MU-NLPC/Calc-aqua_rat huggingface dataset:
Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 1/4 brand X and 3/4 brand Y. what fraction of the cost of the blend is Brand X?	Choose the correct option:	A) a. 2/5	B) b. 1/5	C) 3. 1/2	D) 4. 2/3	E) 5. 3/4

Solution: Assume Cost of X= Cx = 200 , Cost of Y = Cy=100   The blend contains 0.25 X and 0.75 Y ---> Cost of the blend = Cbl = 0.25*200+0.75*100= 
0.25*200+0.75*100 = 125
125   Thus fraction of X in the blend= 0.25*200/125 = 2/5.   a. 2/5nswer : a. 2/5
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?  Pick one:  A) 54  B) 77  C) 36  D) 88  E) 21

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (180 + 180)/12 => x = 15   Speed of each train = 10 m/sec.   = 15 * 18/5 =- 54 km/hr.   54nswer: 54
Answer: A
A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5,6 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4? Answers
A) 1/5
B) 5/6
C) 21/65
D) 7/3
E) 2/7

Solution: If a number is divisible by 4 the last 2 digits of the number has to be divisible by 4.   If the number ends with 12: Number of possibilities = 4*3 * 2 * 1= 
4*3 * 2 * 1 = 24
24   number ends with 24: Possibilities= 4*3 * 2 * 1= 
4*3 * 2 * 1 = 24
24   number ends with 32: Possibilities=24   number ends with 52: Possibilities = 24   number ends with 36: Possibilities =24   number ends with 16: Possibilities = 24   number ends with 64: Possibilities = 24   Total number of possibilities with restriction = 7*24= 
7*24 = 168
168   Total number of possibilities without restriction= 6! = 720   Probability = 168/720 =21/65   Answer: 21/65
Answer: C
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?  Answers:
A) 22 1/2  B) 22 1/8  C) 22 1/4  D) 22 2/2  E) 23 1/2

Solution: 100 --- 10 DS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 1/2 kmph 22 1/2nswer:22 1/2
Answer: A
Dave has d books, which is 3 times as many as Jercy and 1/2 as many as Pavi. How many books do the three of them have altogether, in terms of d?	Choose the correct choice:
A) 5/6*d B) 7/3*d C) 9/2*d D) 7/2*d E) 10/3*d

Solution: Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.   number of books Dave has = d   number of books Jercy has = j   number of books Pavi has = p   We are given that Dave has 3 times as many books as Jercy. We can now express this in an equation.   d = 3j   d/3 = j   We are also given that Dave has ½ as many books as Pavi. We can also express this in an equation.   d = (1/2)p   2d = p   Notice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:   d + d/3 + 2d   Getting a common denominator of 3, we have:   3d/3 + d/3 + 6d/3 = 10d/3 = 10/3*d   The answer is 10/3*d
Answer: E
If (5!)^2–(4!)^2=2^a3^b13^c and a, b, and c are integers, then what is the value of a + b + c?  Choose the correct choice from the following: A) 12 B) 10 C) 2 D) 1 E) 0

Solution: (5!)^2 -(4!)^2=2^a3^b13^c   = [5^2*(4!)^2]-(4!)^2   =[25*(4!)^2]-(4!)^2=24*(4!)^2   = 24*(24^2)=24^3   =[2^3*3]^3=2^9*3^3   so a=9 b=3 c=0   hence a+b+c=9+3+0= 
9+3+0 = 12
12   answer=12
Answer: A
A retailer buys 60 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? Choose the correct choice from the following
A) 40	B) 65	C) 72	D) 78	E) 20

Solution: let the market price of each pen be $1   then, Cost Price of 60 pens = $ 36 Selling Price of 60 pens =99% of $60=$ 59.40   profit %=((23.40*100)/36)= 
((23.40*100)/36) = 65
65%   Answer 65
Answer: B
Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31.5¢, then what is the average price, in cents, of the two returned peanut butter cans?	Choose the correct answer:	A) 46.5	B) 11	C) 47.5	D) 66	E) 67.5

