MU-NLPC/Calc-aqua_rat huggingface dataset:
A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is?
Choose the correct choice from the following
A) 1250m  B) 1750m  C) 950m  D) 1000m  E) 1300m

Solution: Speed = 15*5/18 = 15/18 m/sec   Distance covered in 35 minutes = 15/18 *35 *60= 
15/18 *35 *60 = 1_750
1750 m   Answer is 1750m
Answer: B
A Refrigerator is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be Choose the correct choice from the following answers:  A) 18%  B) 19%  C) 21.2%  D) 21.81%  E) 22.07%

Solution: Simple interest SI = (P*R*T)/100   where P is the principal amount   R is the rate of interest   and T is time in years   the way I see it: For Refrigerator on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000   For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)   thus, SI = 2000 or   2000 = (P*R*T)/100   2000 = (22,000*R*5)/(100*12)   R = (2,000*12*100)/22,000*5   R = 21.81%   Therefore answer is 21.81%
Answer: D
A boat crossed a lake from East to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed?	Select.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: One way of solving this is:   Speed of boat on still water (lake)=5kmph   Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph   =>Speed downstream = speed in still water + speed of river = 5+1= 
5+1 = 6
6kmph   Ans is 6
Answer: C
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?	Choose the correct choice from the following options.
A) 2777
B) 2987
C) 1200
D) 9977
E) 1671

Solution: 1200P* (76/100) = 912   1200P1200 * (76/100)= 
1200 * (76/100) = 912
912   1200P= 12 * 100= 
12 * 100 = 1_200
> 1200P= 1200   Answer: 1200
Answer: C
If |x^2 − 20| = x, which of the following could be the value of x?
Choose the correct choice from the following options
A) -5 B) -4 C) 1 D) 4 E) 10

Solution: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.   First, let's assume that x^2-20 is negative.   -(x^2 - 20) = x   x^2 + x - 20 = 0   (x+5)(x-4) = 0   x = 4 or x = -5 (However, x can not be negative.)   Then x = 4 is a possible value for x.   The answer is 4.
Answer: D
If a company allocates 25 percent of its budget to advertising, 30 percent to capital improvements, and 35 percent to salaries, what fraction of its budget remains for other allocations?
Choose the correct choice from the following:
A) 1/10	B) 1/5	C) 1/4	D) 1/3	E) 1/2

Solution: 100%-(25%+30%+35%)=10% remains for other allocations --> 10% 100 -(25 +30 +35 )= 
100 -(25 +30 +35 ) = 10
10% remains for other allocations --> 10% = 10/100   --  10= 
  --  10 = 10
10/100= 1/10.   1/10nswer: 1/10.
Answer: A
3 candidates in an election and received 1136, 5636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
Select the correct option.
A) 40%  B) 55%  C) 57%  D) 63.2%  E) 62%

Solution: Total number of votes polled = (1136 + 5636 + 11628)= 
(1136 + 5636 + 11628) = 18_400
18400   So, Required percentage= 11628/18400 * 100 = 63.2%   63.2%
Answer: D
The difference between compound and d simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum? Answers
A) 28882	B) 27772	C) 23123	D) Rs.13500	E) 28811

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300 *6 2/3)]   P = 13500   Answer: Rs.13500
Answer: D
A vendor sold two things at same cost of 13 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much  Choose the correct option.
A) 0.65 loss B) 0.70 loss C) 0.80 loss D) 0.55 loss E) 0.40 loss

Solution: CP when profit of 25% = 10.4   CP when loss of 20% = 16.25   Total CP = 26.65   Total SP = 26.00   Total loss = 0.65   0.65 lossNSWER:0.65 loss
Answer: A
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 6 revolutions ? (use Ï€ = 22â„7)
Choose the correct choice from the following.
A) 40 m2  B) 44 m2  C) 52.8 m2  D) 36 m2  E) None of these

Solution: Required area covered in 5 revolutions   = 6 Ã— 2Ï€rh = 6 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 2 = 52.8 m2   Answer 52.8 m2
Answer: C
A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work?  Choose the most appropriate option:
A) 10  B) 12  C) 22  D) 28  E) 20

