MU-NLPC/Calc-aqua_rat huggingface dataset:
In his pocket, a boy has 3 red marbles, 6 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?  Choose the correct option:  A) 12  B) 13  C) 14  D) 15  E) 16

Solution: The worst case scenario would be that he has taken 6 blue and 6 green, a total of 12 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 13, will surely be red as only the red marbles are left in his pocket.   The answer is 13.
Answer: B
by what least number 4320 be multiplied to obtain a number which is a perfect cube ?
Choose the correct choice from the following choices.
A) 25
B) 50
C) 70
D) 30
E) 60

Solution: Solution   Clearly, 4320 = 23 * 33 * 22 * 5.   to make it a perfect cube, it must be multiplied by 2 * 52 i.e., 50 .   Answer 50
Answer: B
If w > a and L < a, which of the following cannot be true?  Choose the correct choice from the following options
A) d + L = 14	B) d - L = 7	C) d - L = 1	D) a - w = 9	E) a + d = 9

Solution: Is the answer D?   If w>a, then w-a>0 (always positive). The converse would be a-w<0 (always negative). Option a - w = 9 states that a-w=9, which can never be true.
Answer: D
In a garden, there are 12 rows and 14 columns of mango trees. The distance between two trees is 2metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is Options:
A) 20m  B) 22m  C) 24m  D) 26m  E) 28m

Solution: Each row contains 14 plants.   Leaving 2 corner plants, 12 plants in between have (12 x 2) metres & 1 metre on each side is left.   Length = (24 + 2)= 
(24 + 2) = 26
26m.   ANSWER:26m
Answer: D
Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 550. The income of the deceased was? Choose the correct choice from the following choices
A) Rs. 692.80  B) Rs. 820  C) Rs. 990  D) Rs. 1385  E) None

Solution: Answer   Income of the deceased = Total income of 4 members - total income of remaining 3 members.   = 735 x 4 - 550 x 3 Rs.   = 1290 Rs.   Correct Option: None
Answer: E
Given a spinner with four sections of equal size labeled T, B, C, and D, what is the probability of NOT getting an T after spinning the spinner two times?  Choose the correct choice
A) 15/16	B) 9/16	C) 1/2	D) 1/4	E) 1/8

Solution: The probability of NOT getting an T after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).   Answer: 9/16.
Answer: B
From the integer n, if n*n*n*n is odd, then what is true from below options?	Select.
A) n is odd	B) n*n is even	C) n is odd and n*n is even	D) n is even	E) None

Solution: n is odd   Option n is odd
Answer: A
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?  Choose the correct choice:
A) 12 %	B) 16 %	C) 18 %	D) 20 %	E) 22 %

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.   Number of such number =14   Required % = (14/70)x100 % =20 %   answer : 20 %
Answer: D
If xy not equal 0 and x^2*y^2 -xy = 42, which of the following could be y in terms of x?
I. 1/2x
II. -7/x
III. 6/x Choose the correct choice from the following answers:
A) II  B) III  C) IV  D) II and III  E) I &II

Solution: x2y2 â€“ xy = 6   x2y2-xy-42 = 0   (xy-6)(xy+7)=0   xy = 6 or xy=-7   y = 6/x or y = -7/x   II and III only   II and III
Answer: D
In how many different number of ways 9 men and 2 women can sit on a shopa which can accommodate persons?	Options
A) A)160  B) B)170  C) C)190  D) D)210  E) E)1663200

Solution: 11p7 = 11 x 10 x 9 x 8 x 7 × 6 × 5 = 1663200   Option '1663200'
Answer: E
2001+1015  Choices:
A) 8390 B) 3016 C) 2808 D) 3890 E) 2080

Solution: 3016
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?	Answers:
A) 186 m B) 100 m C) 872 m D) 150 m E) 765 m

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train   = (Speed x Time) = (50/3 * 6)= 
(50/3 * 6) = 100
100 m.   Answer: 100 m
Answer: B
A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%. If the annual profit is Rs 561. What was the initial capital? Choose the correct choice from the following answers.
A) Rs 66098  B) Rs 6608  C) Rs 6628  D) Rs 6600  E) Rs 6691

