MU-NLPC/Calc-aqua_rat huggingface dataset:
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 5 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? Choose the most appropriate option
A) 25	B) 34	C) 50	D) 60	E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 5 oz can= 300 oz/5 oz = 60   Answer 60, 60 cans
Answer: D
A and B are two circles. The radius of A is four times as large as the diameter of B. What is the ratio between the areas of the circles?
Choose the correct choice from the following options.
A) 1:8.
B) 1:2.
C) 1:24.
D) 1:64.
E) 1:6.

Solution: Given : The radius of A is 4 times as large as the diameter of B. => R(a) = 4*D(b) = 4*2*R(b) = 8R(b). The radius are in ratio of 1:8 thus the area will be in the ratio of square of radius. 1:64. Hence 1:64..
Answer: D
In State X, all vehicle license plates have 3 letters from the 26 letters of the alphabet followed by 2 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
Select the correct option.
A) 23,400 B) 60,840 C) 67,600 D) 608,400 E) 1,757,600

Solution: The choices give us the answer without any calculations--   2 one digits places can take 10*10 ways..   3 letter places can be filled up in 26 * 26 *26 ways   ans= 26*26*26*10*10= 
26*26*26*10*10 = 1_757_600
1757600   ans 1,757,600
Answer: E
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1947, What is the value of n?
Choose the correct choice from the following answers:
A) 22
B) 38
C) 62
D) 122
E) 118

Solution: Factorise 1947.. 3*11*59..   So n has to be a multiple of largest prime number,61..   So n=2*59=118..   Ans :118
Answer: E
In a certain game, you pick a card from a standard deck of 52 cards. If the card is a clever, you win. If the card is not a clever, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a clever, and the point is to measure how many draws did it take before the person picked a clever and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her clever on the third draw or later?
Choose the correct choice from the following choices:  A) 11/16  B) 9/16  C) 14/16  D) 13/16  E) 15/16

Solution: Probability of picking a heart on any draw = 1/4   Probability of NOT picking a heart on the first draw 11/16ND on the second draw = [1-(1/4)] X [1-(1/4)] = 3/4 X 3/4 = 9/16   11/16nswer : 11/16
Answer: A
A can complete a work in 10days and B can do the same work in 5days. If A after doing 2days, leaves the work, find in how many days B will do the remaining work? Choose the correct answer:  A) 2days  B) 4days  C) 6days  D) 7days  E) 10days

Solution: The required answer = (10-2)*5 / 10 = 40/10= 
40/10 = 4
4days   Answer is 4days
Answer: B
The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs.800 per sq. metre.
Choose the correct choice from the following
A) 16200 B) 16350 C) 16500 D) 16750 E) 16250

Solution: Area =5.5×3.75 sq. metre.   Cost for 1 sq. metre. = Rs.800   Hence, total cost   =5.5×3.75×800=5.5×3000= Rs.16500   Answer is 16500.
Answer: C
A bag contains nine white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Options
A) 5/8
B) 6/13
C) 5/16
D) 5/13
E) 5/11

Solution: Two balls can be picked from thirteen balls in 13Câ‚‚ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.   The required probability = (9 * 4)= 
(9 * 4) = 36
36/78= 6/13   Answer: 6/13
Answer: B
when W is divided by 13, the reminder is 0. if W is one lesser than it value and when divided by 5 its remainder is 0. what is the value of W ?  Options: A) 13 B) 25 C) 26 D) 52 E) 65

Solution: W is divided by 13 so that is multiple of 14 as 13,26,39...   W-1 is divided by 5 the remainder is 0 so it is divisible by 5. 26onsider from option let us take the number is 13 it is divisible by 13 but 13-1 is not divisible by 5 so it is not answers so let us take 2nd option 25 which is not divisible by 13 in 3rd option 26 is divisible by 13 and 26-1 is divisible by 5 so ans is 26
Answer: C
A goods train runs at the speed of 72 km/hr and crosses a 80 m long platform in 26 sec. What is the length of the goods train? Choose the correct choice from the following choices:	A) 382	B) 440	C) 278	D) 270	E) 881

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 80)/26 = 20   x = 440m.   Answer: 440
Answer: B
The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 35% profit?
Select the correct option: A) $480 B) $450 C) $960 D) $864 E) $660

Solution: Let C.P. = $ x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 135% of $ 640 = $ 864   $864
Answer: D
Half percent, written as a decimal, is Choose the correct choice from the following options
A) 0.2
B) 0.02
C) 0.005
D) 0.05
E) None

