MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 820 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?
Options
A) 510	B) 540	C) 480	D) 520	E) 589

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (820 + x)/60 = 65/3   x = 480 m.   Answer: Option 480
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?  Choose the correct choice from the following answers
A) 11	B) 90	C) 36	D) 99	E) 27

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (300 + 300)/12 => x = 25   Speed of each train = 25 m/sec.   = 25 * 18/5 =- 90 km/hr.   Answer: 90
Answer: B
Side of a square is 10 cm. after joining the mid point of all sides makes a another inner square and this process goes to infinite.Find the sum of perimeter of all squares. Select the correct option: A) 333 B) 278 C) 27 D) 8 E) 81

Solution: You can calculate the side of the small square in two ways. Take half of the side which is equal to 5 cm. Using Pythagorean theorem, x2=52+52x2=52+52 ⇒x2=50⇒x2=50 ⇒x=50−−√=52–√=102–√⇒x=50=52=102   In another way, we can equate the squares of the sides of the small square to square of the side which is equal to 10. ⇒x2+x2=102⇒x2+x2=102   ⇒2x2=100⇒2x2=100⇒x=50−−√=52–√=102–√⇒x=50=52=102   So if you observe carefully, the side of the small square is 12–√12 part of the side of the bigger square.   So the side of the square inside the small square = 102–√×12–√=102=5102×12=102=5 and so on...   So areas of the perimeters = 4(10+102–√+102+...)4(10+102+102+...)   = 40(1+12–√+12+...)40(1+12+12+...)   The terms in the bracket are in GP withe common ratio of 12–√12   So Sum of the perimeters = 40⎛⎝⎜11−12–√⎞⎠⎟40(11−12) = 40(2–√2–√−1)   Answer:278
Answer: B
If x = 55 + 2q and y = 4q + 41, then for what value of q, x is equal to y ?
Pick:	A) -14	B) 14	C) -7	D) 7	E) 0

Solution: Explanation:   x = y <=> 55 + 2q = 4q + 41 <=> 2q = 14 <=> q = 7.   Answer: 7
Answer: D
Which of the following numbers is a perfect square? Answers:
A) 1266
B) 1444
C) 2022
D) 4034
E) 8122

Solution: perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.   38*38= 
38*38 = 1_444
1444   ANSWER:1444
Answer: B
The area of a parallelogram is 72 cm^2 and its altitude is twice the corresponding base. What is the length of the base? Choose the correct choice from the following choices.
A) 1 cm	B) 3 cm	C) 6 cm	D) 4 cm	E) 2 cm

Solution: let base= x cm   height = 2x cm   area = x Ã— 2x=2x^2   area=x Ã— 2x=2x^2   Area is given as 72 cm^2   2x^2=72   x^2=36   x=6 cm   ANSWER:6 cm
Answer: C
If 2 dice as rolled, what is the probability of the total score being 2?  Choose the correct choice from the following choices
A) 1/12
B) 5/12
C) 2/3
D) 1/3
E) 1/6

Solution: Using the rules of probability, the likelihood of rolling a 2 would be 1/12, as the total score of rolling a 2 is 1 and 1. 1/12nswer: 1/12
Answer: A
Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam. Choose the most appropriate option.
A) 3082
B) 2887
C) 3087
D) 2887
E) 2812

Solution: Explanation:   Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11   Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400   Therefore Shyam's share = (441/841) * 5887= 
(441/841) * 5887 = 3_087
3087   Answer: 3087) 3087
Answer: C
If q and r are negative integers, which of the following statements must be true?
I. (-q)^r is positive.
II. (-q)^(-r) is positive.
III. q^(-r) is positive.	Answers.
A) None B) II only C) I and II D) I and III E) I, II and III

Solution: Let's q = -2 and r = -3   I. (-q)^r = (2)^(-3) = 1/(2^3) --> Positive   II. (-q)^(-r) is positive. = 2^3 --> Positive   III. q^(-r) is positive. = -2^3 --> Negative   Answer: I and II
Answer: C
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Choices
A) 1.7	B) 1.4	C) 1.2	D) 1.5	E) 1.1

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer: 1.5
Answer: D
The sum of three consecutive odd numbers is always divisible by:
I. 2 II. 3 III. 5 IV. 6 Choose the correct choice from the following:
A) Only I	B) Only II	C) Only I and II	D) Only II and IV	E) none of these

Solution: Let the three consecutive odd numbers be (2x+1), (2x+3) and (2x+5).   Their sum = (6x=9)= 3 (2x+3), which is always divisible by 3.   ANSWER:Only II
Answer: B
What is the positive difference between the sum of the squares of the first 7 positive integers and the sum of the prime numbers between the first square and fourth square? Choose the correct choice from the following choices:
A) 11	B) 52	C) 83	D) 94	E) 99

