MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following must be non-negative? Options
A) (a-0.9)(a-1)	B) (a+1)(a-1)	C) (a+0.9)(a+1)	D) (a-0.9)(a-0.9)	E) a(a+1)

Solution: a^2+a   f'(a)=2a+1=0 => a=-1/2   f''(a) =2>0 => a= -1/2 is point of minima Putting this value in main equation we get -1/2 (-ve)   Option D   F(a)=(a - 0.9)^2   f'(a)= 2(a-0.9)=0 => a=0.9   f''(a)= 2>0 => a= 0.9 is point of minima. Putting in main equation we get 0 which is non negative.   Answer: (a-0.9)(a-0.9)
Answer: D
There are 10 baskets numbered from 1 to 10 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?  Select: A) 330 B) 390 C) 450 D) 510 E) 570

Solution: Each child takes a total of 1+2+3+4+5+6+7+8+9+10 = 10*11/2= 
10*11/2 = 55
55 apples.   The total number of apples taken by 10 children is  10*55= 
 10*55 = 550
550   The number of apples left in the end is  1000 - 550= 
 1000 - 550 = 450
450 apples.   The answer is 450.
Answer: C
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?	Choose the correct choice from the following options:
A) 9 kmph
B) 10 kmph
C) 12 kmph
D) 14 kmph
E) 16 kmph

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   12 kmph
Answer: C
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?	Choose the correct choice from the following choices
A) 10
B) 12
C) 8
D) 15
E) 16

Solution: Explanation :   Let the required hours needed be x   More pumps, less hours (Indirect proportion)   More Days, less hours (Indirect proportion)   ⇒3 × 2 × 8 = 4 × 1 × x   ⇒ 3 × 2 × 2 = x   ⇒ x = 12 . Answer : Option 12
Answer: B
If n > 0 , which of the following must be true?
I n^2 < 1
II	n - n^2 < 0
III	2n - 1 < 0
Choose the correct choice from the following.
A) I only
B) II only
C) III only
D) I and II only
E) none

Solution: I. False for all values of n except 1   When n = 1 ; n^2 = 1   II. True for all values of n except 1   When n = 1 ; n - n^2 = 1 - 1= 
1 - 1 = 0
>0   III	False for all values of n   Hence the correct answer will be (II only)
Answer: B
A certain junior class has 1000 students and a certain senior class has 900 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?	Choose the correct choice from the following:
A) 3/40000  B) 2/30000  C) 9/2000  D) 1/60  E) 1/15

Solution: Let's see   Pick 60/1000 first   Then we can only pick 1 other pair from the 800   So total will be 60 / 900 *1000   Simplify and you get 2/30000   Answer is 2/30000
Answer: B
What is the probability that Company E's advertisement will be one of the first two be shown during the first commercial break? Choose the correct choice from the following answers:
A) 1/ 225	B) 1 / 30	C) 1 /15	D) 2 / 15	E) 4 /15

Solution: E 1/15 + (14/15) * 1/14 = 2/15 2 / 15
Answer: D
Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?  Select:
A) 11%
B) 11 2/9%
C) 11 1/9%
D) 10%
E) 9%

Solution: 900 --- 100   100 --- ? => 11 1/9%   ANSWER:11 1/9%
Answer: C
What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, ?, 1 Choose the correct choice from the following answers
A) 1
B) 2
C) 5
D) 7
E) 9

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   2
Answer: B
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?  Choose the correct choice from the following choices:
A) 5 months  B) 6 months  C) 7 months  D) 8 months  E) 4 months

Solution: Bankers Discount, BD = Simple Interest on the face value of the bill for unexpired time.   True Discount, TD = Simple Interest on the present value for unexpired time.   Simple Interest on Rs. 1600 = True Discount on Rs.1680   => Rs. 1600 is the Present Worth (PW) of Rs. 1680   => Rs. 80 is the Simple Interest of Rs.1600 at 15%   ⇒80=(1600×T×15)/100   ⇒80=16×T×15   ⇒5=T×15   ⇒1=T×3   ⇒T=1/3 year   =12/3= 
12/3 = 4
4 months   ANSW4 monthsR:4 months
Answer: E
When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 8x is divided by 9?	Choose the correct answer.
A) 0	B) 1	C) 3	D) 4	E) 6

