%+22%.17
Answer: C
In the first 12 overs of a one day cricket game, the run rate was only 3 What should be the run rate in the remaining 38 overs of a one day match to reach the target of 282 runs?  Choose the correct choice from the following:
A) 4.47  B) 5.47  C) 6.14  D) 6.47  E) 6.84

Solution: Runs scored in the first 12 overs = 12 × 3 = 36   Total runs = 282   Remaining runs to be scored = 282 - 36= 
282 - 36 = 246
246   Remaining overs= 38   Run rate needed = 246/38   =6.47   ANSWER:6.47
Answer: D
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1881, What is the value of n?
Choose the correct option
A) 22 B) 38 C) 114 D) 122 E) 672

Solution: Factorise 1881.. 3*11*57..   So n has to be a multiple of largest prime number,61..   So n=2*57=114..   Ans :114
Answer: C
Find the value of (X) in the given equation ?
35% of 1500 + X = 45% of 4200 – 320  Options:
A) ANSWER: 1049 B) ANSWER: 1048 C) ANSWER: 1041 D) ANSWER: 1045 E) ANSWER: 10412

Solution: Explanation:   35% of 1500 + X = 45% of 4200 – 320   (35/100 * 1500) + X = (45/100 * 4200) – 320   525 + X = 1890 – 320   X = 1890 – 320 – 525   X = 1890 – 845   X = 1045   ANSWER:ANSWER: 1045
Answer: D
Mike started a business with Rs.45000. After 3 months John joined him with a capital of Rs. 60000. After another 6 months, Tom joined them with a capital of Rs.90000. At the end of the yr, they made a profit of Rs.20000. What would be Tom share in it?	Choices
A) Rs. 2000  B) Rs. 2500  C) Rs. 3500  D) Rs. 4000  E) Rs. 5000

Solution: Just take care of the months of investment, rest all will be simple.   Yogesh:Pranab:Atul = 45000*12:60000*9:90000*3 = 2:2:1   Atul's share = Rs. 20000 * (1/5) = Rs. 4000   (Rs. 4000)
Answer: D
Ram goes to market with a speed of 3km/h and comes back home with a speed of 2km/h. If he takes 5 hours in all, find the distance between home and market.
Choose the correct option
A) 8 km B) 4 km C) 6 km D) 5 km E) 7 km

Solution: Let the required distance be x km. Then time to go to the market =x/3 hrs. Time taken to go come back=x/2 hrs. Total time taken = (x/3+x/2) hrs. = 5x/6 Here 5x/6 =5, ie) x=6 Hence the distance between home and market = 6 km Answer :6 km
Answer: C
A grocer has a sale of Rs. 5255, Rs. 5840, Rs. 5921, Rs. 6022 and Rs. 6499 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5500?	Choose the correct choice
A) 3463  B) 4463  C) 5463  D) 4063  E) 5063

Solution: Total sale for 5 months = Rs. (5255 + 5840 + 5921 + 6022 + 6499) = Rs. 29537.   Required sale = Rs. [ (5500 x 6) - 29537 ]   = Rs. (33000 - 29537)   = Rs. 3463.   ANSWER:4463
Answer: B
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?	Choose the correct option
A) 9 sec
B) 6 sec
C) 8 sec
D) 10 sec
E) 11 sec

Solution: T = 60/36 * 18/5= 
60/36 * 18/5 = 6
6 sec   ANSWER 6 sec
Answer: B
An athlete runs 200 meters race in 24sec. His speed is?	Choose the correct choice from the following answers: A) 20km/hr B) 15km/hr C) 30km/hr D) 25km/hr E) 40km/hr

Solution: speed = 200/24 = 25/3 m/sec   = 25/3 * 18/3 km/hr = 30km/hr   Answer is 30km/hr
Answer: C
Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 6 on the two dice?
Pick
A) 5/9  B) 5/12  C) 7/12  D) 11/18  E) 19/36

Solution: There are 36 possible outcomes for two dice.   The number of outcomes with an even number on the first die is 3*6= 
3*6 = 18
18.   The number of outcomes with a sum of 6 is 5.   We need to subtract the outcomes that have both an even number on the first die and a sum of 6 because we have counted those outcomes twice. This number of outcomes is 2.   The number of outcomes with either an even number on the first die or a sum of 6 is  18+5-2= 
 18+5-2 = 21
21.   The probability is 21/36=7/12.   The answer is 7/12.
Answer: C
If 16% of 40% of a number is 6, then the number is Options.
A) 200 B) 225 C) 93.75 D) 320 E) None of these

