MU-NLPC/Calc-aqua_rat huggingface dataset:
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 23. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
Choose the correct choice from the following:
A) 1 B) 13 C) 15 D) 19 E) 47

Solution: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (15)
Answer: C
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Choose the correct answer:
A) 5
B) 4
C) 7
D) 3
E) 1

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations?
Choose the correct choice:	A) 4/5	B) 3/5	C) 3/20	D) 1/5	E) 1/10

Solution: 15 + 10 + 60= 
15 + 10 + 60 = 85
85% 100 - 85= 15% to all others   3/20
Answer: C
If a and d are both integers, a>d, and -3c>19, then the largest value of d would be? Pick:  A) -5  B) -6  C) -7  D) -8  E) -10

Solution: No, your thinking is incorrect. When we know that a>d and a<-6.33, the largest value of a can be -7 while if a=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.   You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.   Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:   .......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).   So, as per the question if d<a and a = -7 , then d's largest 'possible' value has to be -8.   -10 is smaller than -8=-8
Answer: D
A retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles. What is the percentage of profit made by the retailer?  Select the correct option:
A) 66.67% B) 33.33% C) 40% D) 25% E) 20%

Solution: Let Cost Price = x   Profit = y   Selling Price = x+y   50y = 20(x+y)   30y = 20x   Percentage Profit =y/x∗100=20/30∗100=66.667   66.67%nswer = 66.67%
Answer: A
Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 4000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?	Select
A) 100000
B) 100500
C) 84000
D) Data inadequate
E) None of these

Solution: Let the investment of X in 1995 be x.   ∴ Profit = x⁄5   ∴ Income = (x + x⁄5) = 6⁄5x   Investment of company X in 1996 would be (x – 4000) From the question,   (x - 4000) × 126⁄100 = 6⁄5x ⇒ x = 84000   Answer 84000
Answer: C
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the Mother insists of standing by her younger Child, as the song says?
Answers:
A) 12	B) 24	C) 30	D) 48	E) 120

Solution: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that M and C2 are always together.   Consider F and M to be one unit, then we would have total of four units: {F}, {C1}, {MC2}, {D}. The number of arrangements of these four units is 4!, but M and C2 within their unit can be arranged in 2 ways: {C2M} or {MC2}, so total number of arrangements is 4!*2=48.   Answer: 48.
Answer: D
if 8 people take an hour to complete a piece of work, then how long should 16 people will take to complete the same piece of work?
Choose the most appropriate option
A) 15 min B) 30 min C) 26 min D) 28 min E) 18 min

Solution: if 8 people take an hour to complete a piece of work, then   16 people will take 8*60/16= 
8*60/16 = 30
30 mins to complete the same piece of work.   ANSWER:30 min
Answer: B
.04 × ? = .000016. Select the correct option
A) 0.0004	B) 0.04	C) 4	D) 0.4	E) None of these

Solution: Solution   Let .04 × x = .000016. Then, x = .000016/.04 = .0016/4 = .0004. 0.0004nswer 0.0004
Answer: A
A's speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 25% of the length of the race?  Choose the correct choice from the following options:	A) 44%	B) 48%	C) 52%	D) 42%	E) 61%

Solution: First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race.   Then Add the remaining distance as head start for B to win the race.   Its best to apply Ratios concept here.   Since A's speed is 20/13 of B, therefore, B's speed is 13/20 of A   Distance covered by B = speed x time = (13/20) x (0.6) = 0.39%   (Which means B would have covered 0.39 of the race length during the time in which A has covered 0.6 of the race length.   Therefore to win, B needs a headstart of (1 - 0.39 = ) 0.61 of the race length.   So the answer is 61%
Answer: E
The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
Choose one.
A) Rs. 60 B) Rs. 108 C) Rs. 110 D) Rs. 112 E) Rs. 122

Solution: P.W. = Rs. (540 - 90) = Rs. 450.   S.I. on Rs. 450 = Rs. 90.   S.I. on Rs. 540 = Rs. (90/450)X540	= Rs. 108.   B.D. = Rs. 108.   ANSWER :Rs. 108
Answer: B
What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 40%?  Pick one
A) 95%	B) 90%	C) 85%	D) 96%	E) 25%

Solution: The question is very easy. My logic is the following:   A surface = 6*a^2   After 40% increase A surface = 6* ((1.4a)^2) = 6*1.96*a^2   The increase in the surface area = (6*1.96*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.96-1))/(6*a^2) = 1.96-1= 
1.96-1 = 0.96
0.96= 96%   Answer :96%
Answer: D
A, B and C can do a piece of work in 4 days, 8 days and 20 days respectively. How long will they taken, if all the three work together? Choose one
A) 2 B) 4 C) 5 D) 67 E) 2 6/17

