MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 70% have red flags, what percentage of children have flags of both the colors?
Answers:  A) 5%  B) 10%  C) 15%  D) 20%  E) 30%

Solution: Solution: let the total number of flags be 100(even number)   let the total number of 'blue' flags alone be 'a'   let the total number of 'red' flags alone be 'b'   let the total number of 'both' flags be 'c'   We have given,   total number of blue flags = 60% = 60 = a+c   total number of red flags=70%=70=b+c   total number of flags = a+b+c=100 (since all the flags have been utilized)   So, substituting for c in the third equation, we have,   60-c+c+70-c=100   c=30   Option 30%.
Answer: E
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 4x km.	Options:
A) 16
B) 18
C) 32
D) 19
E) 12

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 4x/(x/8) = 32 kmph   Answer: 32
Answer: C
A motorcyclist goes from Bombay to Pune, a distance of 288 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Choose the correct choice from the following answers.
A) 1:2 B) 1:5 C) 1:4 D) 2:3 E) 1:8

Solution: T = 288/32= 
288/32 = 9
9 h   T= 9 - 3= 
9 - 3 = 6
6   Time Ratio= 9:6 = 3:2   Speed Ratio = 2:3   Answer: 2:3
Answer: D
John bought 2 shares and sold them for $78 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had Choose the correct choice from the following options:  A) a profit of $10  B) a profit of $6.5  C) a loss of $6.5  D) a loss of $10  E) neither a profit nor a loss

Solution: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss   Total Selling Price = 78*2= 
78*2 = 156
$156   Total a loss of $6.5ost Price= 156/(0.96)= 
156/(0.96) = 162.5
$162.5   Loss= 162.5 - 156= 
162.5 - 156 = 6.5
$6.5   Answer: Option a loss of $6.5
Answer: C
A tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume. If 6,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?	Choose the correct choice from the following answers:  A) 1.25%  B) 3.75%  C) 6.25%  D) 6.67%  E) 15%

Solution: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-6,000=4,000 gallons and sodium chloride is 600 gallons (6% of initial solution of 10,000 gallons) then sodium chloride is 600/4,000*100=15% of the remaining solution of 4,000 gallons.   Answer: 15%.
Answer: E
In the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+2y?
Choose the correct option:
A) 8 B) 6 C) 5 D) 3 E) 4

Solution: lets start from z, as per the question stem   z + 6 + 8 = 16   -->> z= 2   similarly, y +2 + 6= 
+2 + 6 = 8
8   --> y= 0   similarly,, x + 0 + 2 = 6   --> x = 4   hence , x+2y = 4-0= 
4-0 = 4
4 --> x+2y=4   ANSW4R:4
Answer: E
If |x + 3| = 15, what is the sum of all the possible values of x? Choose the most appropriate option:
A) -16
B) -12
C) -8
D) -3
E) 11

Solution: There will be two cases   x+3 = 15 or x+3 = -15   => x = 12 or x= -18   sum of both the values will be -18 + 15 = -3   Answer: -3
Answer: D
list of salaries of 8 employees are listed below. What is the median salary? $40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000 Choose the correct answer
A) $20,500 B) $21,000 C) $22,500 D) $30,550 E) $31,500

Solution: Ordering the data from least to greatest, we get:   $27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000   Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.   $31,000 + $32,000 = $63,000   The median salary is $31,500.   $31,500
Answer: E
What is the remainder when 3^26 is divided by 5?  Choose one:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}   26 has the form 4k+2, so the units digit of 3^26 is 9.   The remainder when dividing by 5 is 4.   The answer is 4.
Answer: E
Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Answers
A) 87 B) 25 C) 26 D) 28 E) 21

Solution: Let the pipe B be closed after x minutes.   30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16   => x = 14/16 * 24= 
14/16 * 24 = 21
21.   Answer:21
Answer: E
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 correct choice from the following.
A) 90 sec  B) 28 sec  C) 78 sec  D) 87 sec  E) 26 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
If December 3rd, 1999 is a Friday, what day is January 8th, 2000?  Choose the correct choice from the following choices:  A) Wednesday  B) Thursday  C) Friday  D) Saturday  E) Sunday

