MU-NLPC/Calc-aqua_rat huggingface dataset:
A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 10-sided polygon have?  Select the correct option:  A) 875  B) 35  C) 1425  D) 2025  E) 2500

Solution: There's a direct formula for this.   Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.   Here, n = 10.   Plugging it in, we get 35 diagonals!   Answer (35).
Answer: B
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres?	Choose the correct choice from the following answers
A) 20  B) 200  C) 300  D) 400  E) 100

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 9540   [4L - 40] = 9540 / 26.50= 
9540 / 26.50 = 360
360   4L= 400   L = 400/4= 
400/4 = 100
100 meters. Answer: 100
Answer: E
To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Choices
A) Combined, with a saving of 5 cents  B) Separately, with a saving of 5 cents  C) Combined, with a saving of 15 cents  D) Separately, with a saving of 10 cents  E) Combined, with a saving of 10 cents

Solution: 3 pounds = 1*20+2*5= 
1*20+2*5 = 30
30   5 pounds= 1*20+4*5= 
1*20+4*5 = 40
40   total= 70   8 pound = 1*20+7*5= 
1*20+7*5 = 55
55   dif. 15   Answer : Combined, with a saving of 15 cents
Answer: C
Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?	Pick one:
A) 15%
B) 25%
C) 35%
D) 45%
E) 55%

Solution: Let's TEST X = 4....   On Sunday, Daniel drove 64 miles at 4 miles/hour.   D = (R)(T)   64 = (4)(T)   64/4= 
64/4 = 16
16= T   It takes 16 hours to drive home   On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (32 miles) at  4/2= 
 4/2 = 2
2 miles/hour   D= (R)(T)   32 = (8)(T)   32/8= 
32/8 = 4
4= T   It takes 4 hours for the first part   D = (R)(T)   32 = (2)(T)   32/2= 
32/2 = 16
16= T   It takes 16 hours for the second part   Total time to drive home on Monday = 4+16= 
4+16 = 20
20 hours   We're asked by what percent 20 hours is greater than 16 hours.   20/16= 
20/16 = 5/4 = around 1.25
1.25, so it is 25% greater.   25%
Answer: B
Three fifth of the square of a certain number is 126.15. What is the number?  Answers
A) 210.25 B) 75.69 C) 14.5 D) 145 E) 150

Solution: Let the number be X   Given, 3/5 X^2 = 126.5   X^2 = 126.15 * 5/3   X^2 = 42.05 * 5= 
42.05 * 5 = 210.25
210.25   X= 14.5   Answer 14.5.
Answer: C
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what is the maximum possible sum of the length of x and the length of y? Choose the correct choice from the following
A) 16
B) 14
C) 18
D) 10
E) 20

Solution: we know that : x > 1, y > 1, and x + 3y < 980,   and it is given that length means no of factors.   for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.   hence, lets start with smallest no 2.   2^1 =2   2^2 =4   2^3=8   2^4=16   2^5=32   2^6=64   2^7=128   2^8=256   2^9=512   2^10 =1024 (it exceeds 1000, so, x can't be 2^10)   so, max value that X can take is 2^9 , for which has length of integer is 9.   now, since x =512 ,x+3y<980   so, 3y<468   ==> y<156   so, y can take any value which is less than 162. and to get the maximum no of factors of smallest integer, we can say y=2^7   for 2^7 has length of integer is 7.   SO, combined together : 9+7= 
9+7 = 16
16.   16
Answer: A
.3+33+333+33.3=?	Select.
A) 362.33 B) 399.6 C) 702.33 D) 702 E) None of them

Solution: .3   33   333   33.3   ----------   399.6   ----------   Answer is 399.6
Answer: B
Which of the following will divide evenly into 347,406,520?
Choose the correct choice:
A) 4	B) 11	C) 9	D) 3	E) 13

Solution: Rule:   4: Last two digits should be divisible by 4   the last two digits are 00, which are divisible by 4   4nswer: 4
Answer: A
Integers a, b, c and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad - bc is even? Choices
A) 3/8	B) 7/16	C) 1/2	D) 9/16	E) 5/8

Solution: First of all notice that half of the numbers from from 0 to 2007, inclusive are odd and half even.   Next, let's find the probability of ad - bc being odd and subtract it from 1.   The difference of two integers to be odd we should have either ODD-EVENOREVEN-ODD:   ODD-EVEN = ad - bc = odd*odd-even*evenorodd*odd-odd*evenorodd*odd-even*odd. Three cases. The probability of each is 1/2^4, so the probability of 3 cases is 3/2^4.   The same for EVEN-ODD: p=3/2^4.   P(even) = 1 - P(odd) = 1 - (3/2^4 + 3/2^4) = 10/16 = 5/8.   Answer: 5/8.
Answer: E
The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)? Answers:	A) 2	B) 12	C) 24	D) 144	E) 288

