MU-NLPC/Calc-aqua_rat huggingface dataset:
Rs 70000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?	Choose one.
A) 30000	B) 40000	C) 50000	D) 60000	E) 70000

Solution: let first parrt is x and second part is y then x+y=70000----------eq1   total profit=profit on x +profit on y   8000=(x*10*1)/100 + (y*20*1)/100   80000=x+2y-----------------------------------eq2   80000=70000+y   so y=10000 then x =70000-10000= 
70000-10000 = 60_000
60000   first part=60000   ANSWER:60000
Answer: D
Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 1 hours?  Pick one
A) 1.6.	B) 3.6.	C) 4.2.	D) 5.5.	E) 6.4

Solution: W = 2 desks   T = 2.5 hrs   Rate of 2 carpenters = 2×R   Rate = work done/ time   2xR = 2/2.5   R = 1/2.5 = 2/5 (this is the rate of each carpenter)   Work done by 4 carpenters in 1 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 1 =1.6 desks   1.6. is the correct answer.
Answer: A
Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?  Choose the correct choice from the following options:	A) 14	B) 16	C) 18	D) 20	E) 22

Solution: Let the present ages of Anand and Bala be 'a' and 'b' respectively.   a - 10 = 1/3 (b - 10) --- (1)   b = a + 12   Substituting b = a + 12 in first equation,   a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2= 
+ 2 = 2
> 2a= 32 => a = 16.   ANSWER:16
Answer: B
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth? Choices:  A) 22  B) 77  C) 90  D) 77  E) 21

Solution: SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 15 = Rs. 90.   Answer: 90
Answer: C
If the day after tomorrow is three days before tuesday, do you know which day is today? Select:  A) sunday  B) monday  C) saturday  D) thursday  E) wednesday

Solution: Correct Answer : thursday   three days before tuesday is saturday, now saturday is day after tomorrow, so today is thursday
Answer: D
A and B are two positive number,if A is divisible by 2 but not by 5 and B is divisible by 5 but not by 2, what could be the value of A and B in the following:- [ the answer are given in the order (A,B) ]
Choices:
A) ( 10,10)
B) (8,10)
C) (10,8)
D) (8,15)
E) (15,8)

Solution: In option (A) , (B) and (C) since all are divisible by 2 and 5 so they are wrong.   In (D),   A=8 ; divisible by 2 but not by 5   B=15 ; divisible by 5 but not by 2.   option (E) is just the opposite of ((8,15))   answer: ((8,15)) ie (8,15)
Answer: D
Four of the five parts numbered a, b, c, d and e in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is your answer
Answers.
A) 10.36 + 69.802 + 24.938	B) 2207.1 ÷ 21	C) 16 2⁄3% of 630.6	D) 32.84375 × 3.2	E) 1⁄5 of 1⁄9 of 4729.4

Solution: The other parts are equal to 105.10.   Answer 1⁄5 of 1⁄9 of 4729.4
Answer: E
An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 300 km from the starting point ? Choose the correct choice from the following choices
A) 8 hrs 29 min
B) 6 hrs 28 min
C) 3 hrs 12 min
D) 6 hrs 28 min
E) 1 hrs 28 min

Solution: Explanation:   Time taken to cover 300 km = 300/100= 
300/100 = 3
3 hrs.   Number of stoppages= 300/75 - 1= 
300/75 - 1 = 3
3   Total time of stoppages= 4 x 3 = 12 min   Hence, total time taken = 3 hrs 12 min.   Answer: 3 hrs 12 min
Answer: C
The angle between the minute hand and the hour hand of a clock when the time is 11.30, is  Choose the correct option:
A) 35° B) 65° C) 45° D) 165° E) 95°

Solution: Angle between hands of a clock   When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(H−M/5)+M/2 degree   When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(M/5−H)−M/2 degree   Here H = 11, M = 30 and minute hand is behind the hour hand.   Hence the angle   =30(H−M/5)+M/2   =30(11−30/5)+30/2   =30(11−6)+15   =30×5+15 =165°   Answer is 165°.
Answer: D
Here is a question to keep you busy. Assume that you travel to your friend's place at 20 mph, then how fast you must make the return trip via the same route such that the average speed of your travel becomes 40 mph?  Options:
A) Possible  B) No Idea  C) All above 3  D) Impossible  E) None of above