Solution: Solution: As we know, 1% = 1/100   Hence, 1/2% = (1/2 * 1/100) = 1/200 = 0.005.   Answer: Option 0.005
Answer: C
Enrollment in City College in 1980 was 37 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?  Choose the correct choice from the following choices:
A) 100%  B) 170.27 %  C) 200%  D) 250%  E) 183 1/3%

Solution: Assume 100 enrollments present in 1990   37 % of 1990 = enrollments on 1980   enrollments on 1980 = 37   % change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)   =(100 - 37) *100 / 37   = 6300 / 37   = 170.27 %   Ans - 170.27 %
Answer: B
How many prime numbers are between 26/3 and 85/6?  Select.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 26/3 = 8.xxx   85/6 = 14.xxx   So we need to find Prime numbers between 8 (Exclusive) - 13 (Inclusive)   There are 2 Prime numbers 1113   Hence answer will be (2) 2   2
Answer: B
Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits
Choose the correct answer.
A) 61312432	B) 41312432	C) 51312432	D) 31312432	E) 21312432

Solution: 41312432   41312432
Answer: B
Devon had $56.90 to spend at the toy store. She bought 4 toy cars that cost $2.50 each and a race track that cost $19.10. How much money does Devon have left to buy more toys?	Select:	A) $70	B) $55	C) $33	D) $27.80	E) $14.20

Solution: Step 1: Find the cost of the toy cars.   4 × $2.50 = $10.00   Step 2: Find the total cost of the toys.   $10.00 + $19.10 = $29.10   Step 3: Find the amount of money left.   $56.90 – $29.10  10.00 +  19.10= 
 10.00 +  19.10 = 29.1
$29.10   Step 3: Find the amount of money left.   $56.90 – $29.10= $27.80   Devon has $27.80 left.   Answer is $27.80.
Answer: D
A can finish a work in 60days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
Choose the correct choice from the following answers:
A) 10days	B) 25days	C) 6days	D) 7days	E) 8days

Solution: 25days+C 1day work = 1/9 + 1/12  +  1= 
 +  1 = 1
1/9 + 1/12= 7/36   work done by 25days and C in 3days = 7/36 * 3 = 7/12   Remaining work = 1 - 7/12 = 5/12   1/60 work is done by A in 1day   5/12 work is done by A in  60*5/12= 
 60*5/12 = 25
25days   Answer is 25days
Answer: B
The decimal 0.1 is how many times greater than the decimal (0.01)^5?
Pick
A) 10^6	B) 10^7	C) 10^8	D) 10^9	E) 10^10

Solution: 0.1 = 10^-1   (0.01)^5 = (10^-2)^5 = 10^-10   10^9 * 10^-10 = 10^-1   The answer is 10^9.
Answer: D
3.20 can be expressed in terms of percentage as
Pick.
A) 3.20%
B) 30.2%
C) 320.00%
D) 0.320%
E) None of these

Solution: Explanation:   While calculation in terms of percentage we need to multiply by 100, so   3.20 * 100= 
3.20 * 100 = 320
320   Answer: Option 320.00%
Answer: C
A dishonest dealer uses a scale of 97 cm instead of a metre scale and claims to sell at cost price. His profit is  Choose the correct choice from the following answers
A) 9%  B) 10%  C) 12%  D) 3.1%  E) Cannot be determined

Solution: Solution   Gain%	= (3 / 97 x 100)%   = 3.1%   Answer 3.1%
Answer: D
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is: Pick
A) 400 kg
B) 560 kg
C) 600 kg
D) 640 kg
E) 680 kg

Solution: Profit on 1st part 8%   Profit on 2nd part 18%   Mean Profit 14%   Ration of 1st and 2nd parts = 4 : 6 = 2 : 3   Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg.   Answer:600 kg
Answer: C
There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected? Answers.
A) 1/2  B) 2/3  C) 32/35  D) 11/12  E) 11/14

Solution: answer is 11/14   Total probability=8C2=28   4C2 +4C1*4C1=6+16= 
6+16 = 22
22   therefore the probability that at least one of the fashion magazines will be selected= 22/28=11/14   11/14
Answer: E
Browny owns b video game cartridges. If Browny’s total is one-third the total owned by James and two times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?	Pick:
A) (16/3)b	B) (17/4)b	C) (13/4)b	D) (9/2)b	E) (7/12)b

