MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular field is 20 yards long and 18 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)  Choose the correct choice from the following answers:
A) 330 ft B) 336 ft C) 430 ft D) 330 ft E) 230 ft

Solution: 20 + 18 + 20 + 18= 
20 + 18 + 20 + 18 = 76
76 yds. for   outside of field.   18 + 18= 
18 + 18 = 36
36 yds. for dividing sections    76 + 36= 
 76 + 36 = 112
112 yds. of fencing   112 x 3= 336 ft. of fencing   correct answer 336 ft
Answer: B
On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 45 percent of the sales representatives prefer to stay at Hotel XYZ and 55 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer? Choose the correct answer.
A) 36	B) 39	C) 42	D) 45	E) 48

Solution: 18 people stay in XYZ and 42 people stay in ABC.   27 people prefer XYZ and 33 people prefer ABC.   Let's put all 27 people who prefer XYZ in hotel ABC.   Then 18 people who prefer ABC will stay in XYZ.   The highest possible number who are not given their preference is 27+18= 
27+18 = 45
45.   The answer is 45.
Answer: D
A does a work in 20days and B does the same work in 5days. In how many days they together will do the same work? Choose the correct choice from the following options
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: A+B can finish =AB/A+B = 20*5/(20+5)= 
20*5/(20+5) = 4
4days   Answer is 4
Answer: D
A park shaped like a rectangle has a length of 24 meters and a width of 18 meters. If trees are planted on its sides with gaps of 2 meters between them, how many trees are needed?	Answers:
A) 32 trees. B) 42 trees. C) 52 trees. D) 62 trees. E) None of these

Solution: Solution:   The perimeter of the rectangle is 2 × (24 + 18) = 2 × 42 = 84 meters, so there will be 84 ÷ 2 = 42 trees.   Answer 42 trees.
Answer: B
Of the 8 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 8 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?	Choose the correct option.
A) 30  B) 35  C) 56  D) 70  E) 105

Solution: another approach :   one scenario : [WWWM]   now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.   and 8 ways to select one man   so   5*4*3*3= 
  5*4*3*3 = 180
180   now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways   hence 180/3!= 180/6= 
180/6 = 30
30   30
Answer: A
If equation |x/5| + |y/5| = 2 encloses a certain region on the coordinate plane, what is the area of this region?  Choose the correct choice from the following options:
A) 20
B) 50
C) 200
D) 100
E) 400

Solution: The equation can be reduced to intercept form as |x/10| + |y/10| = 1, so these are lines in four quadrants with x and y intercept as 10, so it is a rhombus with diagonals of 20 each and hence area = 1/2*d1*d2 = 1/2*20*20 1/2* 1* 2= 
1/2* 1* 2 = 1
1/2*20*20= 
1/2*20*20 = 200
200. Answer 200.
Answer: C
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 15 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?  Choose the correct choice from the following answers:
A) 67
B) 45
C) 60
D) 90
E) 120

Solution: I believe there is a better way to do it.   Basically one of the options should satisfy the given criteria.   60 did    1/5 *60= 
 1/5 *60 = 12
12   2/3*60= 
2/3*60 = 40
40   so total distance   52 + remaining 15=67
Answer: C
Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 27 years, then how old is Bruce ?  Pick one
A) 7 years B) 10 years C) 12 years D) 13 years E) 14 years

Solution: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, Bruce's age = 2x = 10 years.   10 years
Answer: B
A, B and C start a business each investing 20,000. After 5 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 69,900 was recorded. Find the share of B
Answers.
A) 20,000	B) 21,200	C) 28,200	D) 20,500	E) None of these

Solution: Ratio of the capitals of A, B and C   = 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7   = 205000 : 212000 : 282000 = 205 : 212 : 282.   B’s share = (69900 × 212⁄699) = 21200;   Answer 28,200
Answer: C
If x is an integer such that 1 < x < 9, 2 < x < 15, 7 > x > –1, 4 > x > 0, and x + 1 < 5, then x is Select the correct option.
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: 1 < x < 9,   2 < x < 15,   -1< x < 7   0< x< 4   x+1<5   From above: 2< x < 4 --> x = 3.   3nswer: 3.
Answer: A
If a 3-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible? Choices:
A) 6	B) 18	C) 20	D) 84	E) 216

Solution: Another way:   1st member can be selected in 9 ways   2nd can be selected in 8 ways   3rd can be selected in 7 ways   So total ways : 504   But to avoid the similar scenarios 504/3!=84   84
Answer: D
The average (arithmetic mean) of 20, 40, and 60 is 7 more than the average of 10, 70, and what number? Choose the correct choice from the following answers
A) 19  B) 25  C) 35  D) 45  E) 55

