MU-NLPC/Calc-aqua_rat huggingface dataset:
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,3), (6,0) and (6,3). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Choose the most appropriate option
A) 1/2
B) 2/5
C) 4/7
D) 1
E) 7/4

Solution: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.   The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (6,3) OR Midpoint of (0,3) and (6,0)   i.e. Either [(0+6)/2, (0+3)/2] OR [(0+6)/2, (3+0)/2] =[3,1.5]   Slope of line passing through points (2,2) and (3,1.5) = (2-1.5)/(3-2)= 
(2-1.5)/(3-2) = 0.5
0.5/1= 1/2   1/2
Answer: A
The sum of ages of 5 children born at the intervals of 8 years each is 90 years. What is the age of the youngest child?
Choose one
A) 2
B) 9
C) 6
D) 4
E) 0

Solution: Let the ages of children be x, (x +8), (x + 16), (x + 24) and (x + 32) years.   Then, x + (x + 8) + (x + 16) + (x + 24) + (x + 32) =90   5x = 10   x = 2.   Age of the youngest child = x = 2 years.   2nswer:2
Answer: A
Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/6 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent? Pick.
A) 2/3
B) 29/60
C) 17/30
D) 19/30
E) 11/15

Solution: Let s assume the platinum card spending limit =x   Gold card spending limit will be =x/2   balance on gold card is =x/2*1/3=x/6   Platinum card unspent limit is= x-1/6x=5/6x   So if gold card balance is transferred then the rest unspent will be   5/6x-x/6=2/3x   So the ans is 2/3
Answer: A
The average age of a family of 6 members is 28 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?	Choose the most appropriate option:  A) 15  B) 18  C) 21  D) 12  E) 19

Solution: Present age of total members = 6 X 28 = 168   7 yrs back their ages were = 6 x 7 = 42   Ages at the birth of youngest member = 168 - 42= 
168 - 42 = 126
126   Therefore, avg age at the birth of youngest member= 126/6= 
126/6 = 21
21.   ANSWER:21
Answer: C
There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 7, how many passengers were on the bus originally?
Choose the most appropriate option:
A) 128
B) 64
C) 32
D) 16
E) 8

Solution: Before stop 7, there were 2 passengers on the bus.   Before stop 6, there were 4 passengers on the bus.   etc...   Before stop x, there were 2^(8-x) passengers on the bus.   Before stop 1, there were 2^7 = 128 passengers on the bus.   The answer is 128.
Answer: A
If √2n = 64, then the value of n is : Choose the correct answer.
A) 6  B) 12  C) 24  D) 48  E) NOne

Solution: Sol.   √2n = 64 ⇔ (2n)1/2 ⇔ 2n/2 = 26 ⇔ n/2   = 6 ⇔ n = 12.   Answer 12
Answer: B
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?  Select the correct option.
A) 18 m
B) 17 m
C) 26 m
D) 27 m
E) 15 m

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer:17 m
Answer: B
A rectangular box measures internally 1.6 m long, I m broad and 60 cm deep.The number of cubical blocks each of edge 20 cm that can be packed inside the box is  Pick one.
A) 30  B) 53  C) 60  D) 120  E) None

Solution: Solution   Number of blocks	= (160×100×60 / 20×20×20)   = 120.   Answer 120
Answer: D
Louie takes out a three-month loan of $1000. The lender charges him 30% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Choices: A) A)333 B) B)663 C) C)402 D) D)433 E) E)483

Solution: Here's the calculation for that case, assume monthly payment is X.   After 1st month: (1000)(1.3)-X = 1300-X   After 2nd month: (1300-X)(1.3)-X = 1690-2.21X   After 3rd month: (1690-2.21X)(1.3)-X = 2197-3.31X   Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:   2197-3.31X = 0   X = 2197/3.31 = 663.74   Answer 663
Answer: B
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 20 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?  Choose the correct choice from the following choices.
A) 20%  B) 25%  C) 30%  D) 35%  E) 40%

