MU-NLPC/Calc-aqua_rat huggingface dataset:
In a meeting of 3 representatives from each of 8 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
Choose the most appropriate option:
A) 242 B) 232 C) 212 D) 262 E) 252

Solution: In fact, all 24 people will shake hands with 21 others.   So, it SEEMS like the TOTAL number of handshakes = (24)(21)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (24)(21) by 2.   So, the TOTAL # of handshakes = (24)(21)/2 = 252   Answer : 252
Answer: E
At the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?  Choose the correct option:
A) 15.3%
B) 25%
C) 30%
D) 33%
E) 40%

Solution: 15.3%nother method is to use the formula for 2 successive percentage changes:   Total = a + b + ab/100   50 = 30 + b + 30b/100   b = 15.3   15.3%nswer (15.3%)
Answer: A
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?  Choose the correct choice:  A) 11  B) 10  C) 99  D) 88  E) 12

Solution: 2420 --- 242   100 --- ? => 10%Answer: 10
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 42 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?  Choose the correct choice from the following answers
A) 22
B) 27
C) 50
D) 99
E) 12

Solution: Relative speed = 42 + 30= 
42 + 30 = 72
72 km/hr.   72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Distance covered= 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 /20= 
1000 /20 = 50
50 sec.   Answer: 50
Answer: C
A small bag contains full of nine yellow ball, three white balls and four red balls. In how many ways can two balls be drawn from the bag?	Choose the correct choice from the following.
A) 16c2  B) 5c7  C) 4c2  D) 32c2  E) 48c2

Solution: tot balls = 9+3+4= 
9+3+4 = 16
16   two balls drawn from 16C2 ways   16c2NSWER 16c2
Answer: A
The ratio of efficiency of A is to C is 5:3.The ratio of no.of days taken by B is to C is 2:3.A takes 6 days less than C,when A and C completes the work individually.B and C left the work after 2 days.the no of days taken by A to finish the remaining work?  Choices
A) 4.5
B) 5
C) 6
D) 28/3
E) 7

Solution: A : B : 6   Efficiency 10 : 9 : 6   No of days 9x : 10x : 15x   given=> 15x-9x = 6   hence, x 15 -9= 
15 -9 = 6
6   hence, x= 1   Number of days taken by A = 9 and daily work done=10   Number of days taken by B= 10 and daily work done=9 (total work =90)   Number of days taken by 6 = 15 and daily work done=6   work done by B and 6 in initial 2 days =30   rest work =60   Number of days required by A to finish = 60/10= 
60/10 = 6
6 days   ANSWER:6
Answer: C
The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
Choose the correct choice from the following
A) 11 : 9	B) 11 : 18	C) 21 : 19	D) 21 : 19	E) None

Solution: Sol.   Let the numbers be x and y.   Then, x+y / x -y = 40/4= 
40/4 = 10
10   ⇔ (x+y)= 10(x-y)   ⇔ 9x = 11y   ⇔ x/y = 11 / 9.   11 : 9nswer 11 : 9
Answer: A
If c is a positive integer, then 3^c + 3^(c +1) = Pick one:
A) 4^a  B) 3^a − 1  C) 3^(2a) + 1  D) 3^a*(a − 1)  E) 4(3^c)

Solution: 3^c + 3^(c +1)   = 3^c + (3^c * 3^1)   = 3^c (1 + 3)   = 3^c(4)   Ans. 4(3^c)) 4(3^c)
Answer: E
If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?	Choose one.
A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B) Ram = Rs.2500, Shyam = Rs.500, Mohan = Rs.250
C) Ram = Rs.1200, Shyam = Rs.1300, Mohan = Rs.750
D) Ram = Rs.1700, Shyam = Rs.1300, Mohan = Rs.750
E) Ram = Rs.1000, Shyam = Rs.1300, Mohan = Rs.750

Solution: 1/2:1/3:1/4   = 6:4:3   Ram = 6/13 * 3250= 
6/13 * 3250 = 1_500
1500   Shyam= 4/13 * 3250= 
4/13 * 3250 = 1_000
1000   Mohan= 3/13 * 3250= 
3/13 * 3250 = 750
750   Ram= Rs.1500, Shyam = Rs.1000, Mohan = Rs.750nswer:Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Answer: A
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is? Choose one
A) Rs.24028 B) Rs.24000 C) Rs.24003 D) Rs.24029 E) Rs.24029

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of Rs.24000 = 6/13 (52000) = Rs.24000   Answer: Rs.24000
Answer: B
Every student in a certain classroom was given one colored marble. 1/2 of the students were given a blue marble, 1/3 of the students were given a yellow marble, and all of the other students were given a red marble. After lunch, 1/3 of the students who had blue marbles and 1/4 of the students who had yellow marbles left the classroom; the other students did not leave. What fraction of all students have either a blue or yellow marble now?	Pick one.
A) 7/9 B) 6/7 C) 5/7 D) 4/7 E) 4/9