Solution: b = Browny’s total   3b = James’s total   (1/2)b = Charlie’s total   Add each total   b + 3b+ (1/2)b = 4b + (1/2)b = = (9/2)b   Answer : (9/2)b
Answer: D
How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
Choose the correct choice from the following choices.
A) 20	B) 15	C) 40	D) 50	E) 25

Solution: Selling price is 48 cents/lb   For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)   Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)   weight of Salt 1/weight of Salt2 = (Salt2 - Salt Avg)/(Salt Avg - Salt 1) = (50 - 40)/(40 - 35)= 
(50 - 40)/(40 - 35) = 2
2/1   We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs.   20nswer (20)
Answer: A
Harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?  Choose the correct choice from the following choices:
A) A)1190  B) B)1065  C) C)1070  D) D)1075  E) E)1080

Solution: Cost of 10 kg grapes = 70 × 10 = 700.   Cost of 9 kg of mangoes = 55 × 9 = 490.   Total cost he has to pay = 700 + 490= 
700 + 490 = 1_190
1190   1190
Answer: A
If the given two numbers are respectively 5% and 25% of a third number, then what percentage is the first of the second ?	Choose the correct choice
A) 20% B) 25% C) 18% D) 30% E) none of these

Solution: Here, l = 5 and m = 25   Therefore, first number = l/m x 100% of second number = 5/25 x 100% of second number = 20% of second number   20%NSWER:20%
Answer: A
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 4225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Select the correct option
A) 140 sq.units	B) 260 sq.units	C) 167sq.units	D) 178sq.units	E) 176sq.units

Solution: Given that the area of the square = 4225 sq.units   => Side of square = √4225 = 65 units   The radius of the circle = side of the square = 65 units Length of the rectangle = 2/5 * 65= 
2/5 * 65 = 26
26 units   Given that breadth= 10 units   Area of the rectangle = lb = 26 * 10= 
26 * 10 = 260
260 sq.units   Answer:260 sq.units
Answer: B
A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? Choose the most appropriate option:
A) A)452000 B) B)200000 C) C)800000 D) D)500000 E) E)652000

Solution: 3 children got = 3*15= 
3*15 = 45
45%   wife got= 30%   orphan house = 5%   total = 45+30+5= 
45+30+5 = 80
80%   remaining= 100-80= 
100-80 = 20
20%   20%= 40000   100% = 40000*100/20= 
40000*100/20 = 200_000
$200000   Answer is 200000
Answer: B
A fruit seller had some oranges. He sells 20% oranges and still has 400 oranges. How many oranges he had originally? Answers
A) 420 B) 700 C) 220 D) 500 E) None of these

Solution: Explanation :   He sells 20% of oranges and still there are 400 oranges remaining   => 80% of oranges = 400   ⇒ (80 × Total Oranges)/100 = 400   ⇒ Total Oranges/100 = 5   ⇒ Total Oranges = 5 × 100 = 500   Answer : Option 500
Answer: D
The sum of two numbers is 35 and their product is 1050. What will be the sum of their reciprocals?	Choose the correct choice
A) (1/30)  B) (11/210)  C) (35/4)  D) (75/8)  E) None

Solution: Solution   x+y=35 xy=1050 1/x+1/y=x+y/xy 35/1050 = (1/30).   (1/30)nswer (1/30)
Answer: A
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Choose one.
A) 18%	B) 71%	C) 28%	D) 12%	E) 72%

Solution: 1500 ---- 270   100 ---- ? => 18%   18%nswer: 18%
Answer: A
Which one of the following numbers is exactly divisible by 11?  Select:
A) 235641
B) 245642
C) 315624
D) 415624
E) Done

Solution: (4 + 5 + 2) - (1 + 6 + 3)= 
(4 + 5 + 2) - (1 + 6 + 3) = 1
1, not divisible by 11.   (2 + 6 + 4) - (4 + 5 + 2)= 
(2 + 6 + 4) - (4 + 5 + 2) = 1
1, not divisible by 11.   (4 + 6 + 1) - (2 + 5 + 3)= 
(4 + 6 + 1) - (2 + 5 + 3) = 1
1, not divisible by 11.   (4 + 6 + 1) - (2 + 5 + 4)= 
(4 + 6 + 1) - (2 + 5 + 4) = 0
0, So, 415624 is divisible by 11.   415624)
Answer: D
If x is divisible by 3 and 7, which of the following must divide evenly into x? I. 60 II. 30 III. 21	Choose the correct choice
A) II only	B) III only	C) I only	D) I,II only	E) I,III only