Solution: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.   the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +...+7^2 = 140   the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13= 
2+3+5+7+11+13 = 41
41.   So the difference between 41 and 140 is 99.   So the answer is (99).
Answer: E
Radha bought a watch for Rs. 144 and got a percentage of profit equal to the cost price of the watch. What is the cost price of the watch?	Choose one.
A) Rs. 72
B) Rs. 78
C) Rs. 80
D) Rs. 90
E) Rs. 92

Solution: SP=144   CP=x   profit %=x   C.P.= (100/(100+gain%))*S.P.   x=(100/100+x) *144   x^2+100x=14400   x^2+180x-80x-14400=0   (x+180) (x-80)=0   x=-180   x=80   ANSWER:Rs. 90
Answer: D
The average of first ten prime numbers which are odd is?  Pick: A) 15.9 B) 15.7 C) 15.1 D) 15.8 E) 15.3

Solution: Sum of first 10 prime no. which are odd = 158   Average   = 158/10= 
158/10 = 79/5 = around 15.8
15.8   Answer:15.8
Answer: D
In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by? Select the correct option:
A) 16
B) 8
C) 4
D) 1/8
E) 1/64

Solution: Say r=6 => V1 = 1/144   when r=3; V2 = 1/36   V2 = 36*V1.   Answer : 4
Answer: C
1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Choose the correct choice
A) 12.8  B) 12.6  C) 12.5  D) 12.2  E) 12.1

Solution: 1000*15 = 1200*x   x = 12.5.Answer: 12.5
Answer: C
The value of x is to be randomly selected from the integers from 1 to 9, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?	Choose the correct choice from the following options:  A) 1/9  B) 2/9  C) 1/3  D) 4/9  E) 1/2

Solution: y will only be negative for x=2.   (We can check the values from 1 to 9 to be certain.)   P(y is negative) = 1/9   The answer is 1/9.
Answer: A
Mangala completes a piece of work in 15 days, Raju completes the same work in 35 days. If both of them work together, then the number of days required to complete the work is	Options:
A) 6 days
B) 10 1/2 days
C) 8 1/2 days
D) 9 days
E) 11 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 = 15 Ã— 35/50 = 10 1/2 days.   10 1/2 days
Answer: B
476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:
Select:
A) 8 and 8 B) 8 and 5 C) 8 and 7 D) 7 and 5 E) 8 and 3

Solution: Explanation:   Let the number be 476ab0   476ab0 is divisible by 3   => 4 + 7 + 6 + a + b + 0 is divisible by 3   => 17 + a + b is divisible by 3 ------------------------(i)   476ab0 is divisible by 11   [(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11   => [3 + (b - a)] is 0 or divisible by 11 --------------(ii)   Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.   if a=6 and b=2,   17 + a + b = 17 + 6 + 2= 
17 + 6 + 2 = 25
25 which is not divisible by 3 --- 7 and 5oes not meet equation(i).Hence this is not the answer   if a=8 and b=2,   17 + a + b = 17 + 8 + 2= 
17 + 8 + 2 = 27
27 which is divisible by 3 --- Meet equation(i)   [3 + (b - a)]= [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---7 and 5oes not meet equation(ii).Hence this is not the answer   if a=6 and b=5,   17 + a + b = 17 + 6 + 5= 
17 + 6 + 5 = 28
28 which is not divisible by 3 --- 7 and 5oes not meet equation (i) .Hence this is not the answer   if a=8 and b=5,   17 + a + b = 17 + 8 + 5= 
17 + 8 + 5 = 30
30 which is divisible by 3 --- Meet equation 1   [3 + (b - a)]= [3 + (5 - 8)= 
3 + (5 - 8) = 0
0 ---Meet equation 2   Since these values satisfies both equation 1 and equation 2, this is the answer   Answer: 7 and 5) 8 and 5
Answer: D
Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission for each sale made. If each of her sales is for $2,000, what is the least number of sales she must make per year if she is not to lose money because of the job change?
Pick.
A) 57  B) 133  C) 178  D) 377  E) 378

Solution: Lets say she sales x items so her commission will be : x * 2000*15/100 = 300x   Salary difference is:   85000 - 45000= 
  85000 - 45000 = 40_000
40000   So commission must at least be equal to salary difference i.e. x= 40000/300= 133 (Approx).   Hence answer is 133
Answer: B
A train 80 m in length crosses a telegraph post in 6 seconds. The speed of the train is?  Select:  A) 16 kmph  B) 88 kmph  C) 54 kmph  D) 48 kmph  E) 19 kmph