Solution: A can do the work in 60/4 i.e., 15 days.   A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12   So A and B together can do the work in 12 days.   Answer: 12
Answer: B
Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part? Select the correct option: A) 17 B) 21 C) 31 D) 45 E) 47

Solution: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation   larger number – smaller number = 7   which is equivalent to   Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.   31
Answer: C
The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices fo x%, then a while later he reduces all the new prices by x%. After one such up-down cycle the price of a painting decreased by $ 441. After a second up-down cycle the painting was sold for $ 1944.81. What was the original price of the painting in $?	Choose the correct choice from the following answers
A) 2756.25  B) 2256.25  C) 2500  D) 2000  E) 5000

Solution: firstly, i will eliminate E because it's too much..   the 1st time reduction is 441   but the price after 2 times reduction is 1944.81   So, we can cut D and B ..   now only 2756 and 2500 left   the final price is 1944.81..   C); 2500 - 1944 = ~550   B); 2756 - 1944 = ~800   because the first reduction is 441 so the 2nd reduction should be lower than 441   but in C ; 550-441 = ~110 .. its too much reduction in the 2nd round   so B; 800-441 = ~ 360 seems quite good..   ANSWER:2256.25
Answer: B
A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is (1/6) hectares. Find the length and breadth of the lawn.	Choices:
A) 50 B) 30 C) 20 D) 40 E) 10

Solution: Let length = 2x meters and breadth = 3x meter.   Now, area = (1/6 )x 1000 m2 = 5000/3m2   So, 2x * 3x = 5000/3 <=> x2 = 2500/9 <=> x = 50/3   therefore Length = 2x = (100/3) m = 33(1/3) m and Breadth = 3x = 3(50/3) m = 50m.   50nswer is 50
Answer: A
V is the volume of a cylinder; the radius of the cylinder is 2.4. The height of the cylinder is 550% more than the radius. Which of the following is true? Choose the most appropriate option
A) 100 < V < 300 B) 300 < V < 500 C) 500 < V < 700 D) 700 < V < 900 E) 900 < V < 1100

Solution: As we see the answers are in form of range we can use approximation   Volume of cylinder is πr^2h   Given π= 22/7 and r = 2.4 so r^2 ~ 6 and h = 6.5 * 2.4 ~ 16   So 22/7 * 6 * 16 ~ 302   so answer should be   B. 300 < V < 500   Answer : 300 < V < 500
Answer: B
An instrument manufactured by a company consists of two parts A and B. In manufacturing part A, 9 out of 100 are likely to be defective and in manufacturing part B, 5 out of 100 are likely to be defective. Calculate the probability that the instrument will not be defective.
Choose the correct choice from the following options:
A) 0.86.	B) 0.91	C) 0.95	D) 0.97	E) None of these

Solution: Explanation :   Let, A ≡ event that part A is non- defective.   B ≡ event that part B is non- defective.   A and B are independent events.   AB ≡ event that part A and part B both are non-defective so that instrument is not defective.   => P(AB) = P(A) x P(B).   => [ 1 - P(~A)] x [ 1 - P(~B)].   Here, P(~A)= 9/100 = probability of part A being defective   and, P(~B) = 5 / 100 = probability of part B being defective.   => P(AB) = [1- (9 / 100 ) ] x [1- (5 / 100)].   => 0.91 x 0.95.   => 0.86.   Hence, the required probability is 0.86.   0.86.nswer : 0.86.
Answer: A
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:	Options:
A) 2:3 B) 1:2 C) 4:5 D) 5:4 E) 3:2

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.4)   = k = 0.4/0.6 = 2/3   Required ratio = 2/3 : 1 = 2:3.   2:3NSWER 2:3
Answer: A
What is the sum of odd integers from 35 to 55, inclusive?
Choose the correct choice from the following options.
A) 495  B) 1,500  C) 1,240  D) 1,120  E) 1,100