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -7 = 33   sum of second list = 33*3= 
33*3 = 99
99   therefore the number= 99 -80= 
99 -80 = 19
19   19NSWER:19
Answer: A
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 22 households had a both a car and a bike and 44 had a car, how many had bike only? Choose the correct choice from the following choices.
A) 30	B) 35	C) 20	D) 18	E) 10

Solution: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-22+11 --> {Bike}=57 --> # those who have bike only is {Bike}-{Both}=57-22= 
57-22 = 35
35.   Answer: 35.
Answer: B
Country X imposes a two-tiered tax on imported cars: the first tier imposes a tax of 30% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 20%. If Ron imported a $50,000 imported car and ended up paying $12000 in taxes, what is the first tier's price level?  Choose the correct choice
A) $22000	B) $20000	C) $23000	D) $24000	E) $25000

Solution: Let T be the tier price, P be total price = 50000   Per the given conditions:   0.30T + 0.20(P-T) = 12000   0.30T+0.20*50000-0.20T =12000   0.10T +10000 =12000   0.10T =12000-10000= 
12000-10000 = 2_000
2000   T= 2000/0.10= 
2000/0.10 = 20_000
20000   Answer $20000
Answer: B
The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Choose the correct choice from the following options.
A) 2  B) 3  C) four  D) 8  E) 9

Solution: Solution   Let the ten's digit be x and units digit be y.   Then, (10x+y) - (10y+x)= 36	‹=›9(x - y) = 36   ‹=›x - y = 4.   Answer four
Answer: C
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct choice from the following options
A) 992  B) 389  C) 500  D) 277  E) 781

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   Answer:500
Answer: C
The sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the youngest child ?
Pick one.
A) 2 year	B) 8 year	C) 10 year	D) None of these	E) 9 year

Solution: Solution   let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.   then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.   âˆ´ Age of the youngest child = x = 2 years. 2 yearnswer 2 year
Answer: A
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?	Answers: A) 1224 B) 1234 C) 1350 D) 1358 E) 1365

Solution: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.   =. Required number of ways = 14C10 = 14C4   = 14!/4!x19! = 1365   1365
Answer: E
If a and b are odd integers, which of the following must be an even integer?	Choose the correct choice from the following choices.
A) a(b – 2)
B) ab + 4
C) (a + 2)(b – 4)
D) 3a + 5b
E) a(a + 6)

Solution: 3a+5b==0dd*odd + odd*odd =odd+odd = even.   ANSWER:3a + 5b
Answer: D
Rs.3150 is divided so that 5 times the first share, thrice the 2nd share and six times the third share amount to the same. What is the value of the third share? Pick: A) s529 B) s527 C) s570 D) s750 E) s507

Solution: A+B+C = 3150   5A = 2B = 6C = x   A:B:C = 1/5:1/2:1/6 = 6:15:5   5/21 * 3150= 
5/21 * 3150 = 750
Rs750   Answer:s750
Answer: D
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses at the restaurant? (Assume that all boxes are filled to capacity.) Select the correct option.
A) 96
B) 240
C) 56
D) 384
E) 480

Solution: 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272= 
12 + 272 = 284
284 glasses at the MINIMUM   Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....   The difference in the number of boxes MUST be 16 though, so we could have....   2 small boxes and 18 large boxes   3 small boxes and 19 large boxes   etc.   With every additional small box + large box that we add, we add   12+16= 
  12+16 = 28
28 MORE glasses. Thus, we can just "add 28s" until we hit the correct answer....   284+28= 
284+28 = 312
312   312+28= 
312+28 = 340
340   340+28= 
340+28 = 368
368   368+28= 
368+28 = 396
396   At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....   396+28= 
396+28 = 424
424   424+28= 
424+28 = 452
452   452+28= 
452+28 = 480
480   Final Answer:480
Answer: E
For 600km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by bus and the rest bycar. The ratio of the speed of the train to that of the cars is?  Choose the correct choice from the following
A) 1:3 B) 3:4 C) 2:5 D) 3:7 E) 3:11

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3:4.   3:4
Answer: B
Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1051. Find the cost of each ice-cream cup?
Choose the correct choice from the following answers:
A) 25	B) 40	C) 77	D) 99	E) 91

Solution: Let the cost of each ice-cream cup be Rs.x   16(6) + 5(45) + 7(70) + 6(x) = 1051   96 + 225 + 490 + 6x = 1051   6x = 240 => x = 40.   Answer: 40
Answer: B
In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 25 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?  Choose the correct choice from the following choices.
A) 50%  B) 53%  C) 54%  D) 55%  E) 57%