Solution: D   Impossible   Let us first denote everything with variables.   d= distance to your friend's place   T = time taken to get there   t = time required to get back   R = Speed while returning back   d = 20T   T = d/20   d = Rt   t = d/R   We have made equations for T and t and now we can derive an equation for the round trip.   2d = 40(T + t)   2d = 40(d/20 + d/R)   2d = 40d(1/20 + 1/R)   1 = 20(R/20R + 20/20R)   20R = 20(R+20)   R = R + 20   Do you see the paradox here? You literally have to travel back at an infinite speed if you want to make the average speed of your trip 40 mph. The faster return speed will have lesser impact of the average speed but consider that the quicker your return trip is, the faster you will make it.   We are talking about travelling double the distance in the same time that was taken for one way trip. Thus, if you travel at infinite speed, you will be able to attain an average of 40 mph.
Answer: D
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 4 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
Select the correct option.
A) 1/7	B) 1/5	C) 1/4	D) 1/3	E) 1/2

Solution: Suppose the portion of her salary that she saved is X   and the remaining portion is Y   X+Y= total take home salary   given, 12X = 4Y   or 3X = Y   Total take-home salary= X+ 3X= 4X   hence, she saved 1/4-th portion of her take home salary   1/4
Answer: C
The average of runs of a batsman of seven innings was 38. How many runs must be made in his next innings so as to increase his average of runs by 3? Choices: A) 72 B) 54 C) 70 D) 62 E) None of these

Solution: Explanation :   Average after 8 innings = 41   Required number of runs = ( 41 8) - (38 7) =328 - 266= 
328 - 266 = 62
62   Answer : 62
Answer: D
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is	Answers
A) 3.34
B) 45
C) 44
D) 33
E) 77

Solution: 3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m   3.34nswer: Option 3.34
Answer: A
A train running at the speed of 300 km/hr crosses a pole in 33 seconds. What is the length of the train?
Pick.
A) 2750  B) 2850  C) 2950  D) 3050  E) 3150

Solution: Speed=(300 x(5/18)m/sec	=(250/3)m/sec.   Length of the train = (Speed x Time).   Length of the train =	((250/3)x 33)m = 2750 m   2750
Answer: A
Two pipes A and B can fill a tank in 6 and 12 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Choices
A) 4  B) 6  C) 8  D) 10  E) 12

Solution: Part filled by A in 1 min. = 1/6   Part filled by B in 1 min. = 1/12   part filled by (A + B) in 1 min. = 1/6 + 1/12 = 1/4.   Both the pipes can fill the tank in 4 minutes.   4nswer: 4
Answer: A
The sum of two numbers is 40 and their difference is 28. Find their product. Choose the correct answer
A) 104  B) 108  C) 114  D) 204  E) None

Solution: Sol.   Let the numbers be x and y.   Then, x + y = 40 and   x - y = 28   2x = 68 => x = 34   y = 6   xy = 34 * 6= 
34 * 6 = 204
204   Answer : 204
Answer: D
If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31  Answers:
A) 3 B) 6 C) 5 D) 8 E) 9

Solution: P ÷ 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 31= 19008 / 31 = 613, remainder = 5   5
Answer: C
An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to n√n. Which of the following integers is prime saturated?	Answers:  A) 6  B) 35  C) 46  D) 66  E) 75

Solution: According to the definition integer is said to be "prime-saturated" if the square of its largest prime is smaller than the integer itself.   Only E satisfies this: 75=3*5^2 --> the largest prime is 5 --> 5^2=25<75.   Answer: 75.
Answer: E
A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family? Choices:
A) 28 4⁄7 years  B) 31 5⁄7 years  C) 32 1⁄7 years  D) 27 1⁄2 years  E) None of these

Solution: Required average = (67×2+35×2+6×3/2+2+3)   = (134+70+18/7)=222/7   = 31 5⁄7 years   Answer 31 5⁄7 years
Answer: B
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	Choose the correct choice from the following answers:
A) 187
B) 278
C) 278
D) 400
E) 277