Solution: i tried plugging in numbers   x = 9q+5   x = 14   8x 9 +5= 
9 +5 = 14
14   8x= 112   8x/9= 9*12+4   remainder is 4.   Answer is 4.
Answer: D
In how many ways Chief Minister and Minister be elected from a team of 12 members?  Choose the correct choice from the following options:
A) 128
B) 131
C) 132
D) 143
E) 145

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
Pipe A can fill a tank in 10 hours. Due to a leak at the bottom, it takes 15 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?  Choose the correct choice from the following choices.
A) 76
B) 84
C) 56
D) 75
E) 30

Solution: Let the leak can empty the full tank in x hours 1/10 - 1/x = 1/15   => 1/x = 1/10 - 1/15 = (3 - 2)/30 = 1/30   => x = 30.   Answer: 30
Answer: E
If 4 men can reap 40 acres of land in 15 days, how many acres of land can 16 men reap in 30 days? Pick
A) 320	B) 240	C) 369	D) 489	E) 125

Solution: 4 men 40 acres 15 days   16 men ? 30 days   40 * 16/4 * 30/15   40 * 4 * 2   40 * 8= 
40 * 8 = 320
320   320nswer:320
Answer: A
Excluding stoppages, the speed of a bus is 48 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Answers.
A) 5	B) 4.15	C) 4.25	D) 5.5	E) None of these

Solution: Due to stoppages, it covers 314 km less.   Time taken to cover 3 km = ((3/48)Ã—60) =4.15 min.   Option(4.15) is correct
Answer: B
A retailer bought a machine at a wholesale price of $117 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?  Choose the most appropriate option
A) 81	B) 100	C) 120	D) 135	E) 159

Solution: My solution: Wholesale Price= 117   Retail Price, be = x   He provides 10 % discount on Retail price= x-10 x/100   This Retail price = 20 % profit on Wholesale price   x-10 x/100 = 117+ 1/5(117)   x=156;   ANSW159R:159
Answer: E
Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 10% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
Select.
A) $15,840	B) $17,820	C) $18,000	D) $19,800	E) $18,810

Solution: 10000 seats --> Full Price : Half Price = 9000 : 1000   Price when all seats are filled = 18000 + 1000= 
18000 + 1000 = 19_000
19000   100 seats are unsold --> Loss due to unfilled seats= 10 + 2*90= 
10 + 2*90 = 190
190   Revenue= 19000 - 190= 
19000 - 190 = 18_810
18810   Answer: $18,810
Answer: E
The denominator of a fraction is 15 greater than the numerator. If the numerator and the denominator are increased by 3, the resulting fraction is equal to 3â„4. What is the value of the original fraction?	Select
A) 23/38  B) 29/44  C) 33/48  D) 38/53  E) 42/57

Solution: Let the numerator be x.   Then the denominator is x+15.   x+3 / x+18 = 3/4.   4x+12=3x+54.   x=42.   The original fraction is 42/57.   The answer is 42/57.
Answer: E
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Choose one.
A) 12
B) 42
C) 62
D) 20
E) 87

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20
Answer: D
The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
Choose the correct choice from the following answers:
A) 45 kg	B) 50 kg	C) 53 kg	D) 55 kg	E) None

Solution: Solution   Weight of the teacher	= (35.4 x 25 - 35 24)kg   = 45 kg   45 kgnswer 45 kg
Answer: A
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1700. The difference between the profit shares of A and C is?	Answers:
A) 288
B) 266
C) 155
D) 680
E) 441

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1700   => 5 parts out of 15 parts is Rs. 1700   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1700) = Rs. 680   Answer:680
Answer: D
A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is	Select:
A) 7000 B) 8000 C) 9000 D) 10000 E) None of these

Solution: Explanation :   Ratio in which profit is divided = 2:3   Assume that B's contribution to the capital = b   => 3500*12 : b*7 = 2:3   => 3500*12/7b = 2/3   => b = (3500*12*3)/(2*7) = 500*6*3= 
500*6*3 = 9_000
9000. Answer : Option 9000
Answer: C
How much is 80% of 40 is greater than 4/5 of 15? Pick.
A) 12 B) 20 C) 18 D) 12 E) 81

Solution: (80/100) * 40 â€“ (4/5) * 15   32 - 12= 
32 - 12 = 20
20   Answer:20
Answer: B
On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 3? Options.
A) 1/8. B) 1/2. C) 1/5. D) 3/8. E) 1/3.