Solution: Number of odd integers = (55-35)/2 + 1   = 20/2 + 1= 
20/2 + 1 = 11
11   Sum of odd integers= (35+55)/2 * 11= 
(35+55)/2 * 11 = 495
495   495nswer 495
Answer: A
In a sequence of 12 numbers, each term, except for the first one, is 12^15 less than the previous term. If the greatest term in the sequence is 12^16, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
Choose the correct choice from the following options:
A) −12^11  B) 0  C) 12^11  D) 11·12^11  E) 12^15

Solution: there are total 12 terms. andgreatestterm is 12^16. Each term is 12^15 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^11 less than previous one')   Therefore, 12^16 is the first term of the AP and -12^15 is the difference between successive terms, the smallest term should be the last one.   Last term = First term + (n-1)*d   therefore, Last term = 12^16+ 11*(-12^15)   => Last term = 12^16 - 11*12^15   => Last term = 12^15 (12-11) = 12^15   Which is the smallest term.   Hence Ans 12^15 it is.
Answer: E
The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?	Choose the correct choice:
A) 18 years B) 21 years C) 12 years D) 19 years E) 12

Solution: Sum of the ages of 14 students   = (16 * 35) - (14 * 21) = 560 - 294= 
560 - 294 = 266
266   Required average= (266/14)= 
(266/14) = 19
19 years.   Answer: 19 years
Answer: D
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? Choose the correct choice from the following answers:	A) 287m	B) 180m	C) 279m	D) 267m	E) 112m

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer:180m
Answer: B
The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 20, what is the age of the youngest sibling?  Choose the correct answer:
A) 14	B) 15	C) 16	D) 17	E) 18

Solution: x + (x+3) + (x+5) + (x+8) = 80   4x + 16 = 80   4x = 64   x = 16   The answer is 16.
Answer: C
Find the fourth proportional to 1.4,3.2 and 6.5?  Choices:
A) 13.19 B) 14.09 C) 14.86 D) 15.36 E) 15.19

Solution: Formula= Fourth proportional =(b x c)/a   a=1.4 , b=3.2 and c=6.5   (3.2 x 6.5)/1.4=14.86   14.86
Answer: C
What would be the perimeter of the square whose side is equal to the diameter of the circle whose perimeter is 52.5 cm?
Options
A) 52.5 B) 60.2 C) 66.8 D) 74.25 E) 80.12

Solution: Diameter of the circle= perimeter/Ï€ = 52.5x7/22 = 16.70   Perimeter of the square=16.70x4=66.8cm   Answer: 66.8
Answer: C
A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Pick: A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) None

Solution: CATEGORY   Formulae   Examples   DIRECTIONS : Problems based on Trains.   11.	A train 280 m long, running with a speed of 63 km/hr will pass a tree in   A. 15 sec.   B. 16 sec.   C. 18 sec.   D. 20 sec.   Solution   Speed	= (63 x 5/18) m/sec   = 35/2 msec   Time taken	= (280 x 2 /35)m/sec   = 16 sec.   12.	A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is ihe length of the train?   A. 120 metres   B. 180 metres   C. 324 metres   D. None of these   Solution   13.	A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?   A. 3.6 sec   B. 18 sec   C. 36 sec   D. 72 sec   Solution   Speed of train relative to jogger	= (45 - 9) km/hr   = 36 km/hr   = (36 x 5/18) m/sec   = 10 m/sec   Distance covered	= (240+120)= 
(240+120) = 360
360 m   Time taken= (360 / 10)= 
(360 / 10) = 36
36 sec.   Answer 36 sec
Answer: C
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A) 100
B) 110
C) 179
D) 209
E) 219

Solution: Explanation:   In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.   Hence we have 4 options as given below   We can select 4 boys ...(option 1)   Number of ways to this = 6C4   We can select 3 boys and 1 girl ...(option 2)   Number of ways to this = 6C3 × 4C1   We can select 2 boys and 2 girls ...(option 3)   Number of ways to this = 6C2 × 4C2   We can select 1 boy and 3 girls ...(option 4)   Number of ways to this = 6C1 × 4C3   Total number of ways   = 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3   = 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]   =   6   ×   5   2   ×   1   +   6   ×   5   ×   4   3   ×   2   ×   1   ×   4   =6×52×1+6×5×43×2×1×4   +   6   ×   5   2   ×   1   ×   4   ×   3   2   ×   1   +   6   ×   4   +6×52×1×4×32×1+6×4   =   15   +   80   +   90   +   24   =209   209)
Answer: D
A is twice as good a workman as B and they took 9 days together to do the work B alone can do it in.
Choose the correct choice from the following choices:  A) 17 days  B) 12 days  C) 29 days  D) 25 days  E) 27 days

