MU-NLPC/Calc-aqua_rat huggingface dataset:
How many odd four-digit integers greater than 9000 are there such that all their digits are different?
Choose the correct choice.
A) 84
B) 104
C) 168
D) 224
E) 280

Solution: Case 1: Numbers starting with 9 followed by an EVEN number   The hundreds digit can take 5 numbers (0,2,4 ,6 , 8) so 5 ways   The unit digit can take 4 numbers (1,3,5,7) to be ODD so 4 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.   Total = 5*4*7= 
5*4*7 = 140
140   Case 2: Numbers starting with 9 followed by an ODD number   The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways   The unit digit can take remaining 3 ODD numbers left after using 2 ODD numbers so 3 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.   Total= 4*3*7= 
4*3*7 = 84
84   Hence 140+84= 
140+84 = 224
224, correct answer is 224
Answer: D
Speed of a boat in standing water is 11kmph and speed of the stream is 2.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is? Select
A) 21.12hours B) 20.12hours C) 19.12hours D) 18.12hours E) 17.12hours

Solution: Speed upstream = 8.5kmph   Speed downstream = 13.5kmph   Total time taken = 105/8.5 + 105/13.5 = 20.12 hours   Answer is 20.12hours
Answer: B
If Jimmy drinks 8 ounces of water each time for 8 times a day. How much gallons of water he would have to prepare ahead to drink for 5 days? (1 ounce = 0.0078125 gallon)  Choose the correct choice from the following choices.
A) 1 B) 1.5 C) 2 D) 2.5 E) 3

Solution: 8 ounces* 8 times/day = 64 ounces of water = 64 * 0.0078125= 
64 * 0.0078125 = 0.5
0.5 gallon. 5 days need   0.5 * 5= 
  0.5 * 5 = 2.5
2.5 gallons. Correct Option: 2.5 Answer: 2.5
Answer: D
If q = 45! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 29
III. 41	Choose the correct choice from the following choices
A) I​ only
B) III only
C) II and III
D) I and II
E) I​, II, and III

Solution: The numbers 11, 29, and 41 are all factors of 45!   Therefore they can not be factors of 45! + 1.   The answer is I​, II, and III.
Answer: E
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? Options: A) 23/35 B) 23/37 C) 23/29 D) 23/30 E) 23/36

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/35   23/35nswer: 23/35
Answer: A
5 cards have to be put into their 5 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the cards go into their respective envelopes?  Select the correct option:
A) 1/30
B) 1/60
C) 1/240
D) 1/120
E) 3/5

Solution: A-B-C-D-E (envelopes)   a-b-c-d-e (letters)   5 letters (a, b, c, d, and e) can be assigned to 5 envelopes (arranged) in 5! ways, out of which only one will be correct, thus the probability is 1/5! = 1/120.   Answer: 1/120.
Answer: D
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people? Choose the correct option:
A) 15! /8!	B) 7! *8!	C) 15C7 *6! *7!	D) 2 * 15C7 *6! *7!	E) 15C8 *8!

Solution: Solution:   'n' objects can be arranged around a circle in (n−1)! ways.   If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.   i.e., number of arrangements =(n−1)! /2.   You can choose the 7 people to sit in the first table in 15C7 ways.   After selecting 7 people for the table that can seat 7 people, they can be seated in:   (7−1)! =6!   The remaining 8 people can be made to sit around the second circular table in: (8−1)! =7! Ways.   Hence, total number of ways: 15C7 *6! *7!.   Answer: Option 15C7 *6! *7!
Answer: C
Solve using synthetic division or long division(x2 + 13x + 40) ÷ (x + 8)  Options:	A) x + 9	B) x + 0	C) x + 5	D) x + 2	E) x + 1

Solution: e solved the division in both the ways;   (x2 + 13x + 40) ÷ (x + 8) by using synthetic division   Synthetic Division   Save   Quotient = x + 5   Remainder = 0   Answer: x + 5
Answer: C
A car traveled 420 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
Choose one
A) 14  B) 16  C) 21  D) 24  E) 27