Solution: Explanation:   Let initial amount that the man invests be A   Let x be the capital   => Profit on 1st investment + Profit on 2nd investment + Profit on 3rd investment   => S.I. = P X R X T   => Remainder of capital = 1 - 1/3 - 1/4 = 5/12x (x being the capital)   => a*1/3 *7/100 + 1/4 *a * 8/100 + 5x/12*a* 10/100 = 561   Therefore, a = 6600   ANSWER: Rs 6600
Answer: D
A and B’s salaries together amount to Rs. 4,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?  Choose one:
A) 2777	B) 1500	C) 3000	D) 2776	E) 2881

Solution: (5/100) A = (15/100) B   A = 3B   A + B = 4000   4B = 4000 => B = 1000   A = 3000   Answer 3000
Answer: C
123 : 36 : : 221 : ? Choose the most appropriate option
A) 52	B) 69	C) 72	D) 25	E) 32

Solution: (1+2+3)^2 = 36   (2+2+1)^2 = 25   ANSWER:25
Answer: D
At 1:20 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
Choose the most appropriate option.
A) 0.5 + (p - 0.5s)/(r + s)  B) (p - 0.5s)/(r + s)  C) 0.5 + (p - 0.5r)/r  D) (p - 0.5r)/(r + s)  E) 0.5 + (p - 0.5r)/(r + s)

Solution: The distance A is going to cover between 1:00 and 1:30   = .5r   now the distance between the two trains = (p-.5r)   the relative velocity = (r-(-s)) = r+s   From 1:30, time is going to take when they meet = (p-.5r)/(r+s)   so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]   ans is (p - 0.5r)/(r + s)
Answer: D
A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 3 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
Select
A) 1/5	B) 1/3	C) 2/3	D) 4/5	E) 6/5

Solution: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B   FOR THE FIRST BUCKET ...   Red color - 2   Blue color - 2   FOR THE SECOND BUCKET   Red color - 3   Blue color -2   In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :   Scenario I - He picks Red color from List A and Blue color from List B   Scenario II - He picks Blue color from List A and Red color from List B   Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5   Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...   Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...   We get 1/5 + 3/10 = 1/3 (1/3)
Answer: B
How many three letter words are formed using the letters of the word TIME?	Pick:
A) 12 B) 20 C) 16 D) 24 E) 30

Solution: Explanation:   The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   ANSWER IS 24
Answer: D
In a office work is distribute between p persons. If 1/6 members are absent then work increased for each person is?
Choose the correct choice from the following choices: A) 10% B) 14.28% C) 15% D) 16% E) 20%

Solution: let total % of work is 100%   total person=p   1/6 person are absent of total person . so absent person is 1/6p ie p/6.   left person is, p-p/6=5p/6.   p person do the work 100%   1 person do the work 100*p%   5p/6 person do the work (100*p*6)/5p%=120.00%   work increased for each person is=(120-100)= 
(120-100) = 20
20%   ANSW20%R:20%
Answer: E
The mean of 50 observations was 30. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
Pick.
A) 35.2  B) 36.1  C) 30.5  D) 39.1  E) None

Solution: Sol.   Therefore correct sum   = ( 30 × 50 + 48 – 23)   = 1525.   Therefore correct mean   = 1525 / 50   = 30.5.   Answer 30.5
Answer: C
A man can row 8 kmph in still water. When the river is running at 1.8 kmph, it takes him 2 hour to row to a place and back. What is the total distance traveled by the man?  Choose the correct choice
A) 8.2 km
B) 6.7 km
C) 7.6 km
D) 7.4 km
E) 6.3 km

Solution: M = 8   S = 1.8   DS = 9.8   US = 6.2   x/9.8 + x/6.2 = 1   x = 3.8   D = 2.88 * 2 = 7.6   Answer:7.6 km
Answer: C
Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Choose the correct choice
A) 11	B) 10	C) 8	D) 12	E) 15