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   Answer:400
Answer: D
If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. b > a  Choose the correct choice from the following.
A) I only B) II only C) III only D) I and III E) I and II

Solution: a has to equal a squared, and that only works if a is 1. There are no positive integers less than 1, so I and III are correct.   Answer : I and III
Answer: D
In the x- y plane, there are 4 points (0,0), (0,4), (7,4), and (7,0). If these 4 points makes a rectangle, what is the probability that x+y<4?	Choose the correct choice from the following.
A) 2/3 B) 3/5 C) 2/7 D) 4/9 E) 7/10

Solution: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.   The points below the line y=-x+4 satisfy x+y<4.   The area of this triangle is (1/2)(4)(4)=8   The area of the rectangle is 28.   P(x+y<4) = 8/28 = 2/7   The answer is 2/7.
Answer: C
Which of the following must be an integer if the integer x is divisible by both 28 and 21?  Choose the correct choice from the following options.
A) x/252  B) x/84  C) x/126  D) x/108  E) x/81

Solution: the integer has to be multiple of LCM of 28 and 21, which is 84..   so x/84 will be an integer   ans x/84
Answer: B
If x is a positive number and 1/2 the square root of x is the cube root of x, then x =  Pick one:
A) 64 B) 32 C) 16 D) 4 E) 1

Solution: 1/2 the square root of x is cube root of x.   if x = 64..   then 1/2 the square root of x = 4 and cube of x is 64.   Option 64.
Answer: A
A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was :	Choose the correct choice from the following answers
A) 14
B) 36
C) 28
D) 29
E) 11

Solution: Explanation:   Let the son's present age be x years .Then, (38 - x) = x x= 19.   Son's age 5 years back = (19 - 5)= 
(19 - 5) = 14
14 years   14nswer: 14) 14
Answer: A
At what rate percent on simple interest will a sum of money double itself in 30 years?  Choose the correct answer
A) 3 1/3%  B) 3 1/6%  C) 3 1/5%  D) 3 5/3%  E) 7 1/3%

Solution: P = (P*30*R)/100   R = 3 1/3%   3 1/3%nswer: 3 1/3%
Answer: A
Davidson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded? Select the correct option:
A) 0.8
B) 0.7
C) 0.6
D) 0.5
E) 0.49

Solution: probability of adams approval = 0.7   baker approval =0.5   corfu approval=0.4   proabability of approval is must adam approval and atleast one approval   = adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+   adam approval*baker not approval*coffu approval( atleast one remaining approval   = 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4   =0.14+0.21+0.14= 
0.14+0.21+0.14 = 0.49
0.49   0.49
Answer: E
A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum? Choices.
A) 7000  B) 7029  C) 7290  D) 7010  E) 7102

Solution: Let the sum be Rs. x.   (x * 18 * 2)/100 - (x * 12 * 2)/100   = 840 => 36x/100 - 24x/100 =840   => 12x/100 = 840 => x   = 7000.   7000nswer:7000
Answer: A
Out of three consecutive odd numbers ten times the first number is equal to addition of thrice the third number and adding 8 to thrice the second . What is the first number?
Choose the most appropriate option
A) 5/6
B) 45/32
C) 14/3
D) 13/2
E) 15/8

Solution: 13/2escription :   => 10x=3(x+2)+8+3(x+4)   => 10x=6x+26   => 4x=26   X=26/4=13/2   Answer 13/2
Answer: D
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?  Options.
A) 9 km/hour
B) 10 km/hour
C) 11 km/hour
D) 12 km/hour
E) 13 km/hour

Solution: Explanation:   We need to calculate the distance, then we can calculate the time and finally our answer.   Lets solve this,   Let the distance travelled by x km   Time = Distance/Speed   x/10−x/15=2   [because, 2 pm - 12 noon = 2 hours]   3x−2x=60x=60.   Time=Distance/Speed   Time@10km/hr=60/10= 
60/10 = 6
6hours   So 2 P.M. - 6= 8 A.M   Robert starts at 8 A.M.   He have to reach at 1 P.M. i.e, in 5 hours   So, Speed = 60/5= 
60/5 = 12
12 km/hr   Option 12 km/hour
Answer: D
Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Choose the correct choice from the following choices:
A) Rs.635.50
B) Rs.613.50
C) Rs.675.50
D) Rs.653.50
E) Rs.673.50