Solution: Let the speed in highway be h mpg and in city be c mpg.   h = c+6   h miles are covered in 1 gallon   420 miles will be covered in 420/h.   Similarly c miles are covered in 1 gallon   336 miles will be covered in 336/c.   Both should be same (as car's fuel capacity does not change with speed)   => 336/c = 420/h   => 336/c = 420/(c+6)   => 336c+336*6=420c   =>c=336*6/84= 
336*6/84 = 24
24   Answer 24.
Answer: D
The y intercept of a line L is 6. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6	Choose the correct answer.
A) I only  B) II only  C) III only  D) I and II  E) I and III

Solution: C) III only   The y-intercept is 6. Therefore we have y=mx+6   It is given that the slope is negative. Therefore the line must go from top left to bottom right.   i.e: the x-intercept has to be positive. That itself rules out III.   If you choose to go with the options directly, here's an approach.   y=mx+6. For the x-intercept, y=0.   i.e. mx+6=0.   We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+6 =0 would never be satisfied.   If x=6, we have 6m+6=0. A value of m=-1 would satisfy this equation. 9answer III only)
Answer: C
A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?  Choose the most appropriate option
A) 650	B) 670	C) 729	D) 740	E) 760

Solution: Choose 5 starters from a team of 12 players. Order is not important.   \inline {\color{Black} 12729_{5}}= 729   729
Answer: C
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?  Choose the correct choice from the following choices
A) 21000  B) 21007  C) 21004  D) 21009  E) 21001

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)   x = 28000   35000 - x = 7000   Difference in the cost prices of televisions = Rs. 21000   21000nswer:21000
Answer: A
If s and t are positive integers such that s/t = 56.12, which of the following could be the remainder when s is divided by t ?	Choose the correct option.
A) 2	B) 4	C) 8	D) 20	E) 90

Solution: The remainder is 0.12 or 12/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.   One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.   90/Y=12/100   12Y=9000   Y=750   Answer: 90.
Answer: E
Bradley owns b video game cartridges. If Bradley’s total is one-seventh the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b? Pick.
A) 27b / 4 B) 29b / 4 C) 31b / 4 D) 33b / 4 E) 35b / 4

Solution: b = Bradley’s total   7b = Andrew’s total   b/4 = Charlie’s total   The total number of cartridges is:   b + 7b+ b/4 = (4b + 28b + b) / 4 = 33b / 4   The answer is 33b / 4.
Answer: D
Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?  Pick:  A) A)1040  B) B)1045  C) C)965  D) D)1060  E) E)1075

Solution: Cost of 8 kg apples= 70 × 8 = 560.   Cost of 9 kg of mangoes = 45 × 9 = 405.   Total cost he has to pay = 560 + 405= 
560 + 405 = 965
965.   965)
Answer: C
Which one of the following numbers is exactly divisible by 11? Choose the most appropriate option
A) 415618  B) 415620  C) 415621  D) 415623  E) 415624

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: E
A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is..??  Choose the correct option
A) 2/11 B) 3/11 C) 4/11 D) 0 E) 1

Solution: total vowels = 4, total number of letters = 11   so probability = 4/11   ANSWER:4/11
Answer: C
The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 4 shirts each of them then average number of shirt each of them now has  Choose the correct choice from the following answers:
A) 66  B) 63  C) 62  D) 64  E) 61

Solution: Required average   = Old average + New average   = 60 + 4= 
60 + 4 = 64
64   answer :64
Answer: D
Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a * b ? Select:
A) 10000	B) 11000	C) 19000	D) 20000	E) 21000

Solution: Yes! there is really a faster way to solve it.   Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2   Here A = sum of even ints from 2 to 20, inclusive   number of even ints = 10,   first int + last int = 2+20= 
2+20 = 22
22   A= 10*22 / 2= 
10*22 / 2 = 110
110   11000= sum of odd ints from 1 to 19, inclusive   number of odd ints = 10,   first int + last int = 1+19= 
1+19 = 20
20   A= 10*20 / 2= 
10*20 / 2 = 100
100   A*11000= 110 * 100= 
110 * 100 = 11_000
11000   Ans : 11000
Answer: B
If two numbers are in the ratio 2:5. If 10 is added to both of the numbers then the ratio becomes 3:7 then find the smallest number? Choose the correct choice from the following answers:  A) 40  B) 80  C) 60  D) 20  E) 100