Solution: If x is divisible by 3,7 means it will be = or > 21, 42,84 etc...   That are not divisible by 60, 30.   So, the answer is III only
Answer: B
The sum of three consecutive odd natural numbers, each divisible by 3 is 84. What is the largest among them?
Choose the correct choice from the following answers
A) 21  B) 24  C) 27  D) 31  E) 45

Solution: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6   Given, X + X+3 + X+6 = 84   3X = 75   X = 25   The numbers are 25, 28, 31   Therefore the largest number is 31   Answer 31.
Answer: D
A goes 8 km East, then 3 km South, 4km West. How far is he from starting point and in which direction?
Choose one.
A) 5 km south west  B) 5 km south east  C) 8 km south  D) 9 km south  E) Don,t remember

Solution: 8E, 3S,4W   Subtract opposite direction 8E-4W,3S=> 4E, 3S   Square root of(4^2+ 3^2)= 5 Km South East.   ANSWER:5 km south east
Answer: B
In how many ways can the letters of the word SPECULATION be arranged such that all the vowels always appear together?  Choose the correct choice from the following choices: A) 6!*5! B) 7!*5! C) 11! D) 11!*6! E) 11!*5!

Solution: The 11 letters can be grouped into 6 consonants and one set of 5 vowels.   The number of ways to arrange 7 units is 7!   Then, for each arrangement, the 5 vowels can be arranged in 5! ways.   The total number of arrangements is 7!*5!   The answer is 7!*5!.
Answer: B
If BASKET is coded as 116,then COLOUR is coded as,  Pick one:	A) 158	B) 168	C) 179	D) 188	E) 198

Solution: NUM168ER THE ALPHA168ETS   168=2, A=1, S=19, K=11, E=5, T=20   168ASKET = 116   2(168+A+S+K+E+T) ==>2(2+1+19+11+5+20) = 2(58) = 116   Similarly C=3, O=15, L=12, O=15, U=21, R=18   2(C+O+L+O+U+R) = 2(3+15+12+15+21+18) = 2(84) = 168   ANSWER:168
Answer: B
The ratio of two numbers is 3 : 6 and their H.C.F. is 7. Their L.C.M. is	Choose the correct choice from the following.
A) 48 B) 42 C) 56 D) 27 E) 67

Solution: Explanation:   Let the numbers be 3x and 6x. Then, their H.C.F. = x. So, x = 7.   So, the numbers 21 and 42.   L.C.M. of 21 and 42 = 42.   Option 42
Answer: B
If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 189, what is their sum?  Choose the most appropriate option:
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: 1^3 = 1   2^3 = 8   3^3 = 27   4^3 = 64   5^3 = 125   6^3 = 216   The two numbers are 3 and 6.   The answer is 9.
Answer: D
Which of the following functions does not intersect with R = 3x^2 + 2x + 1  Pick one.
A) R = 3x^2 + 3x + 1	B) R = 2x^2 + 3x + 1	C) R = 3x^2 + 2x + 3	D) R = 4x^2 + 2x - 3	E) R = x^2 + 2x + 3

Solution: Let’s find the actual intersecting point of given function and each choice R   A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0   B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1   C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.   D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2   E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.   So only choice (C) has no intersecting point. The answer is (R = 3x^2 + 2x + 3).
Answer: C
The owner of a furniture shop charges his customer 30% more than the cost price. If a customer paid Rs. 8450 for a computer table, then what was the cost price of the computer table?	Choose the correct option: A) Rs. 5725 B) Rs. 5275 C) Rs. 6275 D) Rs. 6500 E) None of these

Solution: CP = SP * (100/(100 + profit%))   = 8450(100/130) = Rs. 6500.   ANSWER:Rs. 6500
Answer: D
Twenty times a positive integer is less than its square by 96. What is the integer?  Choose the correct choice
A) 20	B) 24	C) 30	D) 34	E) 38

Solution: Let the integer be x. Then,   x2 - 20x = 96   (x + 4)(x - 24) = 0   x = 24   ANSWER:24
Answer: B
A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag? Choose the correct choice from the following answers:
A) 20 coins
B) 40 coins
C) 60 coins
D) 70 coins
E) None

Solution: 50paisa : Rs.1/- : Rs.2/- = 4 : 2 : 1 ---> coins ratio   = 2 : 2 : 2 ----> money ratio   Rs.2/- * 10 coins = Rs.20/-   Rs.1/- * 20 coins = Rs.20/-   50 Paisa * 40 coins = Rs.20/-   Then 50 paisa coins in that bag = 40 coins   40 coins)
Answer: B
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
Choose the correct option
A) 3488 B) 6240 C) 2776 D) 2889 E) 7721

