MU-NLPC/Calc-aqua_rat huggingface dataset:
Two taps can separately fill a cistern 5 minutes and 10 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in?
Choose the correct option.
A) 7
B) 8
C) 6
D) 4.2
E) 5

Solution: 1/5 + 1/10 - 1/x = 1/15   x = 30/7 = 4.2   Answer: 4.2
Answer: D
A plant manager must assign 8 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers? Choose the correct answer.
A) 243	B) 336	C) 350	D) 486	E) 540

Solution: whatever : my take selecting team of 2 out of 8 to assign to the shifts = 8C2 = 28 ways.   now 2 out of 8 means total of 4 group possible.   so putting them in shifts = counting methode: first, second, third, alt , alt   = 4*3*2*1= 
4*3*2*1 = 24
24   here alt and alt are the same: so  24/2= 
 24/2 = 12
12 ways.   total ways of selecting= (selecting 2 out of 8)*arranging those teams in shifts   = 28*12= 
28*12 = 336
336   Ans: 336
Answer: B
What percent of 250 is 45?  Pick one.
A) 0.25% B) 18% C) 25% D) 40% E) 250%

Solution: 250*x /100 = 45   x = 45*10/25= 
45*10/25 = 18
18   Ans: 18%
Answer: B
Six fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?  Choose the correct option:
A) 20  B) 24  C) 25  D) 30  E) 36

Solution: 6*5= 
6*5 = 30
30   The answer is 30.
Answer: D
If x is an integer and (x)(x^2)(x^3)(x^10) is positive, which of the following could be negative? Choose the correct choice from the following answers
A) x^4  B) (x)(x^3)  C) (x)(x)  D) x + x^9  E) 3x^2

Solution: A) X^4 - always positive (or 0).   B) X(X^3) = X^4 - Again always positive (or 0).   C) (x)(x) = X^2 - Again always positive (or 0).   D) x+x^9 - Could be -ve if x is -ve.   E) 3X^2 - again always positive (or 0)   Answer x + x^9.
Answer: D
Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 40 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales? Choose the correct choice from the following answers:
A) $ 10,000
B) $ 12,750
C) $ 24,000
D) $ 26,000
E) $ 28,000

Solution: Let x be the total sales in $.   For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$   For the remaining (x-11000) $, you get 40% ---> 0.4*(x-11000)   Thus, 0.4*(x-11000) + 2200 = 7300 ----> x= 12,750 $   $ 12,750 is thus the correct answer.
Answer: B
A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift,
customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
Choose the correct choice:  A) 20  B) 10  C) 59  D) 90  E) 100

Solution: to choose the sample of 2 customers from 5. it can be done 5C2 possible ways.   So the answer is B. 10
Answer: B
The revenue from sales items in 1996 increases by x percent, compared in 1995 and the revenue in 1997 decreases by x percent, compared in 1996. If the revenue from sales items in 1997 decreases by 4 percent, compared in 1995, what is the value of x?
Select
A) 10
B) 15
C) 20
D) 30
E) 35

Solution: 1995 - let the value be z   1996 - x% increase - z(1+x/100)   1997 - x% decrease - z(1+x/100)(1-x/100)   from 95 to 97 decrease is 4%   hence, [z-{z(1+x/100)(1-x/100)}]/z = 4/100   solving x = 20%   20 is the answer
Answer: C
What is the greatest prime factor of (15!14!) + (15!16!)?  Choose the correct choice: A) 31 B) 71 C) 181 D) 211 E) 241

Solution: 15!14! + 15!16!   = 15!14! (1+15*16)   = 15!14!(241)   The answer is 241.
Answer: E
A motorcyclist goes from Bombay to Pune, a distance of 224 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 answer:
A) 1:2 B) 1:5 C) 4:7 D) 1:1 E) 1:8

Solution: T = 224/32= 
224/32 = 7
7 h   T= 7 - 3= 
7 - 3 = 4
4   Time Ratio= 7:4   Speed Ratio = 4:7   Answer: 4:7
Answer: C
Three grades of milk are 1 percent, 2 percent and 4 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Choose the correct choice from the following choices.
A) y + 4z B) (y +z) / 4 C) 2y + 3z D) 3y + z E) 3y + 4.5z