Solution: Suppose they meet x hours after 8 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 11 a.m.   11nswer: 11
Answer: A
The H.C.F. of two numbers is 10 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
Choose the most appropriate option:  A) 150  B) 300  C) 299  D) 322  E) 345

Solution: the numbers are (10 x 11) and (10 x 15).   Larger number = (10 x 15) = 150.   150NSWER :150
Answer: A
In the first week of the Year, Mancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Mancy saved during the 52 weeks?	Choose one.
A) $1,326	B) $1,352	C) $1,378	D) $2,652	E) $2,756

Solution: In the first week of the Year, Mancy saved $1.If you don't recall the formula, there is one method:   1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52   Sum of 1stlast digit = 1 + 52= 
1 + 52 = 53
53   Sum of 2nd2nd last digit= 2 + 51= 
2 + 51 = 53
53   Sum of 3rd3rd last digit= 3 + 50= 
3 + 50 = 53
53   .   .   .   .   This is repeated 26 times   So, 26 * 53= 1378   Answer = $1,378
Answer: C
A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
Choose the correct answer:
A) 23
B) 45
C) 15
D) 28
E) 18

Solution: A : 45: C = 10*7 : 12*5 : 15*3 = 2*7 : 12*1 : 3*3 = 14 : 12 : 9   amount that C should pay = 175 * (9/35) = 5*9= 
5*9 = 45
45   Answer is 45
Answer: B
A circle graph shows how the budget of a certain company was spent: 61 percent for salaries, 10 percent for research and development, 6 percent for utilities, 5 percent for equipment, 3 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?  Choose the correct choice from the following answers.
A) 18° B) 36° C) 54° D) 72° E) 90°

Solution: The percent of the budget for transportation is 100 - (61+10+6+5+3)= 
100 - (61+10+6+5+3) = 15
15%   100% of the circle is 360 degrees.   Then (15%/100%)*360 = 54 degrees   The answer is 54°.  (15 /100 )*360= 
  (15 /100 )*360 = 54
54 degrees   The answer is 54°.
Answer: C
If |x – 9/2| = 5/2, and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?
I. xyp is odd
II. xy(p^2 + p) is even
III. x^2y^2p^2 is even
Choose the correct choice from the following answers
A) II only B) III only C) I and III D) II and III E) I, II, and III

Solution: x is in range of 2 and 7 so it can be even or odd   y is median of set of odd integers so it can be even or odd   p is given as odd   using above information only II for sure can be inferred as even.   other two, either can be even or odd   correct response is II only.
Answer: A
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Two years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years? Select:
A) A)24
B) B)89
C) C)67
D) D)56
E) E)16

Solution: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then,	(5x + 2/4x + 2)=11/9   9(5x + 2) = 11(4x + 2)   45x + 18 = 44x + 22   45x - 44x = 22 - 18= 
22 - 18 = 4
4.   Anand's present age= 4x = 16 years.   Answer:16
Answer: E
The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2?
Choose the correct option:
A) 3
B) 8
C) 9
D) 11
E) 12

Solution: Let the number be xy.   Given xy – yx = 36.   This means the number is greater is than the number got on reversing the digits.   This shows that the ten’s digit x > unit digit y.   Also given ratio between digits is 1 : 2 => x = 2y   (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.   Hence, (x + y) – (x – y) = 3y – y = 2y = 8   8
Answer: B
A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 18%. What was its profit on the items sold in February?
Choose the correct answer
A) 27.5%  B) 30%  C) 35%  D) 23%  E) 40%

Solution: Assume the total price = 100x   Price after 20% markup = 120x   Price after 25%further markup = 1.25*120= 
1.25*120 = 150
150x   Price after the discount= 0.82*150= 
0.82*150 = 123
123x   Hence total profit= 23%   Option 23%
Answer: D
By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
Select the correct option.
A) Rs 96
B) Rs 100
C) Rs 150
D) Rs 160
E) Rs 200