Solution: Lets pick smart numbers. Total number of students in the classroom: 12   Blue marble (1/2): 6   Yellow marble (1/3): 4   Red marble (1/6): 2   7/9fter lunch   Blue marble: 4   Yellow marble: 3   Red marble: 2   New Total number of students in the classroom: 9   Blue and Yellow marbles: 7   7/9nswer 7/9 or 7/9
Answer: A
Joe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum?	Choose the correct option:
A) 6%
B) 8%
C) 10%
D) 12%
E) 15%

Solution: In 5 years, the value grew $100, so the simple interest was $20 per year.   In 3 years, the total interest was 3*$20 = $60   The principal is $260 - $60 3* 20= 
3* 20 = 60
$60   The principal is $260 - $60 = 200.   The interest rate is $20/$200 260 -  60= 
260 -  60 = 200
200.   The interest rate is $20/$200= 10%   The answer is 10%.
Answer: C
The average salary of 15 people in the shipping department at a certain firm is $21,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees? Choose the correct choice from the following.
A) $19,250  B) $18,500  C) $21,000  D) $15,850  E) $12,300

Solution: total salary... 15*21k=315k   5 emp @ 25k =125k   4 emp @ 16k =64k   remaing 6 emp sal = 315k-125k-64k =126k   average315 -125 -64= 
315 -125 -64 = 126
126k   average=126k/6 = 21000   Ans: $21,000
Answer: C
How many multiples of 6 are less than 5000, and also multiples of 8?	Choices:
A) 104
B) 208
C) 625
D) 832
E) 833

Solution: LCM of 6 & 8 = 24   Tried dividing 5000 by 24   Got quotient 208.33'So 208 is answer
Answer: B
A train 500 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Select
A) 32  B) 28  C) 49  D) 64  E) 21

Solution: S = (500 + 300)/45 = 800/45 * 18/5= 
800/45 * 18/5 = 64
64   Answer: 64
Answer: D
There are different 20 circles. What is the number of the greatest possible points with which the circles intersect?
Choose the correct choice from the following choices:  A) 380  B) 200  C) 110  D) 180  E) 200

Solution: Maximum points of intersection between n different circles = n*(n - 1) = 20*19= 
20*19 = 380
380   380nswer: 380
Answer: A
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 193 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?	Choose the correct choice from the following answers:
A) 8,208	B) 9,409	C) 11,424	D) 12,586	E) can not be determined

Solution: Let the side for growing cabbages this year be X ft. Thus the area is X^2.   Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.   The area would have increased by 193 sq ft as each cabbage takes 1 sq ft space.   X^2 - Y^2 = 193   (X + Y)(X - Y) = 193   193 is a prime number and thus it will be (97+96)*(97-96).   Thus X = 97 and Y = 96   X^2 = 97^2 = 9409   The answer is 9,409.
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 answers.
A) 6.25	B) 6.5	C) 6.75	D) 7	E) 8

Solution: Solution   Required run rate	= 282 - (3.2 x 10) / 40   = 250 / 40   = 6.25.   6.25nswer 6.25
Answer: A
There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?  Pick one:
A) 7! / 1! 2! 3!  B) 7!  C) 7! / 3  D) 7! / 3!  E) 7! / 4

Solution: Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,   Then, 7C1 x 6C2 x 4C4 = 7! / 1! 2! 3!   7! / 1! 2! 3!NSWER:7! / 1! 2! 3!
Answer: A
The principal that amounts to Rs. 3913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Select.
A) s. 3096  B) s. 4076  C) s. 4085  D) s. 4096  E) s. 5096

Solution: Principal = [4913 / (1 + 25/(4 * 100))3]   = 3913 * 16/17 * 16/17 * 16/17 = Rs. 3096.   s. 3096NSWER:s. 3096
Answer: A
During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 18% on this sale. What is the mark up percentage on each candy? Choose one:  A) 100%  B) 80%  C) 75%  D) 66+2/3%  E) 55%

Solution: Hi Akhil, I can share the way I solved it..   Let's say Marked price = M   So, there's a discount of 20% on M So, new S.P. = 80% of M   Now, the child convinces the owner to sell 20 candies for the price of 14 candies .   Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of  6/20 *100= 
 6/20 *100 = 30
30%   So, the latest S.P.= 70% of 80% of M = 0.7* 0.8 M   Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,   0.7 * 0.8 * M = 1.12 C.P   So, we get, M= 2 C.P.   i.e. Marked price was kept 100% above C.P.   66+2/3%
Answer: D
A bat is bought for Rs.440 and sold at a gain of 20% find its selling price	Choose the correct choice from the following.
A) s.430/-	B) s.480/-	C) s.400/-	D) s.528/-	E) s.600/-