Solution: Soln:   The resulting equation is   => (.01x + .02y + .04z)/(x+y+z) = 1.5/100   => x + 2y + 4z = 1.5x + 1.5y + 1.5z   taking x to one side and y and z to other side we get   => x = y + 4z   y + 4zns is a
Answer: A
A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 30 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]  Choose the correct choice from the following choices:
A) 1/4
B) 7/12
C) 2/3
D) 1
E) 8/7

Solution: Let' take the Number of geese to be 100.   Male = 30. Female = 70.   Now the second part of the Q, Let's take the Number migrated to be 20.   So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *30 = 6 Geese (Males)   And now we know out of the total 20 geese , 6 are male , then 14 have to be female.   Now the ratio part , Male Geese Ratios = 6/30 = 1/5. - A   Female Geese Ratios =14/70=1/5 - B   Cross Multiply Equations A and B and you get =1.   Ans 1
Answer: D
If 6th March, 2004 is sunday, what was the day of the week on 6th March, 2005?  Select: A) monday B) tuesday C) friday D) sunday E) wednesday

Solution: The year 2004 is a leap year. So, it has 2 odd days.   But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.   The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.   Given that, 6th March, 2004 is Sunday   6th March, 2005 is Monday.   mondaynswer: monday) Monday
Answer: A
3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
Answers:
A) 1 : 5	B) 3 : 10	C) 4 : 7	D) 4 : 11	E) 5 : 9

Solution: We have, a = 12, b = 15, c = 25 and x = 312.   ax_ 12 X 312   a+b+c 12+15+25   — 72,   bx _ 15 X 312 3 : 10 — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =   a+b+c 12 + 15+ 25   ...3 : 10-A=18 andC-3 : 10=60   - 150   Thus, their ratio = 18 : 60 or 3 : 10   3 : 10
Answer: B
On a trip covering 450 km, a bicyclist travels the first 300 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?	Choices.
A) 16.5  B) 17.0  C) 17.5  D) 18.0  E) 18.5

Solution: time 1 = 300 / 20= 
300 / 20 = 15
15 hours   time 2= 150 / 15= 
150 / 15 = 10
10 hours   total time= 25 hours   average speed = 450 / 25= 
450 / 25 = 18
18 km/hr   The answer is 18.0.
Answer: D
A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident Choose the correct choice from the following answers:
A) 30%
B) 35%
C) 40%
D) 45%
E) 50%

Solution: Explanation:   Let A = Event that A speaks the truth   35% = Event that 35% speaks the truth   Then P(A) = 75/100 = 3/4   P(35%) = 80/100 = 4/5   P(A-lie) = 1-3/4 = 1/4   P(35%-lie) = 1-4/5 = 1/5   Now   A and 35% contradict each other =   [A lies and 35% true] or [35% true and 35% lies]   = P(A).P(35%-lie) + P(A-lie).P(35%)   [Please note that we are adding at the place of OR]   = (3/5*1/5) + (1/4*4/5) = 7/20   = (7/20 * 100)= 
(7/20 * 100) = 35
35%   Answer: Option 35%
Answer: B
In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different T sets can be produced by this process?  Answers:
A) 41 B) 89 C) 125 D) 243 E) 512

Solution: Case 1: 1 used envelope => 1 way   Case 2: 2 used envelopes   - 4-1-0: Choose 4 from 5 cards: 5 ways   - 3-2-0: Choose 3 from 5 cards: 10 ways   Case 3: 41ll envelopes used   - 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways   - 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15   Total T: 1+5+10+10+15= 
1+5+10+10+15 = 41
41=> 41nswer: 41
Answer: A
A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 10
matches are totally played, how many teams participated?
Choices
A) 4
B) 5
C) 10
D) 7
E) 8

Solution: 2 ways to solve this problem..   summation(x)=n(n-1)/2   n(n-1)/2=10;   n^2-n-20=0   Ans : 5   ANSWER:5
Answer: B
Which one of the following numbers is exactly divisible by 11?
Select the correct option:
A) 415624
B) 415358
C) 415647
D) 425624
E) 415836

Solution: 415624   415624 is exactly divisible by 11.
Answer: A
A woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear? Select
A) 8	B) 12	C) 22	D) 17	E) 18

Solution: total ways = 4*3*2=24..   now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..   the ways in which the pink blouse and green skirt are together=1*1*2=2..   total ways =24-2=22..   ANSWER:22
Answer: C
The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?  Choices
A) 8  B) 9  C) 7  D) 6  E) 1