Solution: Explanation:   Let 16/100×40/100×a=6   a = 6×100×100/16×40=93.75   93.75orrect Option: 93.75
Answer: C
How much 60% of 50 is greater than 40% of 30?  Choose the correct choice from the following options:
A) 18	B) 55	C) 33	D) 22	E) 11

Solution: (60/100) * 50 – (40/100) * 30   30 - 12= 
30 - 12 = 18
18   18nswer: 18
Answer: A
Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 22% vinegar, dressing P comprises what percentage of the new dressing? Choose the correct option.
A) 35%
B) 40%
C) 50%
D) 60%
E) 75%

Solution: Let x be the percentage of dressing P in the new dressing.   0.3x + 0.1(1-x) = 0.22   0.2x = 0.12   x = 0.6 = 60%   The answer is 60%.
Answer: D
For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If p is the smallest prime factor of h(100) +2(100)+1, then p is? Select the correct option:  A) between 1 and 20  B) between 10 and 20  C) between 20 and 30  D) between 30 and 40  E) 1

Solution: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 100. So h(100)+2(100)+1 will have 1 in the units digit so smallest prime factor is 1.   Answer: 1
Answer: E
A computer factory produces 4200 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month? Pick:
A) 2.25	B) 3.125.	C) 4.5	D) 5.225	E) 6.25

Solution: Number of hours in 28 days = 28*24   Number of 30 mins in 28 days = 28*24*2   Number of computers built every 30 mins = 4200/( 28*24*2)= 
4200/( 28*24*2) = 25/8 = around 3.125
3.125   Answer 3.125.
Answer: B
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is?
.	Choose the correct choice:  A) 6  B) 12  C) 24  D) 36  E) 48

Solution: 72 x 1 = 72   72 x 2 = 144   14^4=12^2   Largest possible which can divide 12 is 12   Answer = 12
Answer: B
In a mixture of 13 litres, the ratio of milk and water is 3 : 2. If 3 liters of this mixture is replaced by 3 liters of milk, then what will be the ratio of milk and water in the newly formed mixture?  Choose the correct choice from the following options
A) 9 : 1	B) 9 : 2	C) 9 : 7	D) 9 : 4	E) 9 : 3

Solution: Given: Total quantity of mixture = 13 liters   3 litres of mixture is removed from the container – So, let's forget this altogether!   Now, you are left with only 10 litres of mixture in 3:2 ratio.   Milk in 10 litres mix = 10 x	3	= 6 litres   (2 + 3)   Water in 10 litres mix = 10 x	2	= 4 litres   (2 + 3)   We add 3 litres milk to this.   So, milk in new mix is = 6 liters + 3 litres = 9 litres   Water= 4 litres   Ratio of milk : water = 9 : 4   Correct option: 9 : 4
Answer: D
A circular mat with diameter 7 inches is placed on a square tabletop, each of whose sides is 10 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?	Choose the correct choice:
A) 2/6
B) 3/9
C) 1/6
D) 3/2
E) 1/7

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the Cloth = (pi)(r)^2 which is about (22/7)(7)(7)   Area of the Table = (10)(10)   So the quick way to estimate is looking at the fraction like this:154/100 nearest to 3/2   Answer: 3/2
Answer: D
4 dice are thrown simultaneously on the board. Find the probability show the same face.  Choose the correct choice:
A) 1/115	B) 2/115	C) 1/216	D) 1/213	E) 1/215

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and further to $400 at the end of another 5 years. What was the rate of interest in which he invested his sum?	Choose the correct answer:
A) 12% B) 12.5% C) 6.67% D) 6.25% E) 8.33%