Solution: Total price of six cans = 6*36.5= 
6*36.5 = 219
219   Total price of 4 cans= 4*31.5= 
4*31.5 = 126
126   Total rice of two cans= 219 - 124 = 93   Average price of two cans = 93/2= 
93/2 = 93/2 = around 46.5
46.5 c   Another way to do it is this:   Assume that the four leftover cans were of 31.5c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 5c of cost to other 4 cans.   So cost of the two cans= 2*36.5 + 4*5= 
2*36.5 + 4*5 = 93
93   46.5vg cost of the two cans= 93/2= 
93/2 = 93/2 = around 46.5
46.5c   46.5nswer (46.5)
Answer: A
5n + 7 > 12 and 7n - 5 < 44; n must be between which numbers?	Pick
A) 1 and 8  B) 2 and 6  C) 0 and 9  D) 2 and 7  E) 1 and 7

Solution: 5n+7 > 12   5n > 5   n > 1   7n-5 < 44   7n < 49   n < 7   So n must be between 1 and 7   1 < n < 7   correct answer 1 and 7
Answer: E
Tali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?	Choices
A) 82  B) 96  C) 110  D) 120  E) 192

Solution: Tali want to double the original amount of blocks, not just the red blocks   the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).   192-82= 
192-82 = 110
110   so 110 bricks need to be added to the new 82 brick tower to double the original.   They worded the question ashow many red bricks need to be addedbut really it could be any colour just that 110 more bricks need to be there to equal 192=192
Answer: E
If 'A' completes a piece of work in 3 days, which 'B' completes it in 5 days and 'C' takes 10 days to complete the same work. How long will they take to complete the work , if they work together?  Choose the correct choice from the following choices
A) 1.5 days	B) 4.5 days	C) 7 days	D) 9.8 days	E) 9 days

Solution: EXPLANATION:   Hint:   A's one day work =	1/3   B's one day work =	1/5   C's one day work =	1/10   (A+ B+ C)'s one day work =	1/3	+	1/5	+	1/10	=	1/1.5   Hence, A ,B & C together will take 1.5 days to complete the work.   1.5 daysNSWER IS 1.5 days
Answer: A
After 19 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it? Choose the correct choice from the following options
A) 7 liters	B) 4 liters	C) 3 liters	D) 1 liters	E) 6 liters

Solution: 95% ----------- 19   5% ------------ ?   => 1 liter   Answer: 1 liters
Answer: D
One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Choose the correct choice from the following choices:
A) 5:4 B) 5:9 C) 5:1 D) 5:5 E) 5:2

Solution: 45 * 5/18 = 10   25:20 => 5:4   5:4nswer: 5:4
Answer: A
What will come in place of the x in the following Number series? 612, 207, 72, 27, 12, x
Choices:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: 612612 / 3 + 3 = 207207 / 3 + 3 = 7272 / 3 + 3 = 2727 / 3 + 3 = 1212 / 3 + 3 = 77
Answer: B
A man complete a journey in 30 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 10 km/hr. Find the total journey in km.	Choices:	A) 220 km	B) 224 km	C) 230 km	D) 400 km	E) 234 km

Solution: 0.5x/20 + 0.5x/10 = 30   --> x/20 + x/10=60   --> 3x = 20x60   --> x = (60x 20)/3 = 400 km.   Answer : 400 km
Answer: D
How many of the positive divisors F of 120 are also multiples of 4 not including 120? Select.
A) 3. B) 4. C) 5. D) 7. E) 8.

Solution: 4,8,12,20,24,40,60. (7) is the answer   Other way : factors of 120 = 2^3 * 3*5   Separate 2^2 ( which means 4)   Now, calculate the number of other factors.   F=2*3*5 = total positive factors are 2*2*2= 
2*2*2 = 8
8   This 8 factors include 120   So subtract 1 from 8   Ans is 7=7.
Answer: D
If 1/5th of a number decreased by 5 is 5, then the number is
Choose the correct choice from the following:	A) 25	B) 50	C) 60	D) 75	E) None

Solution: Explanation :   Let the number be a, then   a/5−5=5⇒a/5=10⇒a=50   Correct Option: 50
Answer: B
In what time will a train 45 m long cross an electric pole, it its speed be 108 km/hr?  Choose the correct choice from the following choices:
A) 0.5
B) 1.25
C) 1.5
D) 2.5
E) 3.5