Solution: Let T be the total number of passengers.   Let x be the number of people with round trip tickets.   0.2T had round trip tickets and took their cars.   0.8x had round trip tickets and took their cars.   0.8x = 0.2T   x = 0.25T   The answer is 25%.
Answer: B
If a committee of 4 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?  Select.
A) 20  B) 40  C) 50  D) 80  E) 120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) each to send onerepresentativeto the committee: 5C4=5.   But these 4 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=40.   Answer: 40.
Answer: B
a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 2a = b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. Choose the correct option
A) 124	B) 241	C) 394	D) 421	E) 842

Solution: Ratio of a:b:c= 2:4:1   Two possible greatest single digit values for b are 8 and 4   if b is 8, then x= 482   if b is 4, then x= 241   difference= 482-241= 
482-241 = 241
241   241 is the answer
Answer: B
Six cards numbered from 1 to 6 are placed in a cardboard box . First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 5 ?	Choose the correct choice from the following options.
A) 1/2	B) 1/4	C) 1/5	D) 1/6	E) 1/3

Solution: (6,4) (4,6) (5,5) – only 3 possible scenarios for sum to be 10. One from this 5 has already happened.   From this three cases, only in one we have 5. So, the probability is 1 chances out of 3 that the one that occurred had 5: P=1/3.   Answer: 1/3.
Answer: E
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?  Choose the correct choice from the following choices:  A) 15  B) 16  C) 28  D) 56  E) 64

Solution: Number of ways 2 teams can be selected out of 8 teams:   288/2=8∗7/2=28   Ans:"28"
Answer: C
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Choose the correct choice from the following
A) 8%
B) 4%
C) 5%
D) 3%
E) 2%

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: 4%
Answer: B
Average of 7 numbers is zero. At most how many numbers may be greater than zero Choices.
A) 0	B) 1	C) 6	D) 9	E) 10

Solution: Answer: Option 6
Answer: C
A line that passes through (–1, –4) and (5, k) has a slope = k. What is the value of k?  Choose the correct choice from the following answers:
A) 3/4
B) 1
C) 4/5
D) 2
E) 7/2

Solution: Slope = (y2-y1)/(x2-x1)   => k = (k+4)/(5+1)   => 6k = k+4   => k =4/5   Ans 4/5 it is!
Answer: C
n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 3000m race?  Choose the correct choice from the following options:
A) 300
B) 350
C) 375
D) 400
E) 425

Solution: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40   and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40   solving equation A speed =8 and B=20/3   for 1000m b will take 3000/20/3= 375 sec   375
Answer: C
Tom wants to buy items costing $25.35, $70.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour. Options: A) 8 hours B) 48 hours C) 31 hours D) 18 hours E) 28 hours

Solution: $6.50 x .10 = $.65 is 10% of his hourly income   $  6.50 - .65= 
  6.50 - .65 = 5.85
$5.85 hourly amount available to spend   $25.35 + $70.69 + $85.96 = $182 total needed   $182 ÷ $5.85  25.35 +  70.69 +  85.96= 
 25.35 +  70.69 +  85.96 = 182
$182 total needed   $182 ÷ $5.85= 31.11... rounds to 31 hours   correct answer 31 hours
Answer: C
A and B invested Rs.15000 and Rs.20,000 respectively in a business. How should a loss of Rs.2800 be divided between them at the end of year? (in rupees)
Pick:
A) 1500,1300  B) 1200,1600  C) 1300,1500  D) 1600,1200  E) 1700,1200

Solution: Ratio btwn invest is == 3:4   loss==2800   so 2800/7==400   A==3*400==1200   1200,1600==4*400==1600   ANSWER:1200,1600
Answer: B
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? Choices:
A) 3/5
B) 3/2
C) 3/9
D) 3/6
E) 3/1

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.Answer: 3/2
Answer: B
If 70% of a number exceeds 28% of it by 39.9, then find the number?
Answers:	A) 65	B) 67	C) 100	D) 95	E) 33