Solution: There is difference of 36 days from Dec. 3rd 1999 to Jan. 8th 2000.   36/7 has a remainder of 1.   Jan. 8th is: Friday + 1 day = Saturday   The answer is Saturday.
Answer: D
If the number of fatalities from road accidents declined from 9,680 in 1988 to 9,600 in 1989 and then declined a further 20% from 1989 to 1990, what was the approximate percentage decline in the number of fatalities from 1988 to 1990? Choose the correct choice from the following choices.
A) 12
B) 16
C) 21
D) 37
E) 43

Solution: We have decline from 9,680 to 9,600 (by 80 points) and then by 20%. Now, since 80 is less than 1% of 9,680, thus the overall decline would be slightly more than 20%. Only answer choice C fits.   Answer: 21.
Answer: C
A password for a computer uses four digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
Answers
A) 1/32  B) 1/16  C) 1/8  D) 2/5  E) 1/2

Solution: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 = 10,000 possible combinations.   Prime numbers constitute 2, 3,and 5 . In addition to zero, this is 4 total possibility for each digit. So the number of satisfactory variants is 4 × 4 ×4 × 4 So the probability is 1/2 × 1/2 × 1/2 × 1/2 = 1/16.   The right answer is choice (1/16).
Answer: B
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 12%. Their gross income from sales for one month increases by what percent?
Options
A) 0.4% B) 0.8% C) 2% D) 4% E) 8%

Solution: Let P be the original price and let x be the number of items sold originally.   The original income is P*x.   After the changes, the income is 0.9P*1.12x = 1.008*(P*x), an increase of 0.8%.   The answer is 0.8%.0.9 *1.12= 
0.9 *1.12 = 1.008
1.008*(P*x), an increase of 0.8%.   The answer is 0.8%.
Answer: B
Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 18km/hr, then find the area of square field.
Choose the correct choice.
A) 125
B) 182.25
C) 325
D) 425
E) None of these

Solution: Explanation :   D = 18*3/2= 
18*3/2 = 27
27 km. So side of square is 13.5km, so area – 182.25km^2   Answer – 182.25
Answer: B
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 11 years older than B, the present age of B is  Choices
A) 35  B) 37  C) 39  D) 41  E) 42

Solution: Explanation:   Let B's age = x years.   Then, As age = (x+ 11) years.   (x+11+10)=2(x—10)   hence x=41.   Present age of B = 41 years   Answer: Option 41
Answer: D
Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $209 Choose the correct choice from the following:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Taking the prices of products in ascending order(already arranged)   $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $209   we see that median value is the 6th value as there in total 11 values given   Arithmetic mean = total/number of entries = 1398/11 =127.9090   We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price   as we can clearly see that there is one value between $120 and $127.90, answer is 1 unit   Correct Answer - 1
Answer: B
A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage decrease in area?  Choose the correct answer
A) 26  B) 28  C) 24  D) 20  E) 22

Solution: Formula for percentage change in area is:   =(−x−y+(xy)/100)%   =(−20−10+(20×10)/100)%=−28%   i.e., area is decreased by 28%   Answer is 28.
Answer: B
Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 4. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Answers
A) 3, 8, 24 B) 7, 9, 17 C) 6, 9, 12 D) 5, 15, 18 E) 9, 10, 13

Solution: I didnt get your point on eliminating E.   The number of stamps only one purchased was divisible by 4.Could that not be Cecilia with 9 stamps.   I choose this and marked 9, 10, 13.
Answer: E
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is: Choose the correct choice from the following.
A) 48 B) 49 C) 50 D) 51 E) 52

Solution: Let the length of each train be x metres.   Then, distance covered = 2x metres.   Relative speed = (46 - 36) km/hr   = 10x5/18 m/sec   = 25/9 m/sec   = 2x/36 =25/9   2x =100   X=50   answer :50
Answer: C
A fruit seller had some apples. He sells 30% and still has 420 apples. Originally, he had ?	Choose the correct answer:
A) 30 apples
B) 600 apples
C) 420 apples
D) 70 apples
E) None