Solution: 1/4 + 1/8 + 1/20 = 17/40 => 40/17 => 2 6/17 days   Answer: 2 6/17
Answer: E
A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 20 as remainder. Find the no. is?	Choose the correct choice.
A) 122456
B) 220020
C) 220022
D) 235467
E) 220026

Solution: (555 + 445) * 2 * 110 + 20 = 220000 + 20= 
220000 + 20 = 220_020
220020   220020
Answer: B
The total age of A and B is 14 years more than the total age of B and C. C is how many years younger than A ?  Choose the correct choice from the following.
A) 14 B) 27 C) 21 D) 18 E) 11

Solution: (A+B) - (B+C) = 14   A - C = 14.   C is younger than A by 14 years.   14nswer: 14
Answer: A
When the integer n is divided by 17, the quotient is x and the remainder is 2. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?	Choose one
A) 23x + 17y =19 B) 17x –23y = 12 C) 17x +23y =19 D) 14x + 5y = 6 E) 5x – 14y = -6

Solution: From the problem it follows:   n=17x+2   n=23y+14   So, 17x+2=23y+14   17x-23y=12   The answer is 17x –23y = 12
Answer: B
If 625^(-x) +5^(-2x) + 5^(-4x) = 15, what is the value of x? Select the correct option:
A) -4 B) -1/4 C) 0 D) 1/4 E) 4

Solution: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.   Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....   With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.   With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.   With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.   With Answer C, anything to the '0 power' is 1, so we'd have   1+1+1= 
  1+1+1 = 3
3. This is not 15. Eliminate C.   -4
Answer: A
The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 3 shirts each of them then average number of shirt each of them now has Choose one:	A) 66	B) 63	C) 62	D) 64	E) 61

Solution: Required average   = Old average + New average   = 60 + 3= 
60 + 3 = 63
63   answer :63
Answer: B
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?  Choose the correct option.
A) 42, 33
B) 41, 33
C) 42, 35
D) 41, 35
E) 41, 37

Solution: Let the marks secured by them be x and (x + 9)   Then sum of their marks = x + (x + 9) = 2x + 9   Given that (x + 9) was 56% of the sum of their marks   =>(x+9) = 56/100(2x+9)   =>(x+9) = 14/25(2x+9)   => 25x + 225 = 28x + 126   => 3x = 99   => x = 33   Then (x + 9) = 33 + 9= 
33 + 9 = 42
42   Hence their marks are 33 and 42   42, 33)
Answer: A
If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers?
Choose the correct choice from the following options.
A) 4K	B) 4k^2 -4k	C) 4-4k	D) 4	E) 4k+4

Solution: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1   => n = 10k - 5   Greatest = n + 2 = 10k - 5 + 2 = 10k - 3   Least = n - 2 = 10k - 5 - 2   => 4ifference 4= 10k - 3 - (10k - 7)   = 4   Answer - 410  - 3 - (10  - 7)= 
10  - 3 - (10  - 7) = 4
4   Answer - 4
Answer: D
3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.	Choices
A) 2 : 5	B) 3 : 10	C) 4 : 5	D) 4 : 7	E) 5 : 11

Solution: We have, a = 12, b = 15, c = 25 and x = 312.   ax_ 12 X 312   a+b+c 12+15+25   — 72,   bx _ 15 X 312 3 : 10 — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =   a+b+c 12 + 15+ 25   ...3 : 10-A=18 andC-3 : 10=60   - 150   Thus, their ratio = 18 : 60 or 3 : 10   3 : 10
Answer: B
A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
Choose the correct option:
A) 32
B) 20
C) 24
D) 16
E) 14

Solution: Explanation:   Let cost price of lemons be x.   Selling price of lemons becomes CP - loss.   =>SP=x-(20/100)x   =>40=x(80/100)   =>50   So 45 lemons cost Rs 50   Cost of 1 lemon = 50/45 Rs   Cost of 24 lemons = (50/45)*24 =80/3 Rs   Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32   32NSWER 32
Answer: A
three men invested sum. and their ratio is 5:7:6. profit is 1800.then b's share Options
A) 2000 B) 2100 C) 700 D) 2300 E) 2400

Solution: b's share =7/18*1800= 
7/18*1800 = 700
700   ANSWER:700
Answer: C
A group of people participate in some curriculum, 30 of them practice Yoga, 20 study cooking, 15 study weaving, 5 of them study cooking only, 8 of them study both the cooking and yoga, 5 of them participate all curriculums. How many people study both cooking and weaving?
Choose the correct choice from the following answers:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 2oth cooking and weaving = 20 - (5+8+5)= 
20 - (5+8+5) = 2
2   So, the correct answer is 2.
Answer: B
Three candidates contested an election and received 3834 votes, 7606 votes, and 14560 votes respectively. What percentage of the total votes did the winning candidate receive?	Choose the correct option:	A) 55%	B) 56%	C) 57%	D) 58%	E) 59%