Solution: Use the elimination method to find the correct option.   Of all the options only 95 fits   70% of 95 = 66.5   28% of 95 = 26.6   66.5 - 26.6= 
66.5 - 26.6 = 39.9
39.9   Required number is 95.   ANSWER:95
Answer: D
Find the ratio in which rice at Rs. 7.30 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg	Choose the most appropriate option
A) 2:0  B) 2:3  C) 3:5  D) 2:2  E) 2:8

Solution: By the rule of alligation:   3:5ost of 1 kg rice of 1st kind 3:5ost of 1 kg rice of 2nd kind   Required ratio = 60 : 100 = 3 : 5   Answer: 3:5
Answer: C
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:	Choose the correct answer:
A) Dollar 2000
B) Dollar 10,000
C) Dollar 15,000
D) Dollar 20,000
E) None of these

Solution: Explanation: Principal = Dollar (100 x 5400)/(12x3) = Dollar 15000.   Answer: Option Dollar 15,000
Answer: C
In a certain province in India there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?  Options.
A) 30
B) 105
C) 330
D) 14!
E) 15!

Solution: Method-1:   India has Total Cities = 15 and each city should be connected with every other city   So Total Roads required to connect 1st City with other 14 cities = 14   Now 1st City is connected with all other cities so,   So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13   Now 1st and 2nd Cities are connected with all other cities so,   So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12   ......and so on...   Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1= 
14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105
105=105
Answer: B
There are 6 orators A, B, C, D, E, F. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.  Choose the correct choice from the following choices: A) 6! / 3! B) 8! / 6! C) 5! x 3! D) 8! / (5! x 3!) E) 8! / (5! x 4!)

Solution: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.   The remaining 3 people have to be arranged in 3 places.   Thus, 6C3 x 3! = 6! / 3!   6! / 3!NSWER:6! / 3!
Answer: A
Which of the following is non-negative?
Choose one:
A) (a-0.9)(a-1)	B) (a+1)(a-1)	C) (a+0.7)(a+1)	D) (a-0.7)(a-0.7)	E) a(a+1)

Solution: 5-sec approach:   D. (a-0.7)(a-0.7) = (a-0.7)^2. The square of a number is always non-negative.   Answer: (a-0.7)(a-0.7).
Answer: D
In a group of 3 boys and 2 girls can be formed out of a total of 4 boys and4 girls? Select:
A) 20
B) 22
C) 24
D) 26
E) 29

Solution: Solution: Total number of ways = (select 3 boys from group of 4 boys) * (2 girls from group of 4 girls)   => (4c3) * (4c2) = 24   24
Answer: C
What will come in place of the x in the following Number series? 5,28,57,88,125  Choose the correct answer: A) 122 B) 324 C) 166 D) 175 E) 178

Solution: 28=23+5   57=29+28   88=31+57   125=37+88   166=41+125= 
41+125 = 166
166   166
Answer: C
A sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 1 rupee 50 paisa and Z gets 1 rupee 20 paisa. If the share of X is RS. 125, what is the total amount?
Choose the correct choice from the following:
A) 283.75
B) 193.75
C) 293.75
D) 290.75
E) 313.75

Solution: x:y:z = 200:150:120   20:15:12   20 --- 125   47 --- ? => 293.75   Answer: 293.75
Answer: C
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?  Options
A) 227
B) 268
C) 127
D) 150
E) 187

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 184 – 150 = 34   Answer: 150
Answer: D
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over. What is the sum of the two smallest possible values of n? Choose the correct choice from the following
A) 42.  B) 46.  C) 50.  D) 54.  E) 58.