Solution: Given : GCD of (m and n) = 12 = 2^2*3   i.e. m and n are both multiples of 2^2*3   i.e. m^2 and n^2 will both be multiples of (2^2*3)^2 = 2^4*3^2   i.e. 2m^2 and 2n^2 will both be multiples of 2(2^2*3)^2 = 2^5*3^2 = 288   Answer: Option 288
Answer: E
Age of Raghav who is 30 years old is 3/5 times of Ram and Ram is older than Mohan by 35 years.If vijay's age is just between the age of Ramesh and and Mohan and Ramesh is 21 years old.What is age of vijay?  Answers
A) 20
B) 25
C) 18
D) 17
E) 16

Solution: Solution:   Raghav's age=3/5 Ram's age   =>30=3/5 Ram's age   =>Ram's age=30/3 * 5= 
30/3 * 5 = 50
50   Ram's age=Mohan's age +35   =>Mohan's age=Ram's age -35   =>Mohan's age=50-35   =>Mohan's age =15   Vijay's age=(Ramesh's age +Mohan's age)/2   =>Vijay's age=(21+15)/2   =>Vijay's age=18 years.   Answer 18
Answer: C
A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is	Choices
A) 110sq.m  B) 111.5aq.m  C) 112.5sq.m  D) 114sq.m  E) None of these

Solution: Explanation:   Distance covered in 9 seconds = (6×1000/3600)×9 = 15m   Diagonal of square field = 15m   Side of square =a then diagonal of that square= √2 a   Hence area of the square = a2= (152)/2 =112.5 sq.m   Answer: Option 112.5sq.m
Answer: C
A is half good a work man as B and together they finish a job in 26 days. In how many days working alone B finish the job?	Select.
A) 98 days  B) 21 days  C) 17 days  D) 39 days  E) 19 days

Solution: WC = 1:2   2x + x = 1/26 => x = 1/78   2x = 1/78 => 39 days   Answer:39 days
Answer: D
What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x	Select: A) 195 B) 276 C) 188 D) 166 E) 161

Solution: Explanation:   Given: 139.25 + 223.94 / 4.002 = x   195pproximate 139.25 as 140, 223.94 as 224, 4.002 as 4,   we get, x = 140 + 224 / 4 = 140 + 56= 
140 + 56 = 196
196=>195   195NSWER: 195
Answer: A
A and B can do a piece of work in 6 days, B and C in 7 days, C and A in 8 days. How long will C take to do it?	Options
A) 12.6 days  B) 14.4 days  C) 15.2 days  D) 16.8 days  E) 18.2 days

Solution: 2c = 1/7 + 1/8 – 1/6 = 20/168 = 10/84   c = 5/84 => 84/5= 
84/5 = 84/5 = around 16.8
16.8 days   The answer is 16.8 days.
Answer: D
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
Choose the correct choice.
A) 2/35	B) 2/3	C) 7/35	D) 1/7	E) 7/5

Solution: Let A be the event that Ram is selected and B is the event that Ravi is selected.   P(A) = 5/7   P(B) = 1/5   Let C be the event that both are selected.   P(C) = P(A) x P(B) as A and B are independent events:   = 5/7 x 1/5 = 1/7   ANSWER:1/7
Answer: D
If XY denotes X is raised to the power Y, Find the last two digits of 19413844+ 19714181  Choose the correct choice from the following choices.
A) 154
B) 677
C) 784
D) 148
E) 132

Solution: 1941^3844   unit digit= 1^4=1   10th digit=4*4= 
4*4 = 16
16=2 means last two digit =61   and 1971^4181   unit digit=1   10th digit=7*1= 
7*1 = 7
7 mean last two digit= 71   hence,   71+61= 
71+61 = 132
132
Answer: E
Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7000 less if they could find two more equal investors. How much is the total investment in the new business.  Pick.
A) a)	$ 64,000  B) b)	$ 54,000  C) c)	$ 21,000  D) d)	$ 52,500  E) e)	$3,600

Solution: Initially each invest in x. Hence total investment is 3x.   Total investment is also 5(x-7000).   3x = 5(x-7000)   x= 5*7000/2= 
5*7000/2 = 17_500
17500   3x= 52500 and the answer is d)	$ 52,500.
Answer: D
Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long W would it have taken for him to walk both ways.	Choose the correct choice from the following answers: A) 8 h 45 min B) 7 h 45 min C) 6 h 45 min D) 5 h 30 min E) None of these