Solution: Explanation:   To obtain Rs. 10, investment = Rs. 96.   To obtain Rs. 650, investment = = Rs. 6240   Answer: 6240) 6240
Answer: B
A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color? Choose the correct option.
A) 224/8855 B) 225/8855 C) 245/8855 D) 285/8855 E) 244/8855

Solution: Explanation:   Total marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles   4 marbles are drawn from 23 marbles at random. Therefore,   n(S) = 23C4 = 8855 ways   Let A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is   n(A) = 5C4 + 10C4 + 8C4 = 5 +210 + 70= 
5 +210 + 70 = 285
285   Therefore, by definition of probability of event A,   P(A)= n(A)/n(S) =285/8855   ANSWER:285/8855
Answer: D
Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is Choose the correct choice from the following choices:
A) 60 days
B) 15 days
C) 6 days
D) 51 days
E) 50 days

Solution: Two men and 7 children complete a certain piece of work in 4 days   or 8 men and 28 children complete a certain piece of work in 1 days   4 men and 4 children complete the same work in only 3 days.   or 12 men and 12 children complete the same work in only 3 days.   so 8 men +28 children = 12 men +12 children   1Man = 4 children   4 men and 4 children complete the same work in only 3 days   or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days   or 5 men complete the same work in 3 days   or 1 man will complete the same work in 5* 3= 
5* 3 = 15
15 days   ANSWER:15 days
Answer: B
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following? Choose the correct choice from the following answers.
A) 13  B) 31  C) 49  D) 56  E) 67

Solution: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.   56   Answer: 56
Answer: D
Of the 80 people in a room, 2/5 are women. If 1/2 of the people are married, what is the maximum number of women in the room who could be unmarried?  Choose the correct choice from the following choices.
A) 20
B) 22
C) 26
D) 30
E) 32

Solution: women = 2/5 * 80= 
2/5 * 80 = 32
32   married= 1/2 * 80= 
1/2 * 80 = 40
40   unmarried= 40   max(un-married women) = 32   32
Answer: E
Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 30 miles per hour. How far is it to the school?  Choose the correct choice from the following:
A) 2 miles B) 4 miles C) 4.8 miles D) 8 miles E) 6.9 miles

Solution: Answer: E) 6.9 miles.   Average speed for round trip = 2*a*b/(a+b), where a,b are speeds   so, average speed was = 2*5*30/(5+30) = 6.9 m/hr   the distance between schoolhome should be half of that. ie. 6.9 miles   Answer 6.9 miles
Answer: E
Mangala completes a piece of work in 12 days, Raju completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?
Choose the correct choice:
A) 5.2 days B) 6.2 days C) 7.2 days D) 8.2 days E) 9.2 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 12 Ã— 18/30 = 7.2 days.   7.2 days)
Answer: C
If 35*s is a perfect square then s can be which of the following numbers?  Select:
A) 21
B) 35
C) 54
D) 105
E) 150

Solution: My solution:   For a number to be a perfect square all the prime factors must be in pairs. So,   Prime factors of 35 are 5 * 7   1) 21 = 3 * 7   2) 35 = 5 * 7   3) 54 = 2 * 3 * 3 * 3   4) 105 = 3 * 5 * 7   5) 150 = 2 * 3 * 5 * 5   So only answer choice B completes the pairing of 5 and 7. It adds a3, a5, and a7to the prime factors of 35 (5*7) and makes it a perfect square. 35
Answer: B
A committee that includes 12 members is about to be divided into 3 subcommittees with 4 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member? Choose the correct choice:
A) 39%
B) 35%
C) 31%
D) 27%
E) 23%

Solution: Michael is a member of one of the subcommittees.   P(Annie is on the same subcommittee) = 3/11 which is about 27%.   The answer is 27%.
Answer: D
An empty fuel tank with a capacity of 214 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
Choose the correct option.
A) 160	B) 150	C) 100	D) 80	E) 106

Solution: Say there are A gallons of fuel A in the tank, then there would be 214-A gallons of fuel B.   The amount of ethanol in A gallons of fuel A is 0.12A;   The amount of ethanol in 214-A gallons of fuel B is 0.16(214-A);   Since the total amount of ethanol is 30 gallons then 0.12A+0.16(214-A)=30 --> A=106.   Answer: 106.
Answer: E