Solution: Assume the coin is unbiased.   Possible sums from 3 tosses = 0,1,2,3   O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)   1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or   similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)   So answer will be 1/8. Option 1/8..
Answer: A
An inspector rejects 0.06% of the meters as defective. How many will he examine to reject 2? Choose the correct choice from the following answers
A) A)1500  B) B)2000  C) C)2500  D) D)3000  E) E)3333

Solution: Let the number of meters to be examined be x   Then, 0.06% of x = 2   (6/100)*((1/100)*x = 2   x = 3333   Answer is 3333
Answer: E
A boat running upstream takes 640 min to cover a certain distance, while it takes 280 min to cover the same distance running down stream. What is the ratio between the speed of the boat and speed of water current respectively?  Choose one.
A) 23: 7 B) 22: 9 C) 23: 8 D) 23: 9 E) 23: 11

Solution: Let the speed of the boat=x and speed of the current=y   Relative speed in upstream=x-y and in downstream=x+y   Let the distance 'd' is to be covered in downstream and upstream, then   Time taken in upstream=d/(x-y)=640 or d=640(x-y) ----(i) and   Time taken in downstream=d/(x+y)=280 or d=280(x+y) ----(ii)   Comparing (i) & (ii), 640(x-y) = 280(x+y)   => 16(x-y) = 7(x+y)   => 16x -16y =7x -7y   => 9x = 23y   => x/y= 23/9   ANSWER:23: 9
Answer: D
A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 78 runs, thereby increasing his average by 6 runs. His new average is
Pick
A) 18 runs	B) 28 runs	C) 48 runs	D) 42 runs	E) 46 runs

Solution: Explanation:   Let average for 10 innings be x. Then,   (10x + 78)/11 = x + 6 => 11x + 66 = 10x + 78 => x = 12.   New average = (x + 6) = 18 runs.   18 runsnswer: 18 runs
Answer: A
What is the greatest value of positive integer x such that 2^x is a factor of 100^90?	Choose the correct choice from the following answers.
A) 180 B) 160 C) 140 D) 150 E) 120

Solution: Put in simple words, we need to find the highest power of 2 in 100^90   100 = 2^2*5^2   Therefore 100^90 = (2^2*5^2)^90 = 2^180*5^180   180nswer : 180
Answer: A
For dinner, Cara ate 240 grams of bread which was eight times as much bread as she ate for lunch, and six times as much bread as she ate for breakfast. How much bread did Cara eat in total?  Answers: A) 300 B) 310 C) 320 D) 330 E) 340

Solution: For breakfast, Cara ate  240 / 6= 
 240 / 6 = 40
40 grams.   For lunch, Cara ate  240 / 8= 
 240 / 8 = 30
30 grams.   For dinner, Cara ate 240 grams.   The total is  40 + 30 + 240= 
 40 + 30 + 240 = 310
310 grams.   The answer is 310.
Answer: B
Solution X contains 20% of material A and 80% of material B. Solution Y contains 30% of material A and 70% of material B. A mixture of both these solutions contains 22% of material A in the final product. how much solution X is present in the mixture?  Choose the most appropriate option
A) 40% B) 60% C) 80% D) 100% E) 110%

Solution: We can assume the total weight of the mixture= 100   Conc of A in the final mixture= 22   Let weight of A in the mixture be X. Conc given= 20%=.2   Therefore, weight of B= 100-X. Conc given = 30%= .3   Now, acc to the problem, .2X+ .3(100-X)=22   Solving, we get X=80. Since we assumed the weight of the mixture = 100, Therefore presence of A in the mixture= 80%.   ANSWER:80%
Answer: C
A number of two digits has 3 for its unit’s digit, and the sum of digits is 1/7 of the number itself. The number is	Answers
A) 43  B) 63  C) 73  D) 53  E) 83