Solution: Answer   âˆµ 70% of N = 420   âˆ´ N = (420 x 100)/70 = 600   Correct Option: 600 apples
Answer: B
A man, a woman and a boy can together complete a piece of work in 3 days. If a woman alone can do it in 6 days and a boy alone in 18 days, how long will a man take to complete the work?	Choose the correct choice:	A) 5days	B) 8days	C) 7days	D) 9days	E) 8days

Solution: Explanation:   (1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3   1wo man’s 1 day work = 1/6   1boy’s 1 day’s work = 1/18   man alone can finish the work in 9 days.   Answer: Option 9days
Answer: D
9, 16, 18, 25, 36,49 Choices
A) 9
B) 16
C) 18
D) 25
E) 36

Solution: Each of the numbers except 18, is perfect square.   Answer: Option 18
Answer: C
A man can row downstream at 22 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?	Pick one:
A) 16, 2 B) 16, 4 C) 16, 8 D) 16, 6 E) 16, 7

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 22 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 32 => x = 16, y = 6.   Answer:16, 6
Answer: D
In how many ways 4 Indians and 2 Englishmen can be seated in a row so that they are alternate? Pick one.
A) 120  B) 96  C) 144  D) 48  E) 256

Solution: number of ways = 4!*2! = 48   Answer is 48
Answer: D
A number x is 3 times another number y. The percentage that y is less than x is Choices:
A) 12.5% B) 66.6% C) 80% D) 11% E) 1%

Solution: Say y=1 and x=3.   Then y=1 is less than x=3 by (3-1)/3*100=2/3*100=66.6%.   Answer: 66.6%.
Answer: B
The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:	Choose the correct choice from the following answers.
A) 79.8cm3 B) 79.4cm3 C) 89.8cm3 D) 89.4cm3 E) None of these

Solution: Explanation:   Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm   Volume of cone =1/3πr2h   =1/3∗22/7∗3.5∗3.5∗7   =269.5/3cm3   =89.8cm3   Note: radius is taken as 3.5, as diameter is 7 cm   Option 89.8cm3
Answer: C
Q' = 3Q - 3, what is the value of (6')' ? Choose the correct answer:	A) 120	B) 150	C) 180	D) 210	E) 240

Solution: (6')'=(3*6-3)= 
(3*6-3) = 15
15'=15*15-15= 
15*15-15 = 210
210   Answer 210
Answer: D
What is the remainder when 14,453 × 15,654 × 16,788 is divided by 5?
Choose the correct option:  A) 2  B) 1  C) 5  D) 4  E) 3

Solution: Only the unit's digit of the product will decide the remainder when divided by 5.   Hence, 3*4*8= will give units digit as 5   So, whatever be the number, if it ends in 6, the remainder after dividing with 5 will be 1.   Option1
Answer: B
The ratio of the incomes of Uma and Bala is 8:7 and the ratio of their expenditure is 7:6. If at the end of the year, each saves $2000 then the income of Uma is? Choices.
A) $16800 B) $16500 C) $16000 D) $16300 E) $16200

Solution: Let the income of Uma and Bala be $8x and $7x   Let their expenditures be $7y and $6y   8x-7y = 2000-------1)   7x-6y = 2000-------2)   From 1) and 2)   x = 1000   Uma's income = 8x = 8*2000= 
8*2000 = 16_000
$16000   Answer is $16000
Answer: C
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Pick.
A) 7 sec B) 5 sec C) 4 sec D) 6 sec E) 2 sec

Solution: Speed of train relative to man   = (60 + 6) km/hr   = 66 km/hr   [66 * 5/18] m/sec   = [55/3] m/sec.   Time taken to pass the man   = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: D
10 People take a history test. The following are the scores:
40, 45, 45, 50, 50, 60, 70, 75, 95, 100
Using the mean and median scores, find the amount of scores that fall in between the range of the two	Choose the correct answer.
A) One B) Three C) Five D) Seven E) Nine

Solution: The median = (the average of two middle terms) = (50 + 60)/2= 
(50 + 60)/2 = 55
55.   The mean= (the sum)/(# of terms) = 630/10= 
630/10 = 63
63.   Only 60 is between 55 and 63.
Answer: A
A compact car uses 15 gallons of fuel in traveling 360 miles. In order for the truck to travel the same distance using 12 gallons of fuel, by how many miles per gallon must the car’s fuel mileage be increased? Choose the correct option:
A) 10  B) 6  C) 15  D) 36  E) 27