Solution: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes   2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.   3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.   4.Walking to to a viewpoint+Walking back W=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.   8 h 45 minnswer: 8 h 45 min.
Answer: A
A and B can do a work in 12 days and 36 days respectively. If they work on alternate days beginning with B, in how many days will the work be completed?	Choose the correct choice from the following answers:
A) 11  B) 17  C) 10  D) 17  E) 18

Solution: The work done in the first two days = 1/12 + 1/36 = 1/9   so, 9 such two days are required to finish the work.   i.e., 18 days are required to finish the work.   Answer: 18
Answer: E
Can anyhow help me with an easy solution for this
3, 4, 81, 4, 5, 121, 6, 7, ?
Choose the correct choice from the following answers:	A) 144	B) 121	C) 256	D) 225	E) 376

Solution: 3, 4, 81, 4, 5, 121, 6, 7, ?     3+4= 
  3+4 = 7
7 and   7+2= 
  7+2 = 9
9 and 9^2=81   4+5= 
4+5 = 9
9 and   9+2= 
  9+2 = 11
11 and 11^2=121   6+7= 
6+7 = 13
13 and   13+2= 
  13+2 = 15
15 and 15^2=225   ANSWER:225
Answer: D
If the range E of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?  Choose the correct choice from the following answers:
A) 0  B) 2  C) 12  D) 13  E) 15

Solution: The range E of a set is the difference between the largest and smallest elements of a set.   Without x, the difference between the largest and smallest elements of a set is  14-3= 
 14-3 = 11
11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.   The the difference between the greatest possible value of x and least possible value of x is 15-2= 
15-2 = 13
13.   Answer: 13.
Answer: D
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 5 such machines to perform the same job?
Choose the correct choice from the following answers.
A) 2.25 hours
B) 8.75 hours
C) 12 hours
D) 14.25 hours
E) 9.6 hours

Solution: Let each machine do 1 unit of work for 1 hour   8 machines --> 8 units of work in 1 hour   For 6 hours = 8*6= 
8*6 = 48
48 Units of total work is done.   Now this 48 Units of total work must be done by 5 machines   5 units of work(5 machines) ---> 1 hour   for 48 Units of work   5*9.6 ---> 1*9.6 hours   9.6 hours 9.6 hours
Answer: E
The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ?	Options:
A) 165 B) 185 C) 153 D) 198 E) 199

Solution: 153   Answer is 153
Answer: C
Car R and Car Y traveled the same 80-mile route. If Car R took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car R, how many hours did it take Car Y to travel the route? Choose the correct answer:
A) 2/3  B) 1  C) 4/3  D) 8/5  E) 3

Solution: The speed of car R is (distance)/(time) = 80/2= 
80/2 = 40
40 miles per hour.   The speed of car Y= 3/2*40= 
3/2*40 = 60
60 miles per hour --> (time)= (distance)/(speed) = 80/60 = 4/3 hours.   Answer: C.   Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.   Answer: 4/3.
Answer: C
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:	Pick one:
A) 10	B) 6	C) 5	D) 4	E) None of these

Solution: Explanation:   Speed of the motor boat =15 km/hr   Let speed of the stream =v   Speed downstream =15+v km/hr   Speed upstream =15-v km/hr   Time taken downstream =30/15+v   Time taken upstream =30/15-v   Total time =30/15+v + 30/15-v   Given that total time is 4 hours 30 minutes   =4 1/2hour =9/2hour   ANSWER IS 5
Answer: C
Find the missing number in the series.
2 , 3 , 6 , 0 , 10, -3 , 14...
Choices:
A) -6	B) 8	C) 7	D) 67	E) 65

Solution: Explanation:   There are two series in the question   1.	-6dd 4 : 2+3 = 6, 6+4 = 10   2.	Subtract 3 : 3-3= 
3-3 = 0
0, 0-3 - -3   Thus, following the series:   -3-3= -6   -6NSWER: -6
Answer: A
Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0  Choose the correct answer:
A) If x>y B) If x>=y C) If x < y D) If x<=y E) x=y or relationship cannot be established

Solution: Solution:-   X=4,3   Y=-4,3   So, X>=Y   If x>=y
Answer: B
A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours?  Choose the correct choice from the following answers:
A) 125 miles
B) 225 miles
C) 455 miles
D) 425 miles
E) 525 miles