Solution: Speed = 108 * 5/18= 
108 * 5/18 = 30
30 m/sec   Time taken= 45/30= 
45/30 = 3/2 = around 1.5
1.5 sec.   Answer: 1.5
Answer: C
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?  Choose the correct choice from the following.
A) 10
B) 12
C) 18
D) 24
E) 29

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways   4: Or 4p = — 4:- 4X3X2X1- 24 ways   24
Answer: D
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Choose the correct option:
A) 28 sec	B) 16 sec	C) 36 sec	D) 18 sec	E) 17 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:36 sec
Answer: C
Mrs. Rodger got a weekly raise of $175. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. Choose the correct choice from the following answers.
A) $204	B) $231	C) $156	D) $175	E) $200

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 175.   So after completing the 1st week she will get $ (x+175).   Similarly after completing the 2nd week she will get $ (x + 175) + $ 175.   = $ (x + 175 + 175)   = $ (x + 350)   So in this way end of every week her salary will increase by $ 175.   $175
Answer: D
What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?
Choose the correct choice from the following answers:	A) 50%	B) 20%	C) 25%	D) 16.67%	E) 33.33%

Solution: Explanatory Answer   Quick Approach: Assume cost price as $100 and solve   Let the cost price of the goods to be $ 100.   She had initially marked her goods up by 50%.   Therefore, a 50% mark up would have resulted in her marked price being $100 + 50% of $100 = $100 + $50 = $150.   She finally sells the product at no profit or loss.   i.e., she sells the product at cost price, which in this case is $100.   Therefore, she offers a discount of $50 on her marked price of $150.   Hence, the % discount offered by her 100 +  50= 
100 +  50 = 150
$150.   She finally sells the product at no profit or loss.   i.e., she sells the product at cost price, which in this case is $100.   Therefore, she offers a discount of $50 on her marked price of $150.   Hence, the % discount offered by her= Discount/Marked Price∗100=50/150∗100= 33.33%   Choice 33.33%
Answer: E
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
Select:
A) 22 B) 73 C) 90 D) 77 E) 12

Solution: 200*2= 
200*2 = 400
400   580   -----   180   1----2   ?----180= 90   Answer: 90
Answer: C
If positive integer n is divisible by both 6 and 21, then n must be divisible by which of the following? Choose the correct choice from the following answers:
A) 8 B) 12 C) 14 D) 24 E) 48

Solution: A number divisible by both 6,21 is 42 which s divisible by 14.   IMO : Answer 14 14
Answer: C
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Choose the correct choice from the following answers:
A) 710  B) 720  C) 730  D) 740  E) 750

Solution: 720   Option '720'
Answer: B
Varma can read a book in k minutes. What part of the book can he read in 5 minutes?(k>8)
Options:	A) (k - 8)/k	B) k/8	C) 5/K	D) k-8	E) k-6

Solution: Option C   Explanation:   Part of the book he can read in 1 minute = 1/k   Part of the book he can read in 5 minutes =5/k.   Answer: 5/K
Answer: C
Xavier starts from P towards Q at a speed of 40 kmph and after every 12 mins increases his speed by 20 kmph. If the distance between P and Q is 56 km, then how much time does he take to cover the distance?	Choose the correct answer:	A) 40	B) 48	C) 44	D) 36	E) 30

Solution: first 12min = 40 *12/60= 
40 *12/60 = 8
8 km   2nd 12min= 60*12/60= 
60*12/60 = 12
12 km   3rd 12 min= 80*12/60= 
80*12/60 = 16
16 km   4th 12 min= 100 *12/60= 
100 *12/60 = 20
20 KM   TOTAL time 12.4=48 min   48
Answer: B
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?  Choose the correct choice from the following choices:
A) 6.25 B) 5.5 C) 7.4 D) 5 E) 6

Solution: Explanation:   Runs scored in the first 10 overs = 10 × 3.2 = 32   Total runs = 282   Remaining runs to be scored = 282 - 32= 
282 - 32 = 250
250   Remaining overs= 40   Run rate needed =   250/40= 
250/40 = 25/4 = around 6.25
6.25   6.25NSWER IS 6.25
Answer: A
Martha has 5 dogs and 5 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have? Choose the correct choice from the following answers:
A) 8 B) 9 C) 10 D) 18 E) 20