Solution: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.   60*0.75= 
60*0.75 = 45
45 Democrats are expected to vote for Candidate A;   40*0.25= 
40*0.25 = 10
10 Republicans are expected to vote for Candidate A.   Thus total of   45+10= 
  45+10 = 55
55 registered voters are expected to vote for Candidate A, which is 55% of the total number of registered voters.   Answer: 55%.
Answer: D
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 6 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?	Select: A) 60 gallons B) 100 gallons C) 240 gallons D) 180 gallons E) 130 gallons

Solution: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40   Volume of 1/40 part = 6 gallons\   Volume of whole = 6 * 40= 
6 * 40 = 240
240 gallons.   ANSWER:240 gallons
Answer: C
A sum of Rs.4400 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.  Choose the correct answer:  A) Rs.2860  B) Rs.3120  C) Rs.3320  D) Rs.2760  E) None of these

Solution: Let A be the amount received at the end of the three years.   Rs.2860 = 4400[1 + 10/100][1 + 20/100][1 + 25/100]   Rs.2860 = (4400 * 11 * 6 * 5)/(10 * 5 * 4)   Rs.2860 = Rs.7260   So the interest = 7260 - 4400 = Rs.2860   Rs.2860NSWER:Rs.2860
Answer: A
Beth received 1/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?  Select
A) 1/5  B) 4/7  C) 3/10  D) 7/20  E) 1/2

Solution: Let the total votes be 10. Beth received 1 votes, other votes  10-1= 
 10-1 = 9
9. In order to have received 1/2 of the votes she needed 5 votes so 4 more, which is 4/7 of the other votes.   Answer: 4/7.
Answer: B
In a two-digit number, the digit at unit place is 1 more than twice of the digit at tens place. If the digit at unit and tens place be interchanged, then the difference between the new number and original number is less than 1 to that of original number. What is the original number?
Choose the correct answer.
A) 52 B) 73 C) 25 D) 49 E) 37

Solution: Let the original number be l0 x + y   y = 2x + 1....(i)   and (l0y + x) – (10x + y) = 10x + y – 1   or, 9y – 9x = l0x + y – 1   or, l9x – 8y = 1 ...(ii)   Putting the value of (i) in equation (ii) we get,   19x – 8(2x + 1) = 1   or, 19x – 16x – 8 = 1   or, 3x = 9 or, x = 3   So, y = 2 × 3 + 1 = 7   Answer 37   \ original number = 10 × 3 + 7 = 37
Answer: E
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.310. How much does C have?  Choose the correct option:
A) 50	B) 78	C) 267	D) 29	E) 10

Solution: A+B+C = 500   A+C = 200   B+C = 310   --------------   A+B+2C = 510   A+B+C = 500   ----------------   C = 10   Answer: 10
Answer: E
In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ?
Choose the correct choice: A) 64 B) 1/8 C) 1 D) 4 E) 1/64

Solution: Say r=2 => V1 = 1/16   when r=1; V2 = 1/4   V2 = 4*V1.   Answer : 4
Answer: D
A metallic hemisphere is melted and recat in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then :	Choose the correct choice from the following choices:
A) H = 2R
B) H = 4R
C) H = √4R
D) H = 2/3 R
E) None

Solution: Sol.   2/3 ∏R³ = 1/3 ∏R²H ⇒ H = 2R.   H = 2Rnswer H = 2R
Answer: A
A train 385 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?	Choose the most appropriate option.
A) 75 sec B) 52 sec C) 41 sec D) 62 sec E) 21 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   = [385 * 3/55= 
385 * 3/55 = 21
21 sec   Answer:21 sec
Answer: E
If n is a positive integer, which one of these following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?  Choose the correct choice from the following answers:
A) 125n + 3	B) 240n + 3	C) 380n + 3	D) 590n + 3	E) 700n + 3

Solution: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.   When we divide (240n + 3) by 4, 5, or 6, the remainder must be 3.   The answer is 240n + 3.
Answer: B
The fourth proportional to 6, 11, 36 is:	Pick
A) 64  B) 66  C) 68  D) 70  E) 72

Solution: Let the fourth proportional to 6, 11, 36 be x.   Then, 6 : 11 : 36 : x   6x = (11 x 36)   x =	(11 x 36)/6   x=396/6= 
396/6 = 66
66   Answer: Option 66
Answer: B
Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
Choose the correct choice from the following answers:
A) 14.8
B) 14.4
C) 14.7
D) 14.1
E) 14.5

Solution: Let the present ages of Mahesh, Nilesh and Ramesh be M, N and R respectively.   M/N = 5/x --- (1)   M = R - 18 --- (2)   R + 9 = 47 --- (3)   M - N = R --- (4)   (3) => R = 47 - 9= 
47 - 9 = 38
38 years   (2)=> M = 38 - 18= 
38 - 18 = 20
20 years   (1)=> 20/N = 5/x => N = 4x   (4) => 4x - 20 = 38   => 4x = 58 => x = 14.5   Answer:14.5
Answer: E
Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A) 5  B) 6  C) 9  D) 24  E) 26