Solution: During each hour, the car travels 65 miles. For 7 hours it will travel   65 + 65 + 65 + 65 + 65+ 65 + 65 = 7 × 65 = 455 miles   correct answer is 455 miles) 455 miles
Answer: C
Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be	Choose the correct choice:  A) 9:10  B) 17:19  C) 23:27  D) 16:17  E) 15:23

Solution: Let x be the height of triangle A and y be the height of triangle of B.   since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2   Therefore, (x^2/y^2)=1536/1734   (x^2/y^2)=(16*16*6)/(17*17*7)   (x^2/y^2)=16^2/17^2   x/y=16/17   Ans=16:17
Answer: D
Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/3, 2/7 and 5/9, respectively, what is the probability that Kyle and Catherine, but not David will solve the problem? Select the correct option
A) 35/189 B) 33/129 C) 25/189 D) 24/113 E) 20/189

Solution: P(Kyle will solve)=1/3   P(David will not solve)= 1 - 2/7 = 5/7   P(25/189atherine will solve) = 5/9   P= (1/3)*(5/7)*(5/9) = 25/189   Answer:25/189
Answer: C
A and B invests Rs.5000 and Rs.6000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?  Choices: A) 2:3 B) 82:31 C) 32:45 D) 34:89 E) 35:21

Solution: 2:3 : B   (5000*4)+(2500*8) : (6000*6)+(4000*6)   40000 : 60000   2 : 3   2:3nswer:2:3
Answer: A
A car traveled from San Diego to San Francisco at an average speed of 63 miles per hour. If the journey back took twice as long, what was the average speed of the trip? Choose the most appropriate option:  A) 24.  B) 32.  C) 36.  D) 42.  E) 44.

Solution: Let the time taken be = x   One way distance = 63x   Total distance traveled = 2 * 63= 
2 * 63 = 126
126x   Total time taken= x + 2x = 3x   Average speed = 126x/3x = 42   Answer: 42.126 /3= 
126 /3 = 42
42   Answer: 42.
Answer: D
If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?	Choose the most appropriate option
A) Rs. (xd/y)
B) Rs. xd
C) Rs. (yd/x)
D) Rs. yd
E) None of these

Solution: Explanation :   cost of x metres of wire = Rs. d   cost of 1 metre of wire = Rs.(d/x)   cost of y metre of wire = Rs.(y × (d/x)) = Rs. (yd/x).. Answer : Option Rs. (yd/x)
Answer: C
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride?  Answers
A) 28	B) 30	C) 32	D) 34	E) 36

Solution: The cost of Annie's ride was 2.5+5+(0.25*14)= 
2.5+5+(0.25*14) = 11
$11   Let x be the distance of Mike's ride.   The cost of Mike's ride is 2.5+(0.25*x)= 11   0.25*x = 8.5   x = 34 miles   The answer is 34.
Answer: D
The rowing athletes in a rowing conference voted for coach of the year. Each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference. If each of the 36 coaches received exactly 5 votes (a 36 way tie), how many rowers voted for coach of the year?
Answers:
A) 60
B) 70
C) 75
D) 84
E) 90

Solution: There were 36*5= 
36*5 = 180
180 total votes made. If each voter picked 3 coaches, there were 180/3= 
180/3 = 60
60 voters. 60
Answer: A
A seller uses 900 gm in place of one kg to sell his goods. Find
his actual % profit or loss When he sells his articles at 5 % profit
on cost price ? Choose the most appropriate option
A) 15.5 %	B) 16.5 %	C) 16.67 %	D) 17 %	E) None of these

Solution: Explanation :   =[100-x]*z/y-100   =[100+5]1000/900-100=16.67 %   Answer : 16.67 %
Answer: C
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar? Choose the correct choice from the following choices:  A) Rs. 1(2/7)  B) Rs. 2(1/9)  C) Rs. 3(2/11)  D) Rs. 2(2/13)  E) Rs. 2(2/7)

Solution: Here r = 10 % ,x = 100 and A = 5 kg   Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)   Rs. 2(1/9)
Answer: B
By selling an shirt for $300, a shop keeper gains 20% . During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is: Answers.
A) 2	B) 14	C) 8%	D) 12	E) 10

Solution: C   8%   Marked price = $300   C.P. = 100/120 * 300= 
100/120 * 300 = 250
$250   Sale price= 90% of $300 = $270   Required gain % = 20/250 * 100= 
20/250 * 100 = 8
8%.
Answer: C
The probability that A will not tell truth is 75% and the probability that B will tell truth is 60%.what is the probability that an incident described by them is true?	Choose the correct choice from the following answers:
A) 10%	B) 12%	C) 15%	D) 17%	E) 19%