Solution: 5 dogs, 5 cats; park/barber shop   1 dog - 2 options - either park or barber shop, so, 5 dogs - 10 options and 5 dogs - 10 options.   Total = 20 options.   20
Answer: E
Line k is in the rectangular coordinate system. If the b-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k? Pick
A) -3b + 2y = 6	B) 3b + 2y = -6	C) 3b - 2y = 6	D) 2b - 3y = 6	E) -2b - 3y = 6

Solution: This question can be solved in much simpler way.   To find the b intercept   Put y=0 in the equation of the line.   To find the y-intercept   Put b=0 in the equation of the line.   So   Sub b=0 in the answer choices check whether you are getting y=3.   A. -3b + 2y = 6 --- y = 3   B. 3b + 2y = -6 --- y = -3   C. 3b - 2y = 6 ----- y = -3   D. 2b - 3y = 6 --- y = -2   E. -2b - 3y = 6 --- y =-2   Eliminate answer B,C,D and E.   So the answer is -3b + 2y = 6.
Answer: A
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets E can be created from this process?  Choose the correct choice from the following answers.
A) 35  B) 105  C) 210  D) 420  E) 630

Solution: E=7C4 * 3C2 = 105 Answer B.   7C4 ways to choose 4 numbers for Box 1   3C2 ways to choose 2 numbers for Box2   1 way for Box 3 .   every combination will give a different product and can be arranged least to highest only in one way .105
Answer: B
If x^3 > y^2 > z, which of the statements could be true?
I. x > y > z
II. x < z < y
III. y < x < z
Pick one
A) I only  B) III only  C) I and II only  D) II and III only  E) I, II and III

Solution: Given : x^3 > y^2 > z   I. x > y > z is true for x=5, y=2, z=1 i.e. Answers can only be Options A, C or E   II. x < z < y is true for x=3, y=5, z=4 i.e. Answers can only be Options C or E   III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options I, II and III   Answer: option I, II and III
Answer: E
A Boeing 757 flies a direct route from Dallas, TX, to Phoenix, AZ and then returns to Dallas, TX. The flight is 900 miles one way. It took 2 hrs and 15 minutes for the flight to Phoenix and 2 hrs for the flight back to Dallas. What was the speed of the wind in mph? Choose the correct choice from the following answers:	A) 20 mph	B) 25 mph	C) 30 mph	D) 35 mph	E) 40 mph

Solution: Explanation:   Change the times in the problem to minutes first.   Speed of airplane from Dallas to Phoenix: (900/135) X 60 = 400 mph   Speed of airplane from Phoenix to Dallas: (900/120) X 60 = 450 mph   Wind speed: 1/2 (450 - 400) = 50/2= 
50/2 = 25
25 mph   Answer: Option 25 mph
Answer: B
7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country.
Choose the correct choice from the following choices:	A) 250	B) 300	C) 400	D) 500	E) 600

Solution: Let x be the total grown quantity of wheat. According to the question   (7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = — 400 million tonnes rice grown   400
Answer: C
Line k is in the rectangular coordinate system. If the v-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k? Select the correct option:
A) -3v + 2y = 6  B) 3v + 2y = -6  C) 3v - 2y = 6  D) 2v - 3y = 6  E) -2v - 3y = 6

Solution: This question can be solved in much simpler way.   To find the v intercept   Put y=0 in the equation of the line.   To find the y-intercept   Put v=0 in the equation of the line.   So   Sub v=0 in the answer choices check whether you are getting y=3.   A. -3v + 2y = 6 --- y = 3   B. 3v + 2y = -6 --- y = -3   C. 3v - 2y = 6 ----- y = -3   D. 2v - 3y = 6 --- y = -2   E. -2v - 3y = 6 --- y =-2   Eliminate answer B,C,D and E.   So the answer is -3v + 2y = 6.
Answer: A
Sum of two numbers prime to each other is 8 and their L.C.M. is 15. What are the numbers? Choose the correct option:	A) 3 and 5	B) 3 and 4	C) 4 and 5	D) 5 and 10	E) 6 and 8

Solution: 3 and 5s two numbers are prime, only options satisfy ie option 3 and 5 and B and C   but option D will not make the product of numbers i.e 15   3 and 5NSWER:3 and 5
Answer: A
Meg and Bob are among the 3 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?	Pick one: A) 24 B) 3 C) 60 D) 90 E) 120