Solution: The total number of votes polled = (3834 + 7606 + 14560)= 
(3834 + 7606 + 14560) = 26_000
26000   The winner's percentage= 14560/26000 * 100= 
14560/26000 * 100 = 56
56%   The answer is 56%.
Answer: B
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive? Choose the correct choice: A) 420 B) 840 C) 1,260 D) 2,520 E) 5,040

Solution: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.   420nswer: 420.
Answer: A
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?  Choose the correct choice from the following answers
A) 49
B) 44
C) 77
D) 25
E) 29

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352 => T = 44.Answer:44
Answer: B
Let Q represent a set of five distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?  Pick one
A) 1
B) 2
C) 3
D) 5
E) 7

Solution: Q = p1+p2+p3+p4+p5 = even (and all primes are distinct)   if the least prime is 2 then we have sum of Q = even   Ans. B. 2
Answer: B
A boat crossed a lake from North to South at the speed of 6 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 5 km/h that day, what was its approximate downstream speed?
Choose the correct choice from the following choices:
A) 12
B) 15
C) 16
D) 17
E) 18

Solution: Another way will be:   Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed   If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D   =>5D/5 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)   => 5/5= 
5/5 = 1
1/6 + 2/3 +2/x (div. both sides by D)=> 1.0 = .16+.66 +.16/x => x=11.98 ~12   option 12
Answer: A
Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?  Choose the correct choice from the following options:
A) 1/15
B) 4/5
C) 4/15
D) 1/5
E) 2/5

Solution: tot students=x   1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)   2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)   hence 1/5   1/5
Answer: D
If m and n are both odd prime numbers andm < n, then how many different positive integer factors does2mnhave?  Choose the correct choice from the following options:
A) 3	B) 8	C) 6	D) 4	E) 12

Solution: m and n are both odd prime numbers- It means either m or n is not 2   and since prime numbers have only two factors - 1 and the number itself   m and n each will have (1+1)= 
(1+1) = 2
2 factors   Hence 2mn will have (1+1)(1+1)(1+1)= 8 factors   8 is the answer
Answer: B
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Choose the correct answer:
A) 46%
B) 57%
C) 74%
D) 63%
E) 68%

Solution: B   57%   Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400.   Required percentage=(11628x100/20400)% = 57%.
Answer: B
Two trains 190 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Pick:
A) 10.6 sec  B) 18.8 sec  C) 14.6 sec  D) 10.8 sec  E) 12.6 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 190 + 160= 
190 + 160 = 350
350 m.   Required time= 350 * 9/250 = 63/5= 
63/5 = 63/5 = around 12.6
12.6 sec.   Answer: 12.6 sec
Answer: E
A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?	Options
A) 1978  B) 2707  C) 7728  D) 7008  E) 7291

Solution: 35:15 => 7:3   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*7/10= 
8640*7/10 = 6_048
6048 + 960= 
6048 + 960 = 7_008
7008   Answer: 7008
Answer: D
if p/q=3/4
then3p+7q=?	Answers:  A) 37/4  B) 25/2  C) 20/4  D) 35/4  E) 25/3

Solution: 3p+7q=?   Divided by q,   3(p/q)+7=x   3*(3/4)+7=37/4   37/4NSWER:37/4
Answer: A
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 choices: A) 99 B) 277 C) 48 D) 99 E) 22

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
If (x^2 + x - 8) ≤ x + 1, then x could be represented by which of the following? Pick one:
A) − 4 ≤ x ≤ − 3
B) − 4 ≤ x ≤ 3
C) − 3 ≤ x ≤ 3
D) − 3 ≤ x ≤ 4
E) 3 ≤ x ≤ 4

Solution: IMO − 3 ≤ x ≤ 3 is correct answer   solving through eqautions   x^2 +x-8<= x+1   (x+3)(x-3)<=0
Answer: C
If r and h are two positive integers and r/h = 1.60, then r can equal which one of the following? Choose the correct choice from the following options:
A) 9  B) 24  C) 20  D) 22  E) 23

Solution: r/h = 1.60 = 160/100 = 8/5   So, r COULD equal 24   Answer: 24
Answer: B
A bag contains 8 red, 7 blue and 6 green dress. If one dress is picked up randomly then ewhat is the probability that it is neither red nor green?
Choose the correct option:
A) 1/3
B) 2/3
C) 2/5
D) 3/7
E) None of these