Solution: 100 % ------> 440   120 % ------> 440*120/100   Selling price = Rs.528/-   s.528/-
Answer: D
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:	Choose the correct choice from the following.
A) 22  B) 23  C) 24  D) 26  E) 28

Solution: let hens be x and cows be y   now,   feet: x*2+y*4=140   heads: x*1+y*1=48   implies, 2x+4y=140 and x+y=48   solving these two equations, we get x=26 and y=22   Therefore, hens are 26.   ANSWER:26
Answer: D
One hour after Yolanda started walking from X to Y, a distance of 17 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
Choose the correct choice from the following options:  A) 24  B) 23  C) 22  D) 21  E) 8

Solution: When B started walking Y already has covered 3 miles out of 17, hence the distance at that time between them was   17-3= 
  17-3 = 14
14 miles.   Combined rate of B and Y was   3+4= 
  3+4 = 7
7 miles per hour, hence they would meet each other in  14/7= 
 14/7 = 2
2 hours. In 6 hours B walked  2*4= 
 2*4 = 8
8 miles.   Answer: 8.
Answer: E
Find the simple interest on Rs. 70,000 at 16 2/3% per year for 9 months.	Choose the correct choice.
A) 7500	B) 6500	C) 8750	D) 9500	E) None of them

Solution: P = Rs.70000,R = 50/3% p.a and T = 9/12 years = 3/4years.   Simple Interest = (P*R*T)/100 = Rs.(70,000*(50/3)*(3/4)*(1/100))= Rs.8750   Answer is 8750.
Answer: C
Each of the 26 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 11 students sign up for the poetry club, 17 students for the history club, and 15 students for the writing club. If 5 students sign up for exactly two clubs, how many students sign up for all three clubs?	Choose the correct option: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: The total number in the three clubs is 11+17+15= 
11+17+15 = 43
43.   All 26 students signed up for at least one club.   5 of those students signed up for exactly one more club.   43 - 31= 
43 - 31 = 12
12 so 6 students must have signed up for exactly three clubs.   The answer is 6.
Answer: E
7858,3929,163.70,20.46, ? Options:	A) 1.25	B) 2.69	C) 3.87	D) 2.04	E) 4.12

Solution: Explanation :   Terms are continuously divided by 2,4,6 ,8, and so on   7858   7858Ã· 2= 3929   3929 Ã· 4 =982.25   982.25 Ã· 6 = 163.70   163.70 Ã· 8= 20.46   20.46Ã·10=2.04   Answer : Option 2.04
Answer: D
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1280. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ? Options
A) 2480 B) 3490 C) 6785 D) 8255 E) 9255

Solution: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:   16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2   Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.   = (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)   Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:   2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15= 
15*2*8*15 = 3_600
3600   So the sum must be  3375 + 1240 + 3600= 
 3375 + 1240 + 3600 = 8_215
8215   Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of   30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)   then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)   and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have   = 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)   In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals     15*15*62/2= 
  15*15*62/2 = 6_975
6975   and adding back the 1280, we get the answer of 8255.(ANS 8255)
Answer: D
John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?	Answers.
A) 6 days	B) 8 days	C) 10 days	D) 12 days	E) 14 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 = 10 × 40/50 = 8 days   8 days)
Answer: B
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?  Choose the correct choice from the following options: A) 17 B) 19 C) 18 D) 14 E) 11

Solution: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer: 14
Answer: D
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 16 hours respectively. The ratio of their speeds is? Choose the correct choice from the following answers:
A) 4:5
B) 4:3
C) 4:4
D) 4:9
E) 4:2

Solution: Let us name the trains A and B.   Then, (4:5's speed) : (B's speed)   = √b : √a = √16 : √25 = 4:5   4:5nswer:4:5
Answer: A
How many three-digit integers between 311 and 401, exclusive, are divisible by 3 when the tens digit and the hundered digit are switched?
Choose the correct choice from the following choices:	A) 30	B) 19	C) 22	D) 3	E) 90

Solution: Answer is 30   No of digits between 311 and 401 (exclusive) = 401-311-1= 
401-311-1 = 89
89   No Intergers divisble by 3=~ 89/3 ~ 30   Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.   e.g 372 is divisble by 3 (becae 3+7+2= 
3+7+2 = 12
12 (divisble by 3))   switch digits 732 also divisble by 3 (becae 7+3+2= 
7+3+2 = 12
12 (divisble by 3))   Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.   You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1=30.   30nswer : 30
Answer: A
Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
Choose the correct choice from the following answers
A) 29	B) 30	C) 20	D) 50	E) 55