Solution: Given ratio - 2:5   2x + 10 : 5x + 10 = 3 : 7   7[2x + 10] = 3[5x + 10]   14x + 70 = 15x + 30   15x - 14x = 70 - 30= 
70 - 30 = 40
40   Then smallest number is= 2   2x = 80   ANS - 80
Answer: B
An Olympic diver received the following scores: 5, 6, 3, 2. The standard deviation of her scores is in which of the following ranges?
Choose the correct answer
A) 5.01 to 5.99  B) 3.01 to 3.99  C) 4.01 to 4.99  D) 2.01 to 2.99  E) 1.01 to 1.99

Solution: 5+6+3+2/4=4   ∣5-4∣^2 =1^2 = 1   ∣6-4∣^2 =2^2 = 4   ∣3-4∣^2 =1^2 = 1   ∣2-4∣^2 =2^2 = 4   sqrt 10/4 =1.58   Answer : 1.01 to 1.99
Answer: E
Claire has 3 books. She averages the amount of pages of each book to have 305 pages. If her mom buys her a new book which has 400 pages, what will the new average be?  Select:  A) 342.5  B) 328.75  C) 330.87  D) 342.75  E) 335

Solution: (sum of the pages of the 3 books)/3 = 305   sum of the pages of the 3 books = 915   new sum = 915+400= 
915+400 = 1_315
1315   new average= 1315/4= 
1315/4 = 1_315/4 = around 328.75
328.75   ans: 328.75
Answer: B
When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 16, what was the speed of the leak, in terms of Vâ€™?	Choose the correct answer
A) 2Vâ€™  B) 4Vâ€™  C) Vâ€™/2  D) Vâ€™/4  E) 16Vâ€™

Solution: When h=4 v=V'   So V' = k.16   Hence k = V'/16   Now when h=16   v=(V'/16).16^2   v=V'.16   v=16V'   Ans : 16Vâ€™
Answer: E
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Choose the correct choice from the following answers:
A) 6
B) 9
C) 5
D) 3
E) 4

Solution: 2: 5: 13   2x 5x 13x   15 7.5 2.5   30x + 37.5x + 32.5x = 100x/20x   Average 30  + 37.5  + 32.5= 
30  + 37.5  + 32.5 = 100
100x/20x   Average = 5   Answer: 5100 /20= 
100 /20 = 5
5   Answer: 5
Answer: C
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?	Choose the correct choice from the following.
A) 90	B) 180	C) 360	D) 540	E) 720

Solution: 3 Blue Marble:   Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1   Case (1) 3 possibilities   Case (2) 6 possibilities ,   Case (3) 1 possibility   tot. 10 possibilities.   One Green Marble :   3 possibilities (one for each cup at the time)   First Red marble:   3 possibilities (one for each cup at the time)   Second Red marble:   2 possibilities ( because can't go in the same cup with the other Red marble)   TOTAL:   10*3*3*2= 
10*3*3*2 = 180
180 , answer, 180 .
Answer: B
If c is an integer greater than 6, which of the following must be divisible by 3?	Choose the correct choice from the following options:
A) c (c+4) (c-2)  B) c (c+2) (c-1)  C) c (c+3) (c-5)  D) c (c+1) (c-4)  E) c (c+5) (c-6)

Solution: anything in the form of (c-1) (c) (c+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.   c (c+1) (c-4) = c (c+1) ((c-1)-3) is equivalant to (c-1) (c) (c+1)   c (c+2) (c-1) is equivalant to (c+1) missing.   c (c+3) (c-5) is equivalant to (c-1) missing and c repeating.   c (c+4) (c-2) is equivalant to odd/even consqcutive integers   c (c+5) (c-6) is equivalant to (c+1) missing and c repeating.   Answer : c (c+1) (c-4)
Answer: D
The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 40 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?	Select:
A) 210/(30+10A) B) 210/(30+60A) C) 210/35A D) 210/(30+10A) E) 220/40A