Solution: Answer   Initial amount invested = $ X   Amount at the end of year 3 = $ 300   Amount at the end of year 8 (another 5 years) = $ 400   Therefore, the interest earned for the 5 year period between the 3rd year and 8th year = $400 - $300 = $100   As the simple interest earned for a period of 5 years is $ 100, interest earned per year 400 -  300= 
400 -  300 = 100
$100   As the simple interest earned for a period of 5 years is $ 100, interest earned per year= $20.   Therefore, interest earned for 3 years = 3 * 20= 
3 * 20 = 60
$ 60.   Hence, initial amount invested X= Amount after 3 years - interest for 3 years   = 300 - 60= 
300 - 60 = 240
$ 240.   Rate of interest= (interest per year/principal)*100 = 20/240*100 = 8.33%   choice is (8.33%)
Answer: E
The cost of 4 bananas and 4 oranges is $36. The cost of 2 bananas and 5 oranges is $33. What is the cost of 1 orange?	Choose the correct choice from the following options:
A) 2	B) 5	C) 4	D) 6	E) 5.5

Solution: Let the cost of 1 banana = x, let the cost of 1 orange = y   4x + 4y = 36   x = (36 - 4y)/4   x = 9 - y   Again,   2x + 5y = 33   2(9 - y) + 5y = 33   18 - 2y + 5y = 33   3y = 15   y = 5   Answer: 5
Answer: B
A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 8 rows or 6 rows or 4 rows, then no tree will be left. Find the least number of trees required  Choose the correct choice from the following choices
A) 22
B) 60
C) 24
D) 76
E) 21

Solution: Explanation:   The least number of trees that are required = LCM(8,6,4) = 24.   Answer: 24
Answer: C
In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 565. What is the sum of the last 5 integers in the sequence?	Choose the correct choice from the following choices.
A) 585  B) 580  C) 575  D) 590  E) 565

Solution: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+565= 
25+565 = 590
590   590
Answer: D
(ab)x−2=(ba)x−7. What is the value of x ? Choices.
A) 1.5  B) 4.5  C) 7.5  D) 9.5  E) 8.7

Solution: Explanation:   (a/b)x−2=(b/a)x−7⇒(a/b)x−2=(a/b)−(x−7)⇒x−2=−(x−7)⇒x−2=−x+7⇒x−2=−x+7⇒2x=9⇒x=92=4.5   Option 4.5
Answer: B
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 65.50, his capital is?
Choose the correct answer:
A) 24,602	B) 26,200	C) 24,600	D) 24,628	E) 24,6012

Solution: Let the capital be Rs. x. Then,   (x * 8 * 1)/100 - (x * 31/4 * 1/100) = 65.50   32x - 31x = 6550 * 4   x = 26,200.   Answer: 26,200
Answer: B
The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-9), how many units is P from the y-axis?
Choose the most appropriate option:  A) 18  B) 12  C) 9  D) 4.5  E) 3

Solution: The x-axis is 9 units from the point P.   Thus the y-axis is 18 units from the point P.   The answer is 18.
Answer: A
If the price of 100 toys is 2500, then what will the price of 50 toys ?	Choose the correct option:
A) 144  B) 1250  C) 117  D) 287  E) 112

Solution: One toy price = 2500/100= 
2500/100 = 25
25   50 toy price= 50 * 25= 
50 * 25 = 1_250
1250   Answer : 1250
Answer: B
A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 120 more than A :
Choose the most appropriate option:
A) 2348	B) 3480	C) 2767	D) 1998	E) 2771

Solution: Explanation:   A 3480 C   investment 3x 4x 5x   Rate of return 6y% 5y% 4y%   Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}   Total = (18+20+20)= 
(18+20+20) = 58
\inline \frac{58xy}{100}   3480's earnings - A's earnings= \inline \frac{2xy}{100} = 120   Total earning = \inline \frac{58xy}{100} = 3480   Answer: 3480) Rs.3480
Answer: B
In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a female or younger than 70 years old?
Options.
A) 7/8
B) 14/15
C) 29/30
D) 44/45
E) 131/135

Solution: The number of people younger than 70 years old is   2700-900= 
  2700-900 = 1_800
1800   The number of females older than 70 years old is   0.6*1200= 
  0.6*1200 = 720
720   The number of people who are either female or younger than 70 is  1800+720= 
 1800+720 = 2_520
2520.   P(a person is younger than 70 or male)= 2520/2700 = 14/15   The answer is 14/15.
Answer: B
On a sum of money, the S.I. for 2 years is $600, while the C.I. is $615, the rate of interest being the same in both the cases. The rate of interest is? Choose the correct choice:
A) 4%	B) 5%	C) 6%	D) 7%	E) 8%