Solution: Explanation :   Here, Large, Medium and Small ships are denoted by the symbol L, M and S.   Now, according to the question,   4L = 7S. ------(i)   3M = 2L + S. ------(ii)   Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-   7: 6 : 4.   Let, the number of journeys required be x. Since, quantity of water remains the same, so :-   =((15×7+7×6+14×4)36) = x (12×7+14×6+21×4).   =>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x   =>x=7308/252   =>x=29.   29nswer : 29
Answer: A
The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is?	Select:
A) 187 B) 169 C) 152 D) 178 E) 175

Solution: 200*(80/100)*(95/100)= 
200*(80/100)*(95/100) = 152
152   Answer:152
Answer: C
Bhavan travelled for 20 hours. He covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Bhavan?
Choose the correct choice from the following answers:
A) 888.89
B) 788.89
C) 899.89
D) 688.89
E) 899.99

Solution: Let the distance travelled be x km.   Total time = (x/2)/50 + (x/2)/40= 20 => x/100 + x/80 = 20 => (4x + 5x)/400 = 20   => x = 888.89 km   888.89nswer:888.89
Answer: A
Mary purchased Brand X pens for $2 apiece and brand Y for $1 apiece. If Elena purchased a total of 12 of these pens for $20.00, how many brand X pens did she purchase?
Choose the correct choice from the following
A) 8  B) 9  C) 5  D) 4  E) 6

Solution: 2x+y=20 -only one positive integers solutions x=8 and y=4   8nswer is 8
Answer: A
Of the families in City X in 1994, 35 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 20 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?	Choose the correct choice from the following options
A) 50.12%
B) 40.52%
C) 40.56%
D) 40.38%
E) 40.14%

Solution: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40   Number of families owning computer in 1998 = 35 * 120/100= 
35 * 120/100 = 42
42   Number of families in 1998= 104   The percentage = 42/104 * 100 = 40.38%.   Option: 40.38%
Answer: D
A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange marbles, and 2 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen? Choose the most appropriate option: A) 1/60 B) 1/45 C) 2/45 D) 3/22 E) 6/22

Solution: I started by finding the 2 probabilities, without calculation, like this:   P(YYR)   P(YRY)   P(RYY)   I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.   This helped me realise that for the 6 possible orderings the probabbility is the same. So, it should be (1/22)*(6), which indeed is 6/22.   6/22
Answer: E
A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and
4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
Choose the correct choice from the following answers
A) 40 m	B) 10 m	C) 20 m	D) 30 m	E) 50 m

Solution: Let speed of the train be v kmph   (v-2) :(v-4) = 10:9   9 v -18=10 v-40   v=22   Length of the train=(22-2) x 5/18 x 9=50 metre   Answer: 50 m
Answer: E
In a room there are 12 people. Each person shook hands with every other person. How many hand shakes were there? Choose the correct choice.
A) 58  B) 60  C) 62  D) 64  E) 66

Solution: 12C2 = 66   The answer is 66.
Answer: E
six years ago, the ratio of the ages of kunal and sagar was 6:5. four years hence, the ratio of their ages will be 11:10. what is sagar's age at present?
Choose the correct option:  A) 18 years  B) 16 years  C) 22 years  D) 20 years  E) none of these

Solution: the age of kunal and sagar 6 years ago 6x and 5x respectively.   ((6x+6)+4)/((5x+6)+4)=11/10   10(6x+10)=11(5x+10)   5x=10. x=2, sagar's present age = (5x+6)=16 years   correct answer (16 years)
Answer: B
A’s speed is 20/14 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?  Choices
A) 1/17  B) 3/17  C) 1/10  D) 6/20  E) 3/10

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 20 meters, B covers 14 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 6 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 6 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 14 meters) to reach the finish line.   So B should get a head start of 6/20th of the race.   Answer (6/20)
Answer: D
A warehouse had a square floor with are 10,000 sq.metres. A rectangular addition was built along
one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many metres did the addition extend beyond the original building?  Choose the correct choice from the following.
A) 10  B) 20  C) 50  D) 200  E) 500

Solution: length=100,b=?   area of rectangle=l*b   original floor=10,000 sq.metres   increasing the original floor by half of the original floor=10000+1/2(10000)   =15000   so 15000-10000= 
15000-10000 = 5_000
5000(area of rectangular portion)   l*b=5000   l=100 so 100*b=5000 ->b=50   so extended part is of 50metres   ANSWER:50
Answer: C