Solution: Since we are dealing with the variables in the answer choices,the best possible method according to me would be substitution.   Substitute A with 3.meaning tommy would have travelled a distance of ((160-40) + (160-70)) in 60 minutes.   210 Kms in 60 minutes ==> 3.5km/hr.   Substitute A with 3 in the answer options.   Option 210/(30+10
Answer: A
A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 1600.  Choose the correct choice from the following options.
A) Rs. 25600  B) Rs. 8500  C) Rs. 7200  D) Rs. 500  E) None of these

Solution: Explanation:   A = 2B and B = 5C   => A : B = 2:1 and B : C = 5 : 1   => A : B : C = 10 : 5 : 1   Ratio of capitals of A, B and C = 10 : 5 : 1   B's share = Rs.[(5/16) × 1600] = Rs. 500   Answer: Option Rs. 500
Answer: D
A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13? Choose the correct choice.
A) 11	B) 5	C) 8	D) 7	E) 9

Solution: 39 + 20= 
39 + 20 = 59
59/13= 7 (Remainder)   ANSWER 7
Answer: D
The average of eight numbers is 14. The average of six of these numbers is 16.The average of the remaining two numbers is	Choose the correct choice from the following
A) 14×8 – 16×6)/9  B) 14×8 – 16×6)/1  C) 14×8 – 16×6)/2  D) 14×8 – 16×6)/5  E) 14×8 – 16×6)/6

Solution: Average of eight numbers = 14   Average of six numbers = 16   Average will be = (14×8 – 16×6)/2   \Answer:	14×8 – 16×6)/2
Answer: C
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?	Choose the correct choice from the following options:  A) 2.5 sec  B) 2.8 sec  C) 7.5 sec  D) 2.3 sec  E) 1.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secnswer:2.5 sec
Answer: A
A man is trying 2 different pairs of pants &6 different shirts. How many combinations of 1 pair of pants &1 shirt are possible?	Options.
A) 10
B) 12
C) 16
D) 19
E) 21

Solution: Use a tree diagram to illustrate the possible selections. In the diagram, use P1 and P2 to represent the pants and S1, S2, S3, S4, S5, and S6 to represent the shirts.   Using the Fundamental Counting Principle, 2 × 6 = 12 outfits are possible.   12
Answer: B
What is the sum of the greatest common factor and the lowest common multiple of 12 and 36?
Select the correct option
A) 48
B) 22
C) 32
D) 36
E) 38

Solution: Prime factorization of 12 = 2 x 2 x 3   Prime factorization of 36 = 2 x 2 x 3 x 3   GCF = 12   LCM = 36   Sum = 48.   48nswer 48.
Answer: A
On a certain day, Jared's farm harvested 2526 oranges. If Jared distributes his oranges evenly across 7 different retail shops, how many oranges would remain with him? Choose the correct choice from the following options.
A) 4 oranges	B) 7 oranges	C) 1 orange	D) 2 oranges	E) 14 oranges

Solution: This is equivalent to finding the first number that is divisible by 7 that occurs before 2135.   In order to divide the sum in 9 parts, the amount must be divisible by 7   Divisibility rule of 7: The sum of the digits must be divisible by 7   Sum of digits of 2526 = 15 and 7 is divisible by 7.   Hence, we need to remove 1 to this number for it to be divisible by 7   1 orangeorrect Option: 1 orange
Answer: C
A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age six years back was?
Choose the correct choice from the following options:
A) 10 years  B) 12 years  C) 13 years  D) 16 years  E) 18 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 6 years back (19 - 6)= 
(19 - 6) = 13
13 years.   13 years
Answer: C
The compound interest on $ 30,000 at 7% per annum is $4347. The period (in years) is: Choose the most appropriate option:	A) 2	B) 2 1/2	C) 3	D) 4	E) 5