Solution: Total # of ways the race can be finished is 3!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 3!/2=3.   Answer: 3.
Answer: B
If 9 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?  Choose the correct choice from the following options.
A) 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
B) 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
C) 9 × 10
D) 36
E) 45

Solution: 1st person will have 9 handshakes, 2nd will have 8, ....8th will have 1 and 9th will have 0   =8+7+6+5+4+3+2+1= 
8+7+6+5+4+3+2+1 = 36
36   if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.   Ans.36)
Answer: D
Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/4, 1/8, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?  Choose the correct choice from the following choices.
A) 1/16n	B) (n-1)/32n	C) 1/8n	D) (n+2)/2n	E) (3n-2)/2n

Solution: 1/4 * 1/8 * (1-1/n)   = 1/32 * (n-1)/n   = (n-1)/32n   Answer - (n-1)/32n
Answer: B
On dividing 199 by a number, the quotient is 11 and the remainder is 1. Find the divisor.  Choose the most appropriate option
A) A)12 B) B)14 C) C)16 D) D)18 E) E)22

Solution: d = (18-R)/Q   = (199 - 1)/11   = 198/11= 
198/11 = 18
18   18)
Answer: D
Median R of price of the car is 52,000. which could be the median of the other two.
35000, 44000, x, y, 57000.	Choose the correct choice from the following options:  A) 38000  B) 47000  C) 48000  D) 51,000  E) 56,000

Solution: Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits is R=56,000.56,000
Answer: E
Find the L.C.M. of 72, 108 and 2100.	Choose the correct choice from the following:
A) 37800	B) 37600	C) 37200	D) 37500	E) None of them

Solution: 72 = 2^3 x 3^2, 108 = 3^3 x 2^2, 2100 = 2^2 x 5^2 x 3 x 7.   L.C.M. = 2^3 x 3^3 x 5^2 x 7 = 37800.   37800nswer is 37800.
Answer: A
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1100 more than D, what is B's share?	Choices
A) Rs. 500	B) Rs. 1500	C) Rs. 2200	D) Rs. 2500	E) none of the above

Solution: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.   Then, 4x - 3x = 1100   x = 1100.   B's share = Rs. 2x = Rs. (2 x 1100) = Rs. 2200.   Answer = Rs. 2200
Answer: C
Tarun bought a T.V with 20% discount on the labelled price. Had he bought it with 25% discount? He would have saved Rs. 500. At what price did he buy the T.V?
A. Rs. 5000 B. Rs. 10000
Choose the correct choice:
A) Rs.5000	B) Rs.6000	C) Rs.7500	D) Rs.80000	E) Rs. 10000

Solution: Explanation:   Labelled price be Rs. 100   S.P in 1st case = Rs. 80   S.P in 2nd case = Rs. 75   Saving is Rs. 5 labelled price = Rs. 100   Saving is Rs. 500 labelled price   = Rs. (100/5 × 500) = Rs. 10000   ANSWRs. 10000R:Rs. 10000
Answer: E
It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
Answers:
A) 220 B) 250 C) 320 D) 420 E) 560

Solution: No more than 7 children attending the party means the number of children could be 1,2,3,4,5,6,7.   We need to find a number that is divisible by each of these. Out of the choices given only 420 is divisible by each of these numbers.   Hence , answer is 420.
Answer: D
We had $3500 left after spending 30% of the money that we took for shopping. How much money did we start with?
Options
A) $4600	B) $4800	C) $5000	D) $5200	E) $5400

Solution: Let x be the amount of money we started with.   0.7x = 3500   x = 5000   The answer is $5000.
Answer: C
If y > 0, (2y)/20 + (3y)/10 is what percent of y?
Select the correct option.
A) 40%
B) 50%
C) 60%
D) 70%
E) 80%

Solution: soln:-   can be reduced to y/10+3y/10 =2y/5=40%   40%NSWER:40%
Answer: A
If 148/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer  Choices:
A) I only B) III only C) I and II only D) II and III only E) I, II and III

Solution: I think, here we should use the greatest common factor.   The greatest common factor for 148 and 108 is 36.   So 36/x is an integer.   For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.   Ans is I and II only.
Answer: C
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
Options:
A) 7!	B) 8!	C) 9!	D) 10!	E) 11!

Solution: Ans.(B)   Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B