Solution: WC = 2:1   2x + x = 1/9   x = 1/27 => 27 days   ANSW27 daysR:27 days
Answer: E
The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is	Select.
A) 91 B) 910 C) 61 D) 1911 E) None

Solution: olution   Required number of students.   = H.C.F of 671 and 610.   â€¹=â€º 61.   Answer 61
Answer: C
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.	Choose the correct answer
A) 3
B) 4
C) 5
D) 6
E) 87

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists.3nswer: 3
Answer: A
1,4,9,16,....	Choices
A) 58  B) 60  C) 61  D) 62  E) 25

Solution: 1*1= 
1*1 = 1
1   2*2= 
2*2 = 4
4   3*3= 
3*3 = 9
9   4*4= 
4*4 = 16
16   5*5= 
5*5 = 25
25   ANSW25R:25
Answer: E
What is the smallest integer E greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?  Choose the correct choice from the following answers:
A) 21	B) 41	C) E=121	D) 241	E) 481

Solution: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder E as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.E=121
Answer: C
In jar A there are 3 white balls and 2 green ones, in jar B there is one white ball and three green ones. A jar is randomly picked, what is the probability of picking up a white ball out of jar A?  Choose the correct choice from the following answers.
A) 2/5
B) 3/5.
C) 3/10
D) 3/4
E) 2/3

Solution: Prob of picking jar A = 1/2   Prob of picking a white ball from jar A = 3/5   Prob of picking up a white ball out of jar A = 1/2*3/5 = 3/10   Hence, answer will be 3/10.
Answer: C
A and B started a business jointly A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is Select
A) 23477	B) 28000	C) 28877	D) 1987	E) 1771

Solution: Explanation:   Suppose B invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.   So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.   B's profit : Total profit = 1 : 7.   Let the total profit be Rs. x Then, 1/7 = 4000/x or x = 28000.   Answer: 28000) 28000
Answer: B
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team. Options:
A) 20	B) 21	C) 22	D) 23	E) 25

Solution: Number of members in the team = 11   Let the average age of of the team = x   => (Sum of ages of all 11 members)/11=x   => Sum of the ages of all 11 members = 11x   Age of the captain = 26   Age of the wicket keeper = 26 + 3= 
26 + 3 = 29
29   Sum of the ages of 9 members of the team excluding captain and wicket keeper=11x−26−29=11x−55   Average age of 9 members of the team excluding captain and wicket keeper   =(11x−55)/9   Given that (11x−55)/9=(x−1)   ⇒11x−55=9(x−1)   ⇒11x−55=9x−9   ⇒2x=46   ⇒x=46/2= 
46/2 = 23
23 years   Answer is 23.
Answer: D
In a span of 24 hours, how many times would the two hands of a clock point exactly in opposite directions ? Choose the correct choice from the following answers:
A) 10  B) 11  C) 23  D) 22  E) 24

Solution: Explanation:   In every hour, the two hands (minute and hour) of the clock would be exactly opposite to each other once. But, from 5 o'clock to 6 o'clock and from 6 o'clock to 7 o'clock (a span of hours), they would be exactly opposite only once (at exact 6 o'clock).   Thus, during the span of 12 hours, the two hands would be exactly opposite 11 times. Hence, in the span of 24 hours they would be exactly opposite 22 times.   ANSWER 22
Answer: D
The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Choose the correct option:
A) 81 years
B) 21 years
C) 51 years
D) 31 years
E) 61 years