Solution: S = 80/6 * 18/5= 
80/6 * 18/5 = 48
48 kmph   Answer: 48 kmph
Answer: D
At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 14th highest price and the 21st lowest price among the prices of the items sold, how many items were sold at the garage sale?  Choose the correct choice from the following answers
A) 33  B) 34  C) 35  D) 36  E) 37

Solution: There were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio. Including the radio, there were 13 + 20 + 1= 
13 + 20 + 1 = 34
34 items sold.   The answer is 34.
Answer: B
Roger can read a book in k minutes. What part of the book can he read in 5 minutes? (k>8)  Choices.
A) 8+k  B) 8/k  C) k/8  D) (k+ 8)/k  E) (k-8) / k

Solution: Let's sayk = 24   That is, it takes 24 minutes to read the entire book.   So, in 8 minutes, Roger can read1/3of the book   So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24   A) 8+24=32(k-8) / kLIMINAT(k-8) / k   B) 8/24=1/3K(k-8) / k(k-8) / kP   C)24/8 =3(k-8) / kLIMINAT(k-8) / k   D) (24+ 8)/24=32/24 = 4/3(k-8) / kLIMINAT(k-8) / k   (k-8) / k) (24-8) /24=16/24 = 2/3(k-8) / kLIMINAT(k-8) / k   Answer: (k-8) / k
Answer: E
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?	Select
A) 399 km B) 162 km C) 277 km D) 887 km E) 668 km

Solution: 12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.Answer: 162 km
Answer: B
Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 10:00 am and Pipe B at 11:00 am, at what time will the pool be full?  Choose the correct choice from the following answers
A) 22:00 B) 20:00 C) 21:00 D) 18:00 E) 17:00

Solution: Pipe A fills the pool in 4 hrs.   1 hour's work : 1/4   Pipe B empties the pool in 6 hrs.   1 hour's work : 1/6   Together if they work, 1 hour's work = 1/4 -1/6 = 1/12   Given : Pipe A started at 10:00 a.m and Pipe 20:00 at 11:00 a.m   Pool filled after 1 hour by Pipe A : 1/4 or 3/12   After 11:00 a.m   Pool filled after 1 hour with both the pipes on : 1/12   Pool filled after 9 hours with both pipes on : 9/12   Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12= 
3/12 +9/12 = 1
1   Therefore, it takes 10 hrs to fill the pool   As Pipe A started at 10:00 a.m, pool is full at 20:00 hrs   Answer : 20:00
Answer: B
Tarun got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price he bought. What was the labelled price ?
Choose the correct answer
A) 10000	B) 22438	C) 28789	D) 10002	E) 27910

Solution: Explanation:   Cost Price = = Rs. 7000. Let the labelled price be Rs. x.   Then,   = Rs.10000   10000nswer: 10000) 10000
Answer: A
A basketball player succeeds with 50% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?  Choose the most appropriate option.
A) 0.585	B) 0.625	C) 0.75	D) 0.875	E) 0.925

Solution: P(missing all 3 free throws) = 0.5^3 = 0.125   P(succeeding at least once) = 1 - 0.125= 
1 - 0.125 = 0.875
0.875   The answer is 0.875.
Answer: D
Commodious means ‘spacious’, large, voluminous and extensive.  Choices.
A) 22	B) 28	C) 277	D) 199	E) 11

Solution: 22nswer:22
Answer: A
John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4070. What is the difference between Rose ’s and Tom ’s share in the profit?	Choose the correct choice.
A) s.340  B) s.362  C) s.370  D) s.382  E) s.390

Solution: John : Rose : Tom   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rose’s and Tom’s share = 1 share   :.i.e. = Rs. 4070 × 1/11 = Rs.370.   s.370)
Answer: C
How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.  Choose the correct option:
A) 2000
B) 5000
C) 7000
D) 4000
E) 8000

Solution: (600×400×200)/(40×30×10) = 4000   Answer is 4000
Answer: D
One copy machine can make 30 copies a minute, and a second copy machine makes 15 copies a minute. If the two copiers work together, how long would it take them to make 900 copies? Choose the correct choice from the following options
A) 15 minutes B) 20 minutes C) 25 minutes D) 30 minutes E) 35 minutes

Solution: Total work done by both machines in a minute = 30 + 15= 
30 + 15 = 45
45 copies   Total number of copies required= 900   Time = 900/45= 
900/45 = 20
20 mins   Answer 20 minutes
Answer: B
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 41 kmph. For how many minutes does the bus stop per hour?	Choose the most appropriate option:  A) 7 min  B) 8 min  C) 14.4 min  D) 10 min  E) 11 min