Solution: There are two sets 15G1 gallons and 12G2 gallons details given.   15 gallons covering 360 miles   Then 1 G1 is used to cover 24 miles.   Now for 12, G2 covering 360 miles.   then 1 G2 is used to cover 30 miles.   Therefore, 30 - 24 = 6 miles per gallon increment is needed for 12 gallons to improve the mileage to cover 360 miles.   Thus, 6 is the correct answer.
Answer: B
Mangala completes a piece of work in 12 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
Pick:	A) 7.5 days	B) 7.6 days	C) 7.7 days	D) 8.7 days	E) 9.7 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 12 Ã— 20/32 = 7.5 days.   7.5 days)
Answer: A
If selling price is doubled, the profit triples. Find the profit percent:  Choose the correct choice from the following
A) 66 2/3
B) 100
C) 105 1/3
D) 120
E) 150

Solution: Let C.P. be Rs. x and S.P. be Rx. y.   Then, 3(y - x) = (2y - x) => y = 2x   Profit = (y - x) = Rs. (2x - x) = Rs. x   Profit % = x/x * 100 = 100%.   ANSWER:100
Answer: B
X, Y and Z can do a work in 9 , 10 and 15 days respectively. They completed the work and got Rs.600. What is the total amount earned by X and Y?	Choose the correct choice from the following options:
A) 476 B) 356 C) 456 D) 466 E) 450

Solution: The ratio of their working rates = 1/9 : 1/10 : 1/15 = 10 : 9 : 6.   Since, they work together, the share of X   = 10/25 * 600 = Rs.240   the share of Y = 9/25 * 600 = Rs.216   total amount earned by X and Y = 240 + 216 = Rs.456   Answer: 456
Answer: C
If a 10 percent deposit that has been paid toward the purchase of a certain product is $120, how much more remains to be paid? Pick
A) $880 B) $990 C) $1,000 D) $1,100 E) $1,080

Solution: 10/100P = 120 >> p= 120*100/10= 
120*100/10 = 1_200
1200   1200 - 120= 
1200 - 120 = 1_080
1080   ANSW$1,080R:$1,080
Answer: E
How many odd 4-digit positive integers R that are multiples of 5 can be formed without using the digit 3?
Choose the correct choice:
A) 648  B) 729  C) 900  D) 1296  E) 3240

Solution: I choose A.   Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)   Possible n° of 2nd digit: 9 (3 is excluded)   Possible n° of 3rd digit: 9 (3 is excluded)   Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)   So, R=8*9*9*1= 
8*9*9*1 = 648
648 (648)
Answer: A
If an item that originally sold for A dollars was marked up by x percent and then discounted by N percent, which of the following expressions represents the final price of the item?
Choose the correct answer.
A) (10,000z + 100z(x – y) – xyz)/10,000	B) (10,000z + 100z(y – x) – xyz)/10,000	C) (100z(x – y) – xyz)/10000	D) (100z(y – x) – xyz)/10000	E) (A+ Ax/100) - N/100 ( A +Ax/100)

Solution: .value of item =A ..marked up by x% = Ax/100   total value = A +ax/100 .discounted by N% on Total N/100 * ( A+Ax/100)   Final price =(A+ Ax/100) - N/100 ( A +Ax/100)   (A+ Ax/100) - N/100 ( A +Ax/100)
Answer: E
Three pipes of same capacity A,B,C can fill a tank in 6 hours. If there are only two pipes B and C of same capacity, the tank can be filled in?
Choose the correct answer
A) 2	B) 4	C) 9	D) 12	E) 16

Solution: The part of the tank filled by three pipes in one hour   = 1/6   => The part of the tank filled by two pipes in 1 hour   = 2/3 * 1/6 = 1/9.   The tank can be filled in 9 hours.   Answer:9
Answer: C
The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?	Choose the correct choice from the following choices
A) 1752  B) 1799  C) 1719  D) 1750  E) 1800