Solution: to earn Rs 135 investment = Rs 1620   to earn Rs 8 investment =>1620/135*8= 
1620/135*8 = 96
96   Rs 96NSWER Rs 96
Answer: A
The average of five numbers id 28. If one number is excluded, the average becomes 25. What is the excluded number?
Options.
A) 30	B) 40	C) 32.5	D) 35	E) 37

Solution: Explanation:   Sum of 5 numbers = 5 × 28   Sum of 4 numbers after excluding one number = 4 × 25   Excluded number   = 5 × 28 - 4 × 25   = 140 - 100= 
140 - 100 = 40
40   Answer: Option 40
Answer: B
Find the average (arithmetic mean) of x and y if the average of x, y, and 10 is 20 greater than the average of x, y, 10, and 20.  Choose the correct choice from the following answers
A) 115
B) 130
C) 145
D) 160
E) 175

Solution: consider the statement 30 is 20 greater than 10: 30 = 10 + 20   similarly   the average of x, y, and 10 = (the average of x, y, 10, and 20) + 20   (x+y+10)/3 = (x+y+10+20)/4 + 20   (x+y+10)/3 = (x+y+30)/4 + 80/4   (x+y+10)/3 = (x+y+30+80)/4   (x+y+10)/3 = (x+y+110)/4   cross multiply   4(x+y+10) = 3(x+y+110)   4x+4y+40 = 3x+3y+330   4x-3x + 4y-3y = 330 - 40   x + y = 290   thus   (x+y)/2 = 290/2   (x+y)/2 = 145   thus the average of x and y is 145   145
Answer: C
The sum of two numbers is 16. The difference is 10. What are the two numbers?	Choose the correct choice from the following answers
A) 10-6  B) 8-8  C) 9-7  D) 11-5  E) 13-3

Solution: 13+3= 
13+3 = 16
16   13 - 3= 
13 - 3 = 10
10   The Answer is 13-3
Answer: E
During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 210 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?  Choose the correct choice from the following answers
A) 280	B) 320	C) 360	D) 420	E) 560

Solution: Easy 560 is the answer.   3/4 ( x/2) = 210   x = 210 * 8 /3= 
210 * 8 /3 = 560
560.   Answer 560
Answer: E
All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?  Choose the correct option.
A) 26(26^3 + 26^4) B) 26(26^3 + 26^5) C) 27(26^3 + 26^5) D) 27(26^3) + 26^5 E) 26^3 + 27(26^5)

Solution: 3-letter codes = 26^3;   4-letter codes = 26^4;   5-letter codes = 26^5;   Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.   Answer: 27(26^3) + 26^5.
Answer: D
I buy coffee from 3 different shops at Rs.150,Rs.140,Rs.130 per kg and mix them in proportion 8:5:3.At what price per kg must I sell the mixture to make a profit of 25%?  Pick:
A) 168.906
B) 178.906
C) 188.906
D) 198.906
E) 158.906

Solution: total=16x kg, tot cp=2290x   sp should be=2862.5x   so sp/kg=178.906   ANSWER:178.906
Answer: B
In a game, a person is declared winner, if he gets 4 consecutive tails in five throws of a coin. What is the probability of A to win if he has got a tail in the first throw?
Choose the correct choice from the following answers:
A) 1/5  B) 1/4  C) 1/8  D) 1/16  E) 1/6

Solution: First throw = Tails   For a person to win, the next 3 throws must be tails and the 5th throw can be heads or tails. i.e. TTTTH or TTTTT   So the person can win in 2 ways if the first throw is Tails.   Total number of outcomes for the next 4 throws = 2^4 = 16   Probability = 2/16 = 1/8   Answer: 1/8
Answer: C
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 171? Choose the correct choice from the following answers
A) 2820  B) 3440  C) 4860  D) 5560  E) 6720

Solution: 100 + 102 + ... + 170 =   100*36 + (2+4+...+70) =   100*36 + 2*(1+2+...+35) =   100*36 + 2(35)(36)/2 =   100*36 + 35*36 = 135(36) = 4860   The answer is 4860.
Answer: C
A girl has 8 dolls out of which a pair of is to be selected to take with her. At most, how many different pairs are possible?
Choose the correct choice from the following choices
A) 100	B) 90	C) 50	D) 45	E) 28