Solution: 4000   200 ---- I   200   10 ---- II   ---------------   4410   2210   --------   2000   110 ---- III   110   5.50 ---- IV   -----------   2425.50   2210   -----------   4635.50   4000   ----------   635.50   Rs.635.50NSWER:Rs.635.50
Answer: A
A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 5, what is the value of x?	Choose the most appropriate option:
A) -4
B) -2
C) 2
D) 1 and -5
E) Cannot be determined.

Solution: A number x is multiplied with itself --> X^2   added to the product of 4 and x --> X^2+4X   If the result of these two operations is -4 --> X^2+4X=5   i.e X^2+4X-5=0 is the Quadratic equation which needs to be solved.   (X-1)(X+5) = 0   Hence X=1. C=-5   IMO 1 and -5
Answer: D
If v and k are integers whose product is 400, which of the following statements must be true?	Choose the correct option: A) n + k > 0 B) n is not equal to k. C) Either n or k is a multiple of 10. D) If n is even, then k is odd. E) If v is odd, then k is even.

Solution: If v and k are integers whose product is 400, which of the following statements must be true?   A.n + k > 0n and k should have the same sign, but that means that they can also both be negative   B.n is not equal to k.20 x 20 = 400[i]   C.Either n or k is a multiple of 10. [i]25 x 16 = 400   D.If n is even, then k is odd.k can also be even since even x even will be even   E. If v is odd, then k is even.k must be even since odd x even = even
Answer: E
In a school with 604 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is	Choose the correct option:
A) 150
B) 151
C) 250
D) 350
E) None

Solution: Sol.   Let the number of grils be x.   Then, number of boys = (600 - x).   Then, (11 3/4 × 604)   ⇔ 11x + 12(604 - x) ⇔ x = 7248 - 7097 ⇔ 151.   Answer 151
Answer: B
Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 5000 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : Select the correct option
A) 15%
B) 16%
C) 0.125%
D) 0.2083%
E) none

Solution: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/5000)x100 =9.6%in percentage terms.   But the question asks ratio between his total land to total cultivated land. Hence the answer is 9.6%x (100/60) = 16%   The correct answer is (16%).
Answer: B
The ratio of the volumes of two cubes is 2744 : 3375. What is the ratio of their total surface areas?	Choose the most appropriate option:
A) 71:76 B) 71:131 C) 71:145 D) 71:167 E) 71:113

Solution: Ratio of the sides   = ³√2744: ³√3375 = 14 : 15   Ratio of surface areas   = 142 : 152 = 71:76   71:76nswer:71:76
Answer: A
Two vessels A and B contain mixtures of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34 per cent of spirit. Find the percentage of spirit in A and B.
Choose the correct option:
A) 35, 25
B) 40, 20
C) 25, 35
D) 50, 50
E) none of these

Solution: Let X% be the percentage of spirit in A and Y% in B   3X/100 + 2Y/100 = 29% of (3 + 2)   3X/100 + 2Y/100 = 1.45   3X + 2Y = 145 ----------(i)   X/100 + 9Y/100 = (34/100) x 10   X + 9Y = 340 ----(ii)   Solving (i) and (ii) we get X = 25 and Y = 35   A contains 25% spirit and B contains 35% of spirit.   35, 25NSWER:35, 25
Answer: A
Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 10 as remainder
Choose the correct choice from the following options
A) 1235
B) 1456
C) 1567
D) 1636
E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 10   5x = 1355   x = 271   Large number = 271+1365= 
271+1365 = 1_636
1636   1636
Answer: D
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following choices:
A) 7 sec
B) 6 sec
C) 4 sec
D) 2 sec
E) 1 sec