Solution: Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are   0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1= 
  0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5
5 cases....5
Answer: A
In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many R eggs does the plant process per day?
Choose the correct choice from the following answers.
A) 100 B) 300 C) 400 D) 3,000 E) 4,000

Solution: Straight pluggin in for me. As usual, I started with C and got the answer.   Lets' back calculate and see what we get   Let us consider eggs processed each day to be 400   So Initial ratio of eggs processed and rejected is 96:4 or 24:1   So out of 400 eggs, there will be 384 eggs processed and 16 rejected.   Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there R=384+12= 
384+12 = 396
396 eggs accepted and 4 rejected...and the ratio will be 99:1   Bingo...this is what the questions says....   Its always a good idea to start with 400.
Answer: C
15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?	Choose the correct choice from the following answers.
A) 87 B) 18 C) 17 D) 16 E) 10

Solution: 18inders 18ooks Days   15 1400 21   x 1600 20   x/15 = (1600/1400) * (21/20) => x = 18   Answer:18
Answer: B
How many multiples of 10 are there between 11 and 1001? Pick
A) 98  B) 99  C) 100  D) 97  E) 95

Solution: 10 * 2= 
10 * 2 = 20
20   10 * 100= 
10 * 100 = 1_000
1000   Total multiples= (100 - 2) + 1= 
(100 - 2) + 1 = 99
99   Answer 99
Answer: B
A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed? Pick one:
A) 12
B) 11
C) 99
D) 27
E) 99

Solution: Let the work be completed in x days   (x-4)days of 12 + (x-6)days of B + x days of C = 1   \inline \Rightarrow \inline \frac{x-4}{18}+\frac{x-6}{27}+\frac{x}{36}=1   \inline \Rightarrow \frac{13x-48}{108}=1   x = 12   \inline \therefore Total time = 12 days   12nswer:12
Answer: A
When positive integer X is divided by positive integer Y, the remainder is 1.44. If X/Y = 96.12, what is the value of Y? Choose the correct choice from the following choices:
A) 96  B) 75  C) 48  D) 25  E) 12

Solution: When positive integer x is divided by positive integer y, the remainder is 1.44 --> x=qy+1.44;   x/y=96.12 --> x=96y+0.12y (so q above equals to 96);   0.12y=1.44 --> y=12.   Answer: 12.
Answer: E
Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability R that Jane will be on the same committee as Albert?  Pick.
A) 12%
B) 20%
C) 33%
D) 40%
E) 50%

Solution: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20   No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8   Probability R= (8/20) *100= 
(8/20) *100 = 40
40%.   +1 for me.. :40%
Answer: D
On a game show, a contestant spins three different wheels; each wheel is numbered 1 to 10. What is the probability that the contestant will spin all tens?	Choose the correct choice from the following options:
A) 1/3 B) 1/2 C) 1/50 D) 1/1,000 E) 1/100

Solution: All 10s:   1st wheel = 10 = 1/10   2nd wheel = 10 = 1/10   3rd wheel = 10 = 1/10   (1/10)(1/10)(1/10) = 1/1,000   Answer: 1/1,000
Answer: D
John Purchased 1300 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle? Pick one.
A) $1.63
B) $1.64
C) $1.68
D) $1.70
E) $1.76

Solution: (1300*1.89+750*1.38)/(1300+750) =~1.70   Option ($1.70)
Answer: D
In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father? Choose the correct choice from the following.
A) 27  B) 36  C) 28  D) 46  E) 91

Solution: Raj present age = 32 - 8= 
32 - 8 = 24
24.   After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2= 56, and his present age is 52.   Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46   Answer:28
Answer: C
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
Pick: A) 100 B) 250 C) 260 D) 416 E) None of these

Solution: Explanation:   Let the number of boys and girls be 8x and 5x.   Total number of students = 13x = 13 × 32 = 416.   Answer: 416
Answer: D
R-R-G-G-G-Y-Y-B-R-R-G-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?  Choose the correct choice from the following options:	A) 63	B) 64	C) 65	D) 66	E) 67

Solution: The repeated pattern R-R-G-G-G-Y-Y-B has 8 beads.   But the missing section includes R-R-G-G-G-Y-Y at the end.   Thus the number of beads in the missing section has the form 8k + 7.   The answer is 63.
Answer: A
The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?  Choices.
A) 46	B) 82	C) 45	D) 43	E) 53

Solution: Sum of all the 13 numbers = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 57= 
7 * 57 = 399
399   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 399 - 780= 
427 + 399 - 780 = 46
46.   46nswer:46
Answer: A