Solution: Let the ten’s digit be x.   Then, number=10x+3 and sum of digits=(x+3)   (x+3)=1/7(10x+3)   7x+21=10x+3   3x=18   X=6   The required number is 63   ANSWER 63 63
Answer: B
A can do a job in 5 days and B can do it in 15 days. A and B working together will finish twice the amount of work in ------- days?  Answers
A) 21 ½ days	B) 22 ½ days	C) 23 ½ days	D) 12 ½ days	E) 7 ½ days

Solution: 7 ½ daysxplanation:   1/5 + 1/15 = 4/15 = 4/15   15/4 = 15/4 *2 = 7 ½ days   Answer: 7 ½ days
Answer: E
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°.
If the number of convex corners in such a polygon is 25, the number of concave corners must be Select the correct option:
A) 20  B) 10  C) 21  D) 22  E) 23

Solution: 90(25) + 270(n-25) = (n-2)*180.   =25 + 3(n-25) = (n-2)*2.   = 3n - 50 = 2n-4   = n = 46.   Hence, the required number of corners must be  46 - 25= 
 46 - 25 = 21
21. ANSWER : 21
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?	Choose the correct choice:  A) 1.7  B) 1.4  C) 1.1  D) 1.5  E) 1.2

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
For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
Choose the correct choice from the following.
A) 10
B) 9
C) 8
D) 7
E) 6

Solution: "For any positive integer n , n > 1, the "length" of n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)"   the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6   but we need n < 1000   using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 9 the length of 512.   the answer is (9)
Answer: B
A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?	Answers: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: X PIPES FILL AN4 8-X EMPTY   IN 1hr 1/6th is emptied so :   x/6 - (8-x)/8 = 1/6   ON SOLVING X=4 (FILL PIPES) AN4 8-X=4(EMPTY PIPES)   ANSWER:4
Answer: D
The number 49 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? Choose the correct choice from the following options:
A) 11 B) 16 C) 15 D) 14 E) 13

Solution: I think brute force with some common sense should be used to solve this problem.   Write down all perfect squares less than 49: 1, 4, 9, 16, 25, 36, 49..   Now, 49 should be the sum of 3 of those 7 numbers. Also to simplify a little bit trial and error, we can notice that as 49 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).   We can find that 49 equals to 4+9+36=2^2+3^2+6^2=49 --> 2+3+6=11.   11nswer: 11.
Answer: A
From the set of numbers {t, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)	Choose the correct choice from the following
A) 8 B) 15 C) 16 D) 31 E) 32

Solution: Any letter (v, w, x, y, z) can be included or not.   Thus there are 2^5 combinations - 1 empty combination = 31 combinations   The answer is 31.
Answer: D
Two goods trains each 720 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Select the correct option:
A) 22 sec B) 88 sec C) 48 sec D) 18 sec E) 72 sec

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 750 + 750= 
750 + 750 = 1_500
1500 m.   Required time= 1500 * 6/125= 
1500 * 6/125 = 72
72 sec.   Answer:72 sec
Answer: E
A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
Select.
A) 4 days	B) 2 days	C) 6 days	D) 8 days	E) 9 days

Solution: 6 days   6 days   4/10 + 9/x = 1 => x = 15   1/10 + 1/15 = 1/6 => 6 days
Answer: C
An amount of Rs.1,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?  Choose the most appropriate option:
A) 2378 B) 2697 C) 250 D) 5000 E) 6971

Solution: Explanation:   We have, P = 2Q & S = 4R   Further Q = R & P + Q + R + S = 1,000   Thus we get, 2Q + Q + Q + 4Q = 1,000   8Q = 1,000 or Q = Rs. 125   Thus, R = Rs. 125, P = 250 & S = Rs. 500   Hence, the required difference = (S – P) = (500 – 250) = Rs.250   ANSWER:250
Answer: C
The sum of first 45 natural numbers is?	Choose the correct option:
A) 900	B) 1000	C) 1035	D) 1040	E) 1045