Solution: N=8C2=8!/(6!2!)=8*7/2= 
8*7/2 = 28
28   Correct Option: 28
Answer: E
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
Choose the correct choice from the following options.
A) 22  B) 25  C) 97  D) 27  E) 91

Solution: Answer: 25 y   Explanation:   Average age of 39 students = 15 yrs   Total age of 39 students = 39 × 15 = 585 yrs   Avg age of 39 students + teacher =15+ (3/12)= 
15+ (3/12) = 61/4 = around 15.25
15.25 years   So the total age of (39 student + 1 teacher) or 40 persons= 40 × 15.25 = 610 years   So age of teacher = 610 – 585 = 25 years   Answer:25
Answer: B
Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 50% more than Bert had in savings, and separately, the same price was also 25% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings. Choices:
A) 1:6  B) 1:3  C) 1:2  D) 3:4  E) 5:6

Solution: Suppose bert had 100 so price becomes 150 , this 150 = 1.25 times R's saving .. so R's saving becomes 120   So required ratio is 100:120=5:6   ANSW5:6R:5:6
Answer: E
At a bank, the service charges for transactions were US Dollar 1 for every 5 transactions. The bank recently revised the charges to US Dollar 0.75 for every 3 transactions. By approximately what percent did the ratio of price to transactions increase from the previous charge?
Select:
A) 28  B) 24  C) 23  D) 22  E) 25

Solution: Initial charge/transaction ratio = 1/5 = 3/15   Revised charge/transaction ratio = .75/3 = 3.75/15   Answer: 25
Answer: E
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18600. A's share is?
Choose the correct choice from the following choices:
A) 8876	B) 2765	C) 6000	D) 6200	E) 1261

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18600= 
1/3 * 18600 = 6_200
6200   Answer:6200
Answer: D
If 7^q is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of q?
Choose the correct choice from the following options.
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: So the question just means that we have to find all the multiples q of 7 between 1 to 100   So there are 14 multiples of 7 ( 7 - 98)   But 49 and 98 contain two 7's as factors   so we have to add  14 + 2= 
 14 + 2 = 16
16   16
Answer: E
At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number R of different possible seating arrangements for the group? Answers:
A) 5
B) 10
C) 24
D) 32
E) 120

Solution: 24ircular arrangements= (n-1)!   Hence (4!) = 24=R   Answer is 24
Answer: C
At what price must an article costing Rs.47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price? Options
A) 65.97	B) 62.6	C) 62.1	D) 62.7	E) 62.2

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(90/100)= 59.375   MP = 65.97   65.97nswer: 65.97
Answer: A
Susan, Daisy and Tim need to be seated in 3 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?	Pick one
A) 3
B) 12
C) 80
D) 240
E) 60

Solution: Total # of arrangement of 3 people is 3!.   In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).   So, # of arrangements to satisfy the given condition is 3!/2=3.   3nswer: 3.
Answer: A
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.  Choose the correct choice from the following.
A) 5:28	B) 5:19	C) 5:12	D) 5:13	E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128   = 5:16   Answer:5:16
Answer: E
Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 900 widgets?
Pick one:
A) 1 hour and 20 minutes
B) 1 hour and 24 minutes
C) 1 hour and 30 minutes
D) 1 hour and 36 minutes
E) 1 hour and 40 minutes

Solution: (350+250)t=900   600t=900   t=3/2   t=1 hour and 30 minutes   Answer: 1 hour and 30 minutes
Answer: C
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.600 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?	Select: A) 3999 B) 7799 C) 2500 D) 7500 E) 2912

Solution: A:B:C = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 600   B capital = 45000*1/6= 
45000*1/6 = 7_500
7500.Answer: 7500
Answer: D
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Choose the correct choice from the following answers:
A) 22
B) 27
C) 30
D) 82
E) 21

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer: 30
Answer: C