Solution: Speed = [216 * 5/18] m/sec = 60 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 60 Ã¨ x = 60 * 60 / 2= 
60 * 60 / 2 = 1_800
1800   Answer: 1800
Answer: E
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Choose the correct choice from the following.
A) 278 B) 276 C) 20 D) 288 E) 21

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
In a fuel station the service costs $4.25 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
Choose the most appropriate option:
A) 122.6$	B) 128.9$	C) 243.7$	D) 298.85$	E) 309.85$

Solution: Service cost of 3 van and 2 truck = 4.25*(3+2)= 
4.25*(3+2) = 21.25
21.25   Fuel in 3 Van= 3*65= 
3*65 = 195
195 litre   Fuel in 2 Trucks=2 * 65(1+120/100)= 286   Total fuel(Van+Truck) = 481 Litre   Total Fuel cost = 481*0.6= 
481*0.6 = 288.6
288.6   TOTAL COST=FU309.85$L+S309.85$RVIC309.85$=288.6+21.25= 
288.6+21.25 = 309.85
309.85   ANSW309.85$R IS 309.85$
Answer: E
The speeds of 3 trains in the ratio 4:12:24. The ratio between time taken by them to travel the same distance is?  Pick:  A) 6:2:1  B) 1:2:3  C) 4:8:9  D) 6:5:2  E) 4:8:7

Solution: Ratio of time taken is = 1/4 : 1/12 : 1/24 = 6:2:1   6:2:1nswer is 6:2:1
Answer: A
The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 60 percent of b, what is the value of m/x?  Answers
A) 2/5
B) 3/4
C) 4/5
D) 5/4
E) 2/7

Solution: a/b = 4/5   m/x = (2/5)*5 / (7/4)*4 = 2/7   The answer is 2/7.
Answer: E
The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
Choices
A) 10	B) 15	C) 25	D) 30	E) 35

Solution: ( 2x+5 ) /( 3x+5) = 3/4   or, 8x+20=9x+15   or,x=5   So, Present age of 10 = 2x = (2*5)= 
(2*5) = 10
10   10NSWER:10
Answer: A
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been  Choose the correct choice from the following answers: A) 24 B) 144 C) 292 D) 584 E) None of these

Solution: 5 | x z = 13 x 1 + 12 = 25   --------------   9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233   --------------   13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169   --------------   | 1 -12   585) 1169 (1   585   ---   584   ---   Therefore, on dividing the number by 585, remainder = 584.   Answer:584
Answer: D
The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.	Choices.
A) 37.5 %  B) 38.5 %  C) 42 %  D) 27.5 %  E) none

Solution: Sol.   Let marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.   ∴ Gain % = [24/64 * 100= 
24/64 * 100 = 75/2 = around 37.5
37.5%.   37.5 %nswer 37.5 %
Answer: A
Combine terms: 12a + 26b -4b – 16a.	Choose the correct choice.
A) 4a + 22b  B) -28a + 30b  C) -4a + 22b  D) 28a + 30b  E) 30a-28b

Solution: 12a + 26b -4b – 16a.   = 12a – 16a + 26b – 4b.   = -4a + 22b.   correct answer -4a + 22b
Answer: C
What least number must be added to the least number of six digits so that the resulting number may be a perfect square.  Choose the most appropriate option
A) 489  B) 267  C) 278  D) 199  E) 111

Solution: The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 – 489 Least number to be added = 489.   489nswer:489
Answer: A
what is the remainder when 789456123 is divided by 999  Choose the correct option:
A) 349 B) 359 C) 369 D) 379 E) 389

Solution: there is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..   so you will get  123 + 456 +789= 
 123 + 456 +789 = 1_368
1368 again select last 3 and add them u will get 368 + 001 i.e 369   ANSWER:369
Answer: C
In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?  Pick one
A) 19% B) 15% C) 25% D) 40% E) 9.4%

Solution: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)   Originally,   C = FNP   When number of students decrease by 8%, and the price of food increases by 20%,   C = F(new) * (0.92N) * (1.2P)   => F(new) = F/(0.92*1.2)   => F(new) = 0.906F   Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4%   ANSW9.4%R:9.4%
Answer: E