Solution: n = 4k+1 = 7j+2   Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+2.   1, 5, 9 = 7(1)+ 2   The next such number is 9 + 4*7= 
9 + 4*7 = 37
37.   9+37= 
9+37 = 46
46   The answer is 46..
Answer: B
The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?	Choose the correct choice from the following options.
A) 4.7 B) 4.6 C) 4.2 D) 4.1 E) 4.9

Solution: Explanation:   Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.   Required average = (9.2 / 2) = 4.6.   Answer: 4.6) 4.6
Answer: B
what is the least number. which should be added to 0.0355 to make it a perfect square?	Options:
A) 0.0005  B) 0.0016  C) 0.0056  D) 0.0066  E) 0.0006

Solution: 0.0355+0.0006= 
0.0355+0.0006 = 0.0361
0.0361   (0.19)^2   ANSW0.0006R:0.0006
Answer: E
A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
Choose the correct choice from the following choices:
A) 4km
B) 2km
C) 5km
D) 3km
E) 1km

Solution: Speed downstream =(7.5+1.5)km/hr=9 km/hr;   Speed upstream=(7.5-1.5)= 
(7.5-1.5) = 6
6kmph.   Let the required distance be x km.then,   x/9+x/6=50/60.   2x+3x=(5/6*18)   5x=15   x=3.   Hence,the required distance is 3km   ANSWER 3km 3km
Answer: D
Which of the following is a prime number ? Pick:
A) 33  B) 81  C) 93  D) 97  E) 99

Solution: Clearly, 97 is a prime number.   answer -Option 97
Answer: D
A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?	Pick.
A) 23 days
B) 16 days
C) 11 days
D) 24 days
E) 35 days

Solution: 24 days   24 days   2c = ¼ + 1/6 – 1/3 = 1/12   c = 1/24 => 24 days
Answer: D
If n is an integer, f(n) = f(n-1) - n and f(4)=15. What is the value of f(6)?	Pick one:	A) 4	B) 0	C) 1	D) 2	E) 24

Solution: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.   As given that f(4)=15 then f(5)=15-5= 
15-5 = 10
10 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=10-6= 
10-6 = 4
4.   Answer: A.   Questions on funtions to practice:
Answer: A
There are 21 students in a class. In how many different ways can a committee of 3 students be formed?	Options:	A) 1180	B) 1330	C) 1540	D) 1760	E) 1920

Solution: 21C3 = 21*20*19 / 6= 
21*20*19 / 6 = 1_330
1330   The answer is 1330.
Answer: B
Tough and Tricky questions: Exponents.
If 7^(3x-1)*3^(4y-3) = 49^x*27^y, then x + y =  Choose the most appropriate option.
A) 3 B) 4 C) 2 D) 1 E) 5

Solution: Here is my solution.   7^(3x-1)*3^(4y-3) = 49^x*27^y   Here RHS 49^x*27^y= 7^(2x)*3^(3y)   Equating powers on both sides-->   3x-1=2x , thus x 3 -1= 
 3 -1 = 2
2x , thus x=1 and   4y-3=3y giving y=3   So, x+y=4   Option: 4
Answer: B
An error 3% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? Choose the correct choice:
A) 9.09%
B) 4.02%
C) 4%
D) 3%
E) 2%

Solution: Percentage error in calculated area   =(3+3+(3Ã—3)/100)%   =9.09%   9.09%NSWER:9.09%
Answer: A
The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ?	Options:	A) 2	B) 3	C) 1	D) 6	E) 5

Solution: I year 2100II year 2100+147= 
2100+147 = 2_247
22472100+2247=4347So 2 Years2nswer 2
Answer: A
The temperature of a certain cup of coffee 6 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit? Choose the correct choice from the following answers.
A) 65
B) 63.75
C) 80
D) 85
E) 90

Solution: First, we have to find a.   We know that after t=6 minutes the temperature F=120 degrees.   Hence:   120 = 120*(2^-6a)+60   60 = 120*(2^-6a)   60/120 = 2^-6a   1/2 = 2^-6a   2^-1 = 2^-6a   -1 = -6a   1/6 = a   Now we need to find F after t=30 minutes:   F = 120*(2^-1/6*30)+60   F = 120* (2^-5) +60   F = 120* (1/2^5) +60   F = 120*1/32 +60   F = 3.75+60= 
3.75+60 = 63.75
63.75   Answer 63.75!
Answer: B
A committee of 5 people is to be selected from 7 people. How many different committees are possible?
Choose the correct choice from the following choices.
A) 21
B) 40
C) 56
D) D.168
E) 336