Solution: 2x * x = 128   => x= 8   8nswer: 8
Answer: A
Sam wrote 7 letters on Tuesday and 3 letters on Wednesday. How many letters did he write on average per day? Choose the correct choice from the following choices:
A) 10 B) 4 C) 21 D) 3 E) 5

Solution: (7 + 3)/2= 
(7 + 3)/2 = 5
5   The correct answer is 5
Answer: E
If the radius of a circle that centers at the origin is 5, how many W points on the circle have integer coordinates?  Choose the correct choice:
A) 4 B) 8 C) 12 D) 15 E) 20

Solution: I understand this might not be required but I used the equation of a circle.   Since the origin is at 0, x^2+y^2=5^2.   X,Y could be +/- (0,5 or 5,0) - 4 possibilities.   X,Y could be +/- (3,4 or 4,3) - 8 possibilities.   Ans: W=12
Answer: C
Raman mixed 27 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?	Choose the correct choice from the following
A) 129	B) 287	C) 190	D) 188	E) 112

Solution: Explanation:   CP per kg of mixture = [27(150) + 36(125)]/(27 + 36) = Rs. 135.71   SP = CP[(100 + profit%)/100]   = 135.71 * [(100 + 40)/100] = Rs. 190.   Answer:190
Answer: C
If 15 and 20 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 20
III. 40 Select
A) I only	B) II only	C) I and II only	D) II and III only	E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Let x be the length of the third side.   20-15 < x < 20+15   5 < x < 35   The answer is I and II only.
Answer: C
A train of 35 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choose the most appropriate option.
A) 6 B) 3 C) 4 D) 9 E) 3.6

Solution: D = 35 * 60 + 1500= 
35 * 60 + 1500 = 3_600
3600 m   T= 3600/60 * 18/5= 
3600/60 * 18/5 = 216
216 sec= 3.6 mins   Answer:3.6
Answer: E
A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?	Choose the most appropriate option:
A) 20
B) 25
C) 27
D) 30
E) 35

Solution: Time = 1 hr 40 min 48 sec = 1hr +40/60hr+48/3600hr=1+2/3+1/75=126/75hr   distance = 42 km   speed=distance/time   =42/(126/75)=42×75/126   ⇒57 of the actual speed = 42×75/126   ⇒actual speed = 42×75/126×7/5=42×15/18=7×15/3=7×5=35 km/hr   Answer is 35.
Answer: E
A bag marked at $125 is sold for $120. The rate of discount is?
Choose one.
A) 10%  B) 25%  C) 20%  D) 50%  E) 4%

Solution: Rate of discount = 5/125 * 100= 
5/125 * 100 = 4
4%   Answer is 4%
Answer: E
There are r red marbles, b blue marbles and w white marbles in a bag. Write the ratio of the number of blue marbles to the total number of marbles in terms of r, b and w. Answers:
A) r/ (r + b + w)  B) b/ (r + b + w)  C) w / (r + b + w)  D) r / (r + b )  E) r / ( b + w)

Solution: Solution   The total number of marbles is   r + b + w   The total ratio of blue marbles to the total number of marbles is   r / (r + b + w)   r/ (r + b + w)NSWER IS r/ (r + b + w)
Answer: A
If u, v, and w are three different positive integers whose sum is prime, which of the following statements could be true? Choose the correct answer.
A) The average (arithmetic mean) of u, v, and w is prime.  B) Each of u + 3, v + 3, and w + 3 is prime.  C) Each of u + v, u + w, and v + w is prime.  D) Each of u, v, and w is prime.  E) u + v = w

Solution: the question asks could be!!!!   this means that if at least one option works, it is the answer.   3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that Each of u, v, and w is prime. is the answer.
Answer: D
The 106th term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is  Choose the correct answer:
A) h
B) k
C) l
D) o
E) r

Solution: a is one time, b,2 times so on...   so 106=n(n+1)/2..   0r n(n+1)= 212 ... now 15*16=240...14*15<212 so n= 15. and 15th alphabet is O. ans o
Answer: D
A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.140/- extra, then how much amount he took?	Options.
A) s.5500/-	B) s.6000/-	C) s.4000/-	D) s.7000/-	E) s.8000/-