Solution: Total number of dress = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21.   Let E= event that the dress drawn is neither red nor green   = event that the dress drawn is blue.   n(E) = 7.   P(E) =	n(E)	=	7	=	1/3   n(S) 21   1/3
Answer: A
A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 3 new workers. How many different ways can she assign the new workers? Choose the correct choice from the following answers:  A) 2430  B) 2640  C) 3300  D) 4860  E) 5400

Solution: whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12C3 = 220 ways.   now 3 out of 12 means total of 4 group possible.   so putting them in shifts = counting methode: first, second, third, alt , alt   = 4*3*2*1= 
4*3*2*1 = 24
24   here alt and alt are the same: so  24/2= 
 24/2 = 12
12 ways.   total ways of selecting= (selecting 3 out of 12)*arranging those teams in shifts   = 220*24 = 2640   Ans: 2640
Answer: B
In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?  Choose the correct choice from the following answers.
A) 8m/s
B) 9m/s
C) 6m/s
D) 4m/s
E) 1m/s

Solution: Since A beats B by 200 m or 25 seconds, i   t implies that B covers 200 m in 25 seconds.   Hence speed of B = 200/25= 
200/25 = 8
8 m/s.   8m/snswer: 8m/s
Answer: A
Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?  Select the correct option:
A) $3,000
B) $4,000
C) $7,000
D) $11,000
E) $25,000

Solution: Let Mary's income increase by x, then the equation will be   15,000 + x= (55/100)* (15,000 + x + 18000 )   15,000 + x = (11/20) * (33,000 + x)   300,000 + 20x = 11x + 363,000   9 x = 63,000   x = 7,000   So, Answer will be $7,000
Answer: C
If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?  Select the correct option:
A) Rs. 850 B) Rs. 900 C) Rs. 800 D) Rs. 910 E) Rs. 1000

Solution: Sol We have, A : Rs.1U2D   Let the pr xnpal be R5 x   Then mterest u — 12 : wzo — x   Therefore, by u xglurmula.   _umxx   ’ Rx’: (   , _ma>< 1nzn—xv   \4Ve|\a\e,Jc— 5“   :> ~(:51DD—S*(or6x:51UU   or, J: : w 350   . The sum of money burrowed : Rs. 850   Rs. 850)
Answer: A
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
Answers.
A) 187 min
B) 177 min
C) 144 min
D) 189 min
E) 166 min

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min.   Answer:144 min
Answer: C
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?  Choose the correct choice from the following options
A) x + y  B) y – z  C) xy + 1  D) xyz + 1  E) x^2 + y^2

Solution: xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.   Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.   Answer: xyz + 1.
Answer: D
A rectangular tiled patio is composed of 60 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 60 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?  Select the correct option.
A) 5	B) 6	C) 10	D) 13	E) 8

Solution: r*c=60 and (r+4)(c-2)=60 --> r=8 and c=7.   Answer: 8.
Answer: E
The average of first five prime numbers greater than 61 is?	Options
A) 32.2  B) 32.98  C) 74.6  D) 32.8  E) 32.4

Solution: 67 + 71 + 73 + 79 + 83= 
67 + 71 + 73 + 79 + 83 = 373
373/5= 
373/5 = 373/5 = around 74.6
74.6   Answer: 74.6
Answer: C
The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:6, the price of the cheapest item is? Choices.
A) 2379	B) 2889	C) 9288	D) 9000	E) 7500

Solution: Let their prices be 3x, 5x and 7x.   Then, 2x + 4x + 6x = (15000 * 3) or x = 3750.   Cost of cheapest item = 2x = Rs. 7500.   Answer: 7500
Answer: E
Three partners A,B,C start a business.Twice A’s capital is equal to thirce B’s capital and B’s capital is four times C’s capital.Out of a total profit of Rs.16,500 at the end of the year,B’s share is :	Pick one.
A) Rs.4000 B) Rs.6000 C) Rs.7500 D) Rs.6600 E) None of these

Solution: Solution   Let C = x.Then,B = 4x and 2A = 3 4x = 12 x or A = 6x.   ∴ A : B : C = 6x : 4x : x = 6 : 4 : 1 .   So, B’s capital = Rs. (16500x4/11) = Rs. 6000. Answer Rs.6000
Answer: B
if N is a prime number bigger than 5. Which of the following expressions must be even?
Options:	A) (a) (N+2)^2	B) (b) N^2+2.	C) (c) N(N+2).	D) (d) (N+1)(N+2)	E) (e) (N-2)^2

Solution: N=11   a. 169   b. 123   c. 143   d. 180   e. 81   (b) N^2+2.
Answer: B