Solution: Amount = $(30000 + 4347) = $. 34347.   Let the time be n years.   Then, 30000 1 +	7 n	= 34347   100   107 n	=	34347	=	11449	= 107 2   100 30000 10000 100   n = 2 years.   2NSWER 2 - 2
Answer: A
If the cost price is 82% of the selling price, then what is the profit percent?  Choose the correct option
A) 5%  B) 22%  C) 13%  D) 21%  E) 19%

Solution: Let S.P. = $100   C.P. = $82   Profit = $18   Profit% = 18/82 * 100 = 25/6 = 22% approximately   Answer is 22%
Answer: B
Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?  Pick.
A) 880  B) 756  C) 390  D) 610  E) 930

Solution: 930   930   930xplanation:   New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)   10   10 * 0.5 + 5= 
10 * 0.5 + 5 = 10
> 10   10 * 1.0 + 10= 
10 * 1.0 + 10 = 20
> 20   20 * 1.5 + 15= 
20 * 1.5 + 15 = 45
> 45   45 * 2.0 + 20= 
45 * 2.0 + 20 = 110
> 110   110 * 2.5 + 25= 
110 * 2.5 + 25 = 300
> 300   300 * 3.0 + 30= 
300 * 3.0 + 30 = 930
> 930 , desired answer
Answer: E
Calculate the largest 6 digit number which is exactly divisible by 99?
Choose the correct choice from the following options
A) 999991
B) 999965
C) 999912
D) 999936
E) 999930

Solution: Largest 4 digit number is 999999   After doing 999999 ÷ 96 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   ANSWER : 999936
Answer: D
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are? Answers.
A) 11  B) 18  C) 13  D) 17  E) 12

Solution: A:18 = 2:3   18:C = 2:5   A:18:C = 4:6:15   6/25 * 75= 
6/25 * 75 = 18
18   Answer:18
Answer: B
The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers : Choose the correct choice
A) 4  B) 8  C) 12  D) 16  E) 18

Solution: Explanation:   Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.   Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.   or 5x + 20 = 305 or x = 57.   So, required difference = (57 + 8) - 57= 
(57 + 8) - 57 = 8
8 Answer: 8
Answer: B
If $120 invested at a certain rate of simple interest amounts to $160 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?	Select
A) $190 B) $180 C) $200 D) $240 E) $250

Solution: 120 amounts to 160 in 3 years.   i.e (principal + interest ) on 120 in 3 years = 160   120 + 120*(r/100)*(3) = 160 => r = 100/9   150 in 6 years = principal + interest   = 150 + 150*(r/100)*(6)   250   Answer is $250.
Answer: E
A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 9% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture? Choose the correct choice from the following answers.
A) a.	A – 260
B) b.	B – 280
C) c. C – 290
D) d.	D – 330
E) e.	E – 380

Solution: 5%*x + 9% *(480-x)=30   13.2 = 4 %*x   x=330   d.	D – 330
Answer: D
The sum of two numbers is 50 and their product is 1050. What will be the sum of their reciprocals?	Choices:	A) (11/140)	B) (1/21)	C) (35/4)	D) (75/8)	E) None

Solution: Solution   x+y=50 xy=1050 1/x+1/y=x+y/xy 50/1050 = (1/21).   Answer (1/21)
Answer: B
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?	Select
A) 35  B) 43  C) 62.5  D) 71  E) 72.5

Solution: Let the capacity of bucket be 10 Litres   They said that it requires 25 buckets to fill the tank   Therefore capacity of tank=25*10= 
25*10 = 250
250   If the capacity of the bucket is reduced to to 2/5th of original capacity then New capacity of bucket=(2/5)10=4litres   No. of buckets required to fill the tank=250/4= 
250/4 = 125/2 = around 62.5
62.5   answer:62.5
Answer: C
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is	Choose the correct choice from the following answers
A) 35
B) 37
C) 38
D) 41
E) 42

Solution: Explanation:   Let B's age = x years.   Then, As age = (x+ 8) years.   (x+8+10)=2(x—10)   hence x=38.   Present age of B = 38 years   Answer: Option 38
Answer: C