Solution: Explanation:   2 years = Rs.140/-   year = 140/2   Rate of Interest = 1%   100/1% × 140/2 = Rs.7000/-   P = Rs.7000/-   Answer: Option s.7000/-
Answer: D
What is the ratio of 4/7 to the product 3*(7/3)?
Options:
A) 4:49	B) 1:3	C) 3:21	D) 1:7	E) 3:49

Solution: 4/7 / 21/3 = 4/49...   IMO option 4:49.
Answer: A
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:  Choose the correct choice from the following answers:
A) 2%  B) 3%  C) 5%  D) 8%  E) 9%

Solution: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.   S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.   Gain =(80/1600)x100 % = 5%   answer : 5%
Answer: C
How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ? Choose the correct option.
A) 13	B) 25	C) 87	D) 49	E) 63

Solution: Explanation:   Required numbers are 24, 30, 36, 42, ..., 96   This is an A.P. in which a = 24, d = 6 and l = 96   Let the number of terms in it be n.   Then tn = 96 a + (n - 1)d = 96   24 + (n - 1) x 6 = 96   (n - 1) x 6 = 72   (n - 1) = 12   n = 13   Required number of numbers = 13.   13)
Answer: A
The present ratio of students to teachers at a certain school is 70 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers? Choose one.
A) 2 B) 8 C) 10 D) 12 E) 15

Solution: We are given that the ratio of students to teacher is 70 to 1. We can rewrite this using variable multipliers.   students : teachers = 70x : x   We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:   Students/Teachers  25/1 = (70x + 50)/(x + 5)   If we cross multiply we have:   25(x + 5) =70x + 50   25x + 125 = 70x + 50   1.667 = x   x~2   Since x is the present number of teachers, currently there are 2 teachers.   2nswer 2.
Answer: A
workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.60 lacs . How many workers were they?  Pick one
A) 220 B) 230 C) 1200 D) 560 E) 590

Solution: N * 50 = (360000 - 300000)= 
(360000 - 300000) = 60_000
60000   N= 60000 / 50= 
60000 / 50 = 1_200
1200   1200
Answer: C
If |b| ≥ 1 and x= -| a| b, then which one of the following is necessarily true?
Choose the correct choice from the following options:
A) a -xb < 0  B) a -xb ≥ 0  C) a -xb > 0  D) a -xb ≤ 0  E) None of these

Solution: Explanation :   x = –|a| b   Now a – xb = a – (– |a| b) b   = a + |a| b2   ∴ a – xb = a + ab2 … a 0 ≥ OR a – xb   = a - ab2 …a < 0   = a(1 + b2) = a(1 – b2).   Consider first case:   As a ≥ 0 and |b| ≥ 1, therefore (1 + b2) is positive.   ∴ a (1 + b2) ≥ 0   ∴ a – xb ≥ 0   Consider second case.   As a < 0 and |b| ≥ 1, therefore (1 – b2) ≤ 0   ∴ a (1 – b2) ≥ 0 (Since –ve × -ve = +ve and 1 – b2 can be zero also), i.e. a – xb ≥ 0   Therefore, in both cases a – xb ≥ 0.   Answer : a -xb ≥ 0
Answer: B
Mr. loyd wants to fence his Square shaped land of 120Sqft each side.If a pole is laid every 12ft how many poles do he need? Choose the correct choice from the following options:
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: If each side is 120 feet..then total perimeter is 120*4= 
120*4 = 480
480   poles every 12 feet hence no of poles= 480/12= 
480/12 = 40
40   ANSWER:40
Answer: C
In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 3, then what is the increase in the number of pandas?  Pick one:
A) 2  B) 3  C) 9  D) 10  E) 15

Solution: One short cut to solve the problem is   c:p = 1:3   c increased to 4   => 1:3 = 4:x   => x = 12   =>p increased by 9   9 is the answer
Answer: C
The area of a circle is increased by 800%. By what percent has the radius of the circle increased?
Pick:
A) 100%
B) 400%
C) 300%
D) 600%
E) 200%

Solution: The area of the circle is increased by 800%, thus the area is increased 9 times.   The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 3 times (diameter increase 3 times = area increase 9 times), which is increase by 200%.   Answer: 200%.
Answer: E
A pilotless cargo carrier brings water, air and dry food to a space station. A third of the cargo's weight is water and the ratio, by weight, of air to dry food is 2:3. If the cargo contains 1,800 pounds of water, how many pounds of air does it contain?	Choose the correct choice from the following answers
A) 1,200 B) 1,300 C) 1,440 D) 3,000 E) 3,240