Solution: Due to stoppages, it covers 13 km less.   Time taken to cover 13 km =(13/54)x60 = 14.4 min   answer : 14.4 min
Answer: C
50 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. Choose the correct choice from the following:
A) 190	B) 200	C) 1225	D) 220	E) 230

Solution: total no. of handshakes = 49+48+47+...+3+2+1 = 19*(19+1)/2 = 1225   or, if there are n persons then no. of shakehands = n12252 = 5012252 = 1225   Answer : 1225
Answer: C
385, 462, 572, 396, 421, 671, 264	Pick one.
A) 385 B) 421 C) 671 D) 264 E) None of these

Solution: Solution   In each number except 421,the middle digit is the sum of the other two. Answer 421
Answer: B
An express traveled at an average speed of 120 km/hr, stopping for 4 min after every 85 kn. How long did it take to reach its destination 8400 km from the starting point?
Pick one:
A) 5 hrs 21 min
B) 4 hrs 21 min
C) 6 hrs 41 min
D) 7 hrs 32 min
E) 4 hrs 34 min

Solution: D   7 hrs 32 min   Time taken to cover 840 km = 840/120= 
840/120 = 7
7 hrs.   Number of stoppages= 840/85 - 1 = 8   Total time of stoppages = 4 * 8= 
4 * 8 = 32
32 min   Hence, total time taken= 7 hrs 32 min.
Answer: D
There are three leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ? Choose the correct option:  A) 7 leopard and 3 sheep  B) 4 leopard and 7 sheep  C) 6 leopard and 4 sheep  D) 5 leopard and 1 sheep  E) 2 leopard and 1 sheep

Solution: 2 leopard and 1 sheep   2 leopard and 1 sheep   since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: E
Find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm?
Select the correct option
A) 100 cm2
B) 150 cm2
C) 200 cm2
D) 250 cm2
E) 500 cm2

Solution: 1/2 * 50(15 + 5)   = 500 cm2   Answer: 500 cm2
Answer: E
If (a-4)(b-2) =0, which of the following must be true ?
I. a=4 and b=2
II. if a is not = 4, then b=2
III. if a=4, then b is not=2
Choose the correct choice:
A) I only
B) II only
C) III only
D) I and II
E) II and III

Solution: (a-4)(b-2)=0   So either a=4 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.   The answer is II only.
Answer: B
A clock shows the time as 10 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?  Choose one:	A) 45 minutes	B) 55 minutes	C) 35 minutes	D) 25 minutes	E) 40 minutes

Solution: there are 8 hours in between 10 a.m. to 6 p.m.   8*5= 
8*5 = 40
40 minutes.   ANSW40 minutesR:40 minutes
Answer: E
Working alone, machine X can manufacture 1,200 nails in 12 hours. Working together, machines X and Y can manufacture 1,200 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?  Choose the correct option
A) 3 9/17
B) 5 1/3
C) 7
D) 7 1/7
E) 8 4/7

Solution: rate of machine x = 1200/12   (1200/12 + y)5=1200   y=700/5   700/5 * t = 1000   t=7 1/7   7 1/7.
Answer: D
A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 11 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
Choose the correct choice from the following:
A) $54.00
B) $64.80
C) $90.00
D) $100.80
E) $123.20

Solution: Correct Answer: E   The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.11 ($1120) 1720 -  600= 
1720 -  600 = 1_120
$1120. Thus, the amount of tax he has to pay is 0.11 ($1120)= $123.20. The correct answer is $123.20.
Answer: E
Each shelf of a bookcase contained 11 books. If the librarian took out 33 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 6 books, how many shelves does the bookcase have?
Select the correct option.
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Let x be the number of shelves.   11x - 33 = 7(x-1) + 6   4x = 32   x = 8   The answer is 8.
Answer: C
There are two numbers. If 70% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?  Choose the correct choice from the following choices:
A) 5/9
B) 5/7
C) 5/3
D) 5/8
E) 5/14

Solution: Let the two numbers be x and y.   70/100 * x + y = 5/4y   => 7/10 x = 1/4 y => x/y   = 5/14   Answer: 5/14
Answer: E
Find the one which does not belong to that group? Pick one
A) 16
B) 36
C) 21
D) 64
E) 4

Solution: Explanation:   16, 36, 64 and 4 are perfect squares but not 21.   Answer:21
Answer: C
How many kg of pure salt must be added to 30kg of 2% solution of salt and water to increase it to a 10% solution?
Select the correct option
A) 8/3	B) 9/7	C) 7/4	D) 5/2	E) 6/7