Solution: A truth....> 25%   B truth.....> 60%   a&b truth...> 0.25*0.6=0.15=15%   ANSWER:15%
Answer: C
A and B Started a business with Rs.15000 and 12000 respectively. After 6 months B puts Rs.1000 more in his capital while after 8 months A puts Rs.5000 more in his capital. If there is a profit of Rs.35,000 after one year then B will get  Choose the correct answer:
A) Rs.15,000
B) Rs.18,000
C) Rs.16,000
D) Rs.20,000
E) Rs.22,000

Solution: Ratio of Rs.15,000 and B   =15000*8+20,000*4 : 12000*6+1300*6   = 4 :3   Then B will get   = 3/7*35,000   =15,000   Rs.15,000NSWER:Rs.15,000
Answer: A
How long does a train 130 m long running at the speed of 65 km/hr takes to cross a bridge 150 m length?	Choose the correct choice from the following:  A) 15.7 sec  B) 15.1 sec  C) 15.5 sec  D) 17.1 sec  E) 16.7 sec

Solution: Speed = 65 * 5/18   = 18.1 m/sec   Total distance covered   = 130 + 150= 
130 + 150 = 280
280 m.   Required time= 280/18.1 '   = 15.5 sec.   Answer:15.5 sec
Answer: C
What is the next number in the sequence below? 1 4 9 16 25 36 49 64 81 100 121 __ ?  Choose the correct choice from the following choices:	A) 45	B) 64	C) 81	D) 136	E) 144

Solution: as the series of numbers are squares of numbers   1^2=1   2^2=4   3^2=9   and so on   therefore 12^2=144   ANSW144R:144
Answer: E
Find the value of 72519 x 9999 = m?	Options
A) 723437481	B) 725465481	C) 625117481	D) 725117481	E) 725118081

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
In how many ways can 4 rings be arranged in 5 finger (no finger has more than 1 ring)?	Choose the correct choice from the following answers: A) 5C4 B) 5P4 C) (5C4)4! D) B and C E) NONE OF THE ABOVE

Solution: No. of ways of selecting 4 fingers from 5(considering a non-mutant) = 5C4.   No. of ways of arranging the 4 rings= 4!   Answer: (5(5C4)4!4).4!   ANSWER:(5C4)4!
Answer: C
In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is?  Choose the correct option:
A) 35yrs B) 40yrs C) 50yrs D) 60yrs E) 70yrs

Solution: Let B's present age = x years   Then A's present age = x+10 years   x+10+20 = 2(x-20)   x + 30 = 2x - 40   x = 70years   Answer is 70yrs
Answer: E
In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 9 feet between each tree. How many trees can be planted if the road is 151 feet long?	Choose the correct choice from the following answers.
A) 8  B) 9  C) 10  D) 11  E) 16

Solution: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T   To maximize the number of trees, the number of 14 feet spaces between trees should be 1 less than total number of trees.   For example, If there are 3 trees, then there should be 2 spaces between them.   So the number of 9 feet spaces will be T-1. Then, the length of sidewalk required for 9 feet spaces will be 9*(T-1)   It is given that total lenght of sidewalk is 151 feet.   or 9(T-1)+T = 151   or 9T-9+T = 151   or 10T = 160   or T=16   Answer:- 16
Answer: E
If the number 517*326 is completely divisible by 7, then the smallest whole number in the place of * will be:	Pick.
A) 3 B) 1 C) 2 D) 4 E) 5

Solution: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 6) = (24 + x), which must be divisible by 7.   x = 4.   4
Answer: D
What approximate value should come in place of question mark (?) in the following equation?
of 857 of 14% – 5.6 × 12.128 = ?	Choose the most appropriate option:	A) 48	B) 36	C) 60	D) 52	E) 46

Solution: ? = 857 of 14% – 5.6 × 12.128   ≈ 857 of 14% – 5.6 × 12 ≈ 120 – 67 ≈ 52   Answer 52
Answer: D
How many numbers greater than 5000 can be formed with four of the digits 3, 4, 5, 6, 7 where no digit can be repeated.  Answers.
A) 62 B) 72 C) 82 D) 90 E) 95

Solution: 3*4*3*2= 
3*4*3*2 = 72
72   ANSWER:72
Answer: B
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 32 cm?
Choose the correct choice
A) 276 sq.cm B) 268 sq.cm C) 640 sq.cm D) 297 sq.cm E) 600 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 32= 
1/2 * 40 * 32 = 640
640 sq.cm.   Answer:640 sq.cm
Answer: C