Solution: Let the capacity of the cargo be x   W + A + D = X   Given X/3 = W => X = 3*1800= 
3*1800 = 5_400
5400   Now W+A+D= 5400   Now A+D = 5400 - 1800= 
5400 - 1800 = 3_600
> 3600   Given A/D= 2/3   Now air will  2/5*3600= 
 2/5*3600 = 1_440
>1440.   ANSWER:1,440
Answer: C
John found that the average of 15 numbers is 40. If 11 is added to each number then the mean of number is?
Choose the correct option:
A) 51 B) 45 C) 65 D) 78 E) 64

Solution: (x+x1+...x14)/15 = 40   51   Option 51
Answer: A
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,800 nuts and 1,800 bolts?
Pick one.
A) 1,250 seconds  B) 1,500 seconds  C) 1,750 seconds  D) 2,700 seconds  E) 3,000 seconds

Solution: I used the Rate formula (R=\frac{1}{T})   Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}   Rate of 1st machine = Rate of 2nd machine   After this I got lost.   Please can you help how to approach using algebra?   I wouldn't complicate:   1 machine needs 1,800*1 seconds to produce 1,800 bolts, so 2 need half of that, so 1,800/2 seconds.=900   1 machine needs 1,800*2 seconds to produce 1,800 nuts, so 2 need half of that, so 1,800*2/2 seconds.=1800   total =2700 sec   2,700 seconds
Answer: D
Vanessa, Mike and Sarah have missed a total of 17 days of school this year. Vanessa and Mike have missed 14 days total, and Mike and Sarah have missed 12 days total. How many days of school did Vanessa miss alone?
Choose the correct choice from the following
A) 9
B) 4
C) 5
D) 2
E) 3

Solution: Vanessa + Mike + Sarah = 17   V+M=14   M+S=12 <<Use this formula & plug into the original formula, to get Vanessa's total   V + (M + S) = 17   V + 12 = 17   Subtract 12 from both sides   V = 5   Answer: 5
Answer: C
Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $540. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $720. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
Choose the correct choice
A) 12  B) 11  C) 10  D) 15  E) 16

Solution: Let X be pair of shoes and Y be pair of boots.   22x+16y = 540 ... eq1   8x +32y = 720....eq 2.   Now multiply eq 1 by 2 and sub eq 2.   44x = 1080   8x = 720.   36x = 360 => x = 10.   Sub x in eq 2.... we get 80 + 32y = 720... then we get 32y = 640 then y = 20   Differenece between X and Y is 10   Answer : 10
Answer: C
Molly's age in 18 years will be five times her age six years ago. What is Molly's present age? Choose the correct choice from the following: A) 8 B) 9 C) 10 D) 12 E) 14

Solution: Let x be Molly's present age.   x + 18 = 5(x-6)   x = 12   The answer is 12.
Answer: D
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder  Choose one.
A) 1123  B) 1234  C) 1345  D) 1450  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
What is the difference between the local value of 1 and 2 in the number 2124?	Choose the correct option
A) 70 B) 75 C) 20 D) 80 E) 60

Solution: Explanation:   100 â€“ 20 = 80   Answer: 80
Answer: D
The average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women?	Pick:
A) 21 B) 32 C) 30 D) 41 E) 37

Solution: 10 + 12+ 10 * 2= 
10 + 12+ 10 * 2 = 42
42/2= 
42/2 = 21
21   21nswer:21
Answer: A
Gambling with 4 dice, what is the probability of getting an even sum? Choose the most appropriate option
A) 3/4 B) 1/2 C) 2/3 D) 1/4 E) 1/3

Solution: Even sum can be obtained in following cases:   EEEE - one case. Each E can take 3 values (2, 4, or 6), so total for this case is 3^4;   OOOO - one case. Each O can take 3 values (1, 3, or 5), so total for this case is 3^4;   EEOO - 4!2!2!=64!2!2!=6 cases (EOEO, OOEE, ...). Each E can take 3 values (2, 4, or 6) and each O can also take 3 values (1, 3, or 5), so total for this case is 6*3^2*3^2=6*3^4   Total # of outcomes when throwing 4 dice is 6^4.   P=3^4+3^4+6∗3^4/6^4=1/2   Answer: 1/2.
Answer: B