Solution: 8/3mount salt in 30kg solution = 2*30/100= 
2*30/100 = 3/5 = around 0.6
0.6 kg   Let x kg of pure salt be added   then(0.6+x)/(30+x)=10/100   60+100x=300+10x   90x = 240   x = 8/3   8/3nswer is 8/3
Answer: A
The dimensions of a field are 10 m by 10 m. A pit 10 m long, 5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
Answers.
A) 2 m	B) 3 m	C) 4 m	D) 5 m	E) 1.5 m

Solution: The volume of the earth removed is 10*5*4= 
10*5*4 = 200
200 m^3.   The remaining area of the field is   10*10 - 10*5= 
  10*10 - 10*5 = 50
50 m^2.   200 m^3 of the earth evenly spread over the area of 50 m^2 will rise the height by (height)= (volume)/(area) = 200/50= 
200/50 = 4
4 m.   Answer: 4 m
Answer: C
One half of the staffs in a software company are programmers,quarter are testers,one-fifth are administrative and the other 50 are HR. How many workers total are there in the software company?	Choose the most appropriate option:	A) 250	B) 366	C) 400	D) 500	E) 1000

Solution: 1/2x + 1/4x +1/5x = 19/20x   Remaining 1/20 x= 50   x= 50*20= 
50*20 = 1_000
1000   1000 is the answer.
Answer: E
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 6000, the number of valid votes that the other candidate got, was: Select the correct option:	A) 2800	B) 2700	C) 2160	D) 2200	E) 2300

Solution: C   Number of valid votes = 80% of 6000 = 4800.   Valid votes polled by other candidate = 45% of 4800   = (45/100 x 4800) = 2160.
Answer: C
Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit	Pick.
A) Rs. 8510  B) Rs. 8620  C) Rs. 8730  D) Rs. 8820  E) None of these

Solution: Explanation:   =>(8000×(1+5/100)2)   =>8000×21/20×21/20   =>8820   Option Rs. 8820
Answer: D
The Speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, What time it would take to travel the same distance downstream?  Choose the correct choice from the following answers.
A) 26 minutes	B) 23 minutes	C) 15 minutes	D) 19 minutes	E) 28 minutes

Solution: Speed of boat in still water = 25 km/hr   Speed upstream = 10⁄1 = 10 km/hr   Speed of the stream = (25-10)= 
(25-10) = 15
15 km/hr   Speed downstream= (25+15)= 
(25+15) = 40
40 km/hr   Time taken to travel 10 km downstream= 10/40 hours=(10×60)/40= 15 minutes   Answer is 15 minutes
Answer: C
What is the smallest number which, when increased by 5, is divisible by 7, 8, and 24? Choices:	A) 148	B) 153	C) 158	D) 163	E) 168

Solution: LCM(7,8,24)=24x7=168   So the least divisible number is 168, and the number we are looking for is   168-5= 
  168-5 = 163
163.   The answer is 163.
Answer: D
Ravi and Kavi start a business by investing â‚¹ 5000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
Select:
A) 2 : 72
B) 5 : 72
C) 7 : 72
D) 1 : 72
E) 3 : 72

Solution: Ratio of profit = Ratio of investments   = 5000 : 72000 = 5 : 72   Answer : 5 : 72
Answer: B
The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?	Choose the correct answer:
A) 22 years B) 30 years C) 32 years D) 44 years E) None of these

Solution: The total age of 10 students with average 20 = 200   The total age of 12 students with average 22 = 264   The total age of 2 new students = 64   Their average =32   ANSWER:32 years
Answer: C
If x 2 – y 2 = 101, find the value of x 2 + y 2 ,
given that x and y are natural numbers.  Choose the most appropriate option.
A) 5100	B) 5101	C) 5102	D) 5103	E) 5104

Solution: x^2 – y^2 = 101   => (x+y)*(x-y) = 101*1   x+y = 101   x-y = 1   so, x = 51, y = 50   (x^2 + y^2) = 51^2 + 50^2 = 5101   ANSWER:5101
Answer: B
Virginia, Adrienne, and Dennis have taught history for a combined total of 93 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?  Choose one
A) 23 B) 32 C) 40 D) 41 E) 44

Solution: Let number of years taught by Virginia = V   number of years taught by Adrienne = A   number of years taught by Dennis = D   V+A+D = 96   V= A+9   =>A = V-9   V= D-9   => A = (D-9)-9 = D-18   D-9 + D-18 + D = 93   => 3D = 93 + 27= 
93 + 27 = 120
120=> D = 40   Answer 40
Answer: C