Solution: Age of the teacher   = (37 * 15 - 36 * 14)= 
(37 * 15 - 36 * 14) = 51
51 years.   Answer: 51 years
Answer: C
If -1 < h < 1, which of the following has the greatest value?  Pick one
A) a) 1-h  B) b) 1+h  C) c) 1+h^2  D) d) 1-1/h  E) e) 1-1/(h^2)

Solution: easiest way of solving this would be to substitute a value.   lets say h= - 1/2   a) 3/2   b) 1/2   c) 5/4   d) 3   e) - 3   the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.   Answer is c) 1+h^2.
Answer: C
The H.C.F. and L.C.M. of two numbers are 11 and 5040 respectively If one of the numbers is 144, find the other number Choose the correct answer:  A) 400  B) 256  C) 385  D) 420  E) None of these

Solution: Explanation:   Solve this question by using below formula.   Product of 2 numbers = product of their H385F and L385M   144 * x = 11 * 5040   x = (11*5040)/144= 
(11*5040)/144 = 385
385   Option 385
Answer: C
A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Answers
A) 17 cm2
B) 30 cm2
C) 18 cm2
D) 19 cm2
E) 15 cm2

Solution: The circumference of the circle is equal to the permeter of the rectangle.   Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5   => x = 1   Therefore l = 6 cm and b = 5 cm Area of the rectangle   = 6 * 5= 
6 * 5 = 30
30 cm2   Answer: 30 cm2
Answer: B
A candidate got 40% of the votes polled and he lost to his rival by 2000 votes. How many votes were cast?
Choose the correct answer.
A) 10000 B) 2028 C) 2775 D) 5496 E) 6851

Solution: 40%-----------L   60%-----------W   ------------------   20%----------2000   100%---------? => 10000   10000nswer:10000
Answer: A
Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?  Choose one:
A) Rs.16537.76	B) Rs.16537.98	C) Rs.16537.50	D) Rs.16537.56	E) Rs.16537.51

Solution: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year   Amount = [15000 * (1 + 5/100)2]   = (15000 * 21/20 * 21/20)   = Rs.16537.50   Answer: Rs.16537.50
Answer: C
A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?
Select
A) 3/5
B) 2/5
C) 4/25
D) 3/10
E) 15/23

Solution: Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50   Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50   Now comes the condition, hence apply conditional probability:   P(Red)/ P(Red + Black)   (15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23.   ANSW15/23R:15/23
Answer: E
How many seconds will a 900 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Choose the correct option.
A) 48  B) 36  C) 54  D) 11  E) 18

Solution: Explanation:   Here distance d = 900 mts   speed s = 63 - 3= 
63 - 3 = 60
60 kmph= 60 x 5/18 m/s   time t = = 54 sec.   Answer: 54
Answer: C
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 400 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Choose the correct choice from the following options
A) 240 B) 246 C) 252 D) 292 E) 298

Solution: Number of newborns that can die in first month = 1/10 * 400= 
1/10 * 400 = 40
40   Survived= 360   Number of newborns that can die in second month = 1/10 * 360= 
1/10 * 360 = 36
36   Survived= 324   Number of newborns that can die in third month = 1/10 * 324 = 32   Survived = 292   Answer:292
Answer: D
Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^5  Choose the correct choice from the following:
A) 26  B) 32  C) 25  D) 27  E) 29

Solution: (4)^11x (7)^5 x (11)^5   = (2 x 2)^11 x (7)^5 x (11)^5   = 2^11 x 2^11 x7^5x 11^5   = 2^22 x 7^5 x11^5   Total number of prime factors = (22 + 5 + 5)= 
(22 + 5 + 5) = 32
32.   Answer is 32.
Answer: B
Dawson completes a piece of work in 40 days, Rose completes the same work in 60 days. If both of them work together, then the number of days required to complete the work is?  Choose the correct choice from the following answers:  A) 18  B) 20  C) 21  D) 22  E) 24

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 = 40 × 60/100 = 24 days   Answer is 24
Answer: E
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1232?
Options
A) 1000
B) 2217
C) 1100
D) 2777
E) 2991

Solution: 1232 = P [1 + (5*12/5)/100]   P= 1100   Answer: 1100
Answer: C