Solution: et Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.   Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	= 45	x 46 = (45 x 23)   2	2	2   = 45 x (20 + 3)   = 45 x 20 + 45 x 3   = 900 + 135= 
900 + 135 = 1_035
1035.   Shorcut Method:   Sn=	n(n + 1)	=	45(45 + 1)	= 1035.   2	2   1035)
Answer: C
A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
Pick
A) 1218
B) 1219
C) 1210
D) 1211
E) 1212

Solution: π (232 – 122) = 1210   Answer: 1210
Answer: C
A bus can hold 72 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
Answers:	A) 4	B) 8	C) 10	D) 6	E) 12

Solution: No. of seats = 72/12= 
72/12 = 6
6   There are 6 seats in each row   Answer : 6
Answer: D
In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 36% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
Choose the correct option:
A) 35.67%
B) 65.80%
C) 68.57%
D) 69.57%
E) none of these

Solution: Girls = 900, Boys = 1100   Passed = ( 36% of 1100 ) + ( 32% of 900)   = 396 + 288= 
396 + 288 = 684
684   Failed= 2000 - 684= 
2000 - 684 = 1_316
1316   Failed %= [(1316/2000) x 100]%   = 65.8%.   ANSWER:65.80%
Answer: B
For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 191?
Select
A) 4450 B) 5560 C) 6670 D) 7780 E) 8890

Solution: 100 + 102 +...+ 190 = 46*100 + (2+4...+90) = 46*100 + 2(1+2+...+45) =   46*100 + 2(45)(46)/2 = 145*46= 
145*46 = 6_670
6670   The answer is 6670.
Answer: C
If s is a number such that –2 ≤ s ≤ 2, which of the following has the largest possible absolute value?
Choose the correct choice from the following choices
A) 3s – 1 B) x^2 + 1 C) 3 – x D) x – 3 E) x^2 – x

Solution: Ans is A .. leads to the max value of 7 for s = -2
Answer: A
Each child has 4 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? Choose the correct choice from the following answers.
A) 16	B) 12	C) 18	D) 22	E) 32

Solution: 4*8= 
4*8 = 32
32.Answer is 32.
Answer: E
A portion of the 80% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 50% solution of chemicals resulted. What part of the original solution was replaced?  Choose the correct choice from the following:	A) 1/3	B) 1/2	C) 1/4	D) 1/5	E) 1/6

Solution: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.8(1-x)+0.2*x=0.5 --> x=1/2.   Answer: 1/2.
Answer: B
Replace the question mark with the correct number in the series
60 40 40 43 20 46 0 49 ? Choose the correct choice from the following.
A) -20
B) 50
C) 40
D) -10
E) -30

Solution: -20   -20   Its a alternate series riddle   60 40 20 0 (?)   40 43 46 49 (+3)
Answer: A
108.	Triangle A’s base is 9% greater than the base of triangle B, and A’s height is 9% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
Choose one:
A) 9 % less	B) 1 % less	C) Equal to each other	D) 1.3 % more	E) 9 % more

Solution: Wish the question specified that we are talking about corresponding height.   Base of A = 10/9 * Base of B   Height of A = 8/9 * Height of B   Area of A = (1/2) * Base of A * Height of A = 10/9 * 8/9 * Area of B = 80/81 * Area of B   Area of A is 1.3% more than the area of B.   Answer (1.3 % more)
Answer: D
Find the missing in the series: 70, 56, 45, 41,___
Select the correct option.
A) 22  B) 287  C) 2679  D) 276  E) 2771

Solution: Answer:276
Answer: D
If S and T are positive integers, and the remainder obtained when S is divided by T is the same as the remainder obtained when T is divided by S, which of the following is a possible value of ST?
Choose the correct answer:
A) 64  B) 55  C) 42  D) 36  E) 24

Solution: I am not too sure on this. I guess it is possible only when S and T are both same. If they are both same, ST must be a perfect square.   64 is a perfect square.   64ns:64
Answer: A
All the six members of a family A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B. A and C are a married couple. E is the brother of C. D is the daughter of A. F is the brother of B. Who is the mother of B ? Options.
A) C  B) V  C) R  D) A  E) T

Solution: Explanation:   B is the son of C but C is not the mother of B means C is the father of B. A is marned to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C   Clearly. A is the mother of B.   Answer: A
Answer: D