Solution: Because the order does not matter in selecting 5 people for the committee, this is a combination question.   The number of ways to select 5 people from 7 = 7C5 = 7!/5!*2! = 21. Hence 21
Answer: A
The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 30 percent of the budget?
Options:
A) 15 °  B) 36 °  C) 54 °  D) 90 °  E) 108 °

Solution: 100 percent = 360 degrees   30 percent = 360*30/100= 
360*30/100 = 108
108 degrees   Answer is 108 °.
Answer: E
Difference of two numbers is 1860. If 7.5% of the number is 12.5% of the other number , find the number ?	Choose the correct option:
A) 2660, 1000 B) 3660, 2000 C) 3000, 4160 D) 2790, 4650 E) 4660, 3000

Solution: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y   X = 125*y/75 = 5*y/3.   Now, x-y =1860   5*y/3 –y =1860   2*y/3= 1860   y =[ (1860*3)/2= 
(1860*3)/2 = 2_790
2790.   One number= 2790, Second number =5*y/3 =4650.   Answer 2790, 4650.
Answer: D
What is the greatest positive integer n such that 3^n is a factor of 36^450? Choose the correct option:
A) 100	B) 200	C) 300	D) 600	E) 900

Solution: 36 = 3^2 * 2^2.   36^450 = 3^900 * 2^900   The answer is 900.
Answer: E
A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
Pick one.
A) 11 months	B) 17 months	C) 10 months	D) 19 months	E) 12 months

Solution: Let the total profit be Rs. z. Then,   B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.   A : B = z/3 : 2z/3 = 1:2   Let the total capital be Rs, X and suppose B's money was used for x months. Then.   (1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3)= 
(15 * 2 / 3) = 10
10 .   Thus, B's money was used for 10 months.   Answer: 10 months
Answer: C
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value S of z - x?
Choose the correct choice from the following answers.
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: x<y<z and="" be="" can="" closest="" could="" each="" even="" find="" for="" if="" is="" least="" minimum="" need="" number="" number,="" odd="" other.="" possible="" some="" that="" the="" then="" to="" value="" values="" we="" what="" x="" y-x="" z="" z-x;="" z.="">5; y>x+5; minimum value for y</y<z>=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]   Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. 9ifference between two odd numbers is 2]   S=z-x = x+9-x= 9   Ans:9
Answer: D
A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, 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?  Choose the correct choice from the following: A) Rs.3240 B) Rs.3600 C) Rs.3800 D) Rs.4200 E) Rs.5200

Solution: 15:25 => 3:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*3/8= 
8640*3/8 = 3_240
3240 + 960= 
3240 + 960 = 4_200
4200   ANSWER:Rs.4200
Answer: D
What is the place value of 7 in the numeral 2734?	Pick.
A) 450 B) 500 C) 700 D) 800 E) 840

Solution: Option '700'    7 * 100= 
 7 * 100 = 700
700
Answer: C
A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?
Choose the correct choice from the following.
A) 14 cups
B) 15
C) 16
D) 17
E) 18

Solution: lets say total volume of the container = V   Initial water content is half of total volume = V/2   Then 4 cups of water were added.   Current water content = (V/2) + 4 cups = (70/100)V   => V = 20 cups   => current water content is equivalent to = V/2+ 4 cups = 20/2 + 4= 
20/2 + 4 = 14
14 cups; 14 cupsNSWER:14 cups
Answer: A
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 1.00 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?	Choose the correct choice from the following answers:  A) 1/6  B) 1/2  C) 5/8  D) 5/4  E) 15/16

Solution: X - fraction of products Jane inspected   (1 - X) - fraction of products John inspected   0.8(X) + 1.00(1-X) = 0.75   0.2X = 1.00 - 0.75= 
1.00 - 0.75 = 0.25
0.25/0.2   X= 5/4   Therefore the answer is 5/4: 5/6.
Answer: D