Solution: Speed of train relative to man = (60 + 6) km/hr   = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer: 6 sec
Answer: B
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Select:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Area of the park = (60 x 40) m2 = 2400 m2.   Area of the lawn = 2109 m2.   Area of the crossroads = (2400 - 2109) m2 = 291 m2.   Let the width of the road be x metres. Then,   60x + 40x - x2 = 291   x2 - 100x + 291 = 0   (x - 97)(x - 3) = 0   x = 3.   3
Answer: A
Last year a certain bond price with a face value of 5000 yielded 5% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?	Choose the correct option:
A) 4063 B) 3846 C) 5351 D) 6000 E) 6154

Solution: Interest = 0.05*5000 = 0.065*selling price --> selling price = 0.05*5000/0.065 --> selling price = ~3,846   Answer: 3846.
Answer: B
In what time will two trains cross each other completely, which are running on the same parallel lines in opposite directions, each train running with a speed of 90 kmph being 160 m and 140 m in length respectively? Answers:
A) 5.6 sec  B) 6.2 sec  C) 6.0 sec  D) 7.2 sec  E) 6.8 sec

Solution: D = 160m + 140m = 300m * 1/1000 160  + 140= 
160  + 140 = 300
300m * 1/1000 = 0.3 kms   RS 300  * 1/1000= 
300  * 1/1000 = 3/10 = around 0.3
0.3 kms   RS= 90 + 90= 
90 + 90 = 180
180 kmph   T= (0.3/180) * 3600= 
(0.3/180) * 3600 = 6
6.0 sec   ANSWER:6.0 sec
Answer: C
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?	Choose one:
A) Rs.429  B) Rs.480  C) Rs.429  D) Rs.427  E) Rs.482

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 25% = 25% of 640 = Rs.160   SP = CP - Loss = 640 - 160 = Rs.480   Answer:Rs.480
Answer: B
The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 12 km/hr respectively. They will meet for the first time in?  Choose one.
A) 32min  B) 40min  C) 35min  D) 25min  E) 20min

Solution: Clearly, the two will meet when they are 1000 m apart   To be   20+12= 
  20+12 = 32
32 km apart, they take 1 hour   To be 1000 m apart, they take   32 * 1000/1000= 
  32 * 1000/1000 = 32
32 min.   32minnswer is 32min
Answer: A
Which one of the following can't be the square of natural number ?  Choose the correct choice from the following choices:	A) 30976	B) 75625	C) 28561	D) 143642	E) 235685

Solution: Answer: Option D   The square of a natural number nerver ends in 2.   143642 is not the square of natural number.
Answer: D
At a certain university, 68% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
Pick one:
A) 25  B) 37.5  C) 55  D) 62.5  E) 75

Solution: total women = 68%   total men = 40%   total tenured = 70% (both men and women)   therefore, women tenured + women professors + men tenured = 90%   men tenured = 22%   but question wants to know the percent of men that are tenured   22%/40% = 55%   55
Answer: C
The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 25%. By approximately what percent would the output now have to be decreased in order to restore the original output?
Select.
A) 20%  B) 24%  C) 30%  D) 27%  E) 79%

Solution: The original output increases by 10% and then 25%.   Total % change = a + b + ab/100   Total % change = 10 + 25 + 10*25/100= 
10 + 25 + 10*25/100 = 75/2 = around 37.5
37.5%   Now, you want to change it to 0, so,   0= 37.5 + x + 37.5x/100   x = -37.5(100)/137.5 = 27% approximately   Answer is 27%
Answer: D
7^9 - 7^2 is approximation of which of the following? Choose the correct answer:  A) 7^9  B) 9^8  C) 9^9  D) 9^11  E) 9^10

Solution: => Since 9^2 is a small number compared to 7^9, it can be disregarded. Thus, 7^9-7^2=7^9 is derived and the answer is 7^9.
Answer: A
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 42 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast? Choose the most appropriate option:
A) 10%
B) 12%
C) 14%
D) 17%
E) 20%

Solution: Let me try a simpler one.   Lets assume that candidate got 42% votes and total votes is 100.   Candidate won = 42   Remaining = 58   To get 50%, candidate requires 8 votes from 100 which is 8% and 8 votes from 58.   8/58 = .137 = 13.7%   Which is approx 14%. Hence the answer is 14%.
Answer: C