Solution: Difference in C.I. and S.I for 2 years = $615 - $600 = $15   S.I for one year 615 -  600= 
615 -  600 = 15
$15   S.I for one year= $300   S.I. on $300 for 1 year = $15   Rate = (100 * 15)/(300)= 
(100 * 15)/(300) = 5
5%   The answer is 5%.
Answer: B
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?  Pick
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: P(1 + 20/100)n > 2P or (6/5)n > 2   Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.   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 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choose the correct choice from the following options.
A) 22 B) 37 C) 48 D) 266 E) 121

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: 48
Answer: C
The sum of the first 80 positive even integers is 6480. What is the sum of the first 80 odd integers? Choose the correct choice from the following choices
A) 6200 B) 6300 C) 6400 D) 6500 E) 6600

Solution: Sum of first n even numbers = n(n+1) =6480   Sum of first n odd numbers = n^2 = 80*80= 
80*80 = 6_400
6400 (here n=80)   Answer : 6400
Answer: C
The food in a camp lasts for 20 men for 40 days. If ten more men join, how many days will the food last?	Pick:
A) 40 days
B) 20 days
C) 30 days
D) 50 days
E) 45 days

Solution: one man can consume the same food in 20*40= 
20*40 = 800
800 days.   10 more men join, the total number of men= 20   The number of days the food will last = 800/20= 
800/20 = 40
40 days.   40 daysNSWER:40 days
Answer: A
A trouser in bazaar was marked down 40% the first week and another 10% the next week. What percent of the regular price was the final cost of the trouser after the two markdowns?
Choose the correct answer:  A) 30%  B) 36%  C) 40%  D) 50%  E) 54%

Solution: If the price of the trouser is 100, and it is marked down by 40% and then by 10% or charged 60% of the price first and 90% of the price of reduced price, the final price is :-   100*60*90/10000= 
100*60*90/10000 = 54
54   54% is the final price of old price.   54% is the answer
Answer: E
Find the odd man out. 9, 16, 36, 121, 169, 225, 361, 400, 440
Select the correct option.
A) 169	B) 225	C) 361	D) 440	E) 400

Solution: Explanation :   Each of the given numbers except 440 is a perfect square   Answer : Option 440
Answer: D
A worker is paid x rupees for painting every 6 metres of a wall and y rupees for painting every extra metre. During one week, he painted 6 metres on Monday, 7 metres on Tuesday, 8 metres on Wednesday, 9 metres on Thursday and 10 metres on Friday. What is his average daily earning rupees for the five day week?	Pick one
A) x + (8/5)y	B) x+2y	C) 10x + (8/5)y	D) None of these	E) Cannot be determined

Solution: Explanation :   On Monday, the payment = Rs x   On Tuesday, the payment = Rs (x + y)   On Wednesday, the payment = Rs (x + 2y)   On Thursday, the payment = Rs (x + 3y)   On Friday, the payment = Rs (x + 4y)   Average daily earning during the five-day week = (5x + 10y)/5   = x +2y   Answer :x+2y
Answer: B
A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?  Choose the correct option
A) 20 days B) 10 days C) 30 days D) 40 days E) 50 days

Solution: 20 days   20 days   Time taken by 20 days to finish the work = XY/(Y-X)   10 x 20 / (20-10)   200/10   20 days
Answer: A
An odd integer between 600 and 800 is divisible by 7 and also divisible by 9. What is the sum
of its digits? Choose the most appropriate option:
A) 7  B) 12  C) 18  D) 21  E) 27

Solution: The integer is a multiple of 63. There are three such multiples between 600 and 800. They are   630, 693, and 756. Only 693 is odd.   correct answer 18
Answer: C
If k is a positive integer, which of the following must be divisible by 26? Choose the correct choice from the following answers:
A) (k – 4)(k)(k + 3)(k + 7)  B) (k – 4)(k – 2)(k + 3)(k + 5)  C) (k – 2)(k + 3)(k + 5)(k + 6)  D) (k + 1)(k + 3)(k + 5)(k + 7)  E) (k – 3)(k + 1)(k + 4)(k + 6)

Solution: 24=8*3.   Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.   Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.   So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.   Answer:(k + 1)(k + 3)(k + 5)(k + 7).
Answer: D