MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum of the present ages of A, B, C is 51 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?	Choose the correct choice:
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: Three years ago:   a:b:c = 1:2:3   Let a = 1x, b = 2x, and c = 3x.   Today:   (x+3) + (2x+3) + (3x+3) = 51   x = 7   So the present age of A is x+3 = 10   The answer is 10.
Answer: D
Insert the missing number
9, 12, 11, 14, 13, ..., 15	Select.
A) 12  B) 16  C) 10  D) 17  E) 18

Solution: The sequence is consider into two series..   First series(odd) starting with 9 and increasing 2 as follows.   Second series(even) starting with 12 and increasing with 2 as follows.   i.e. 9 = 9 (odd)   12 = 12(even)   9 + 2= 
9 + 2 = 11
11(odd series)   12 + 2= 
12 + 2 = 14
14(even series)   11 + 2= 
11 + 2 = 13
13(odd series)   14 + 2= 
14 + 2 = 16
16(even series)   ANSWER:16
Answer: B
what is the unit digit in (4137)^754? Choose the correct choice from the following options
A) 1
B) 3
C) 7
D) 9
E) None of them

Solution: Unit digit in (4137)^754=Unit digit in [(4137)^4]^188 x (4137)^2 = (1x9)=9   Answer is 9
Answer: D
A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability W that both selected dogs are NOT littermates? Choices
A) 1/6	B) 2/9	C) 5/6	D) 7/9	E) 8/9

Solution: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.   So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.   Work with probabilities:   Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).   The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).   The probability of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).   The required probability is 1/2 + 1/3 = 5/6.   Find the probability for the complementary event: choose AA or BB.   Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.   Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.   Again, we obtain 1 - (1/12 + 1/12) W= 5/6.   Answer: 5/6
Answer: C
Fifteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of four members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?  Options: A) 120 B) 126 C) 252 D) 1200 E) 1365

Solution: My ans is 15C4 = 1365   1365
Answer: E
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 10 p.c?  Choose the correct choice from the following choices
A) 38028 B) 38000 C) 32977 D) 38128 E) 36000

Solution: CP + CP/8 = 45000   CP = 40000   SP = 40000*(90/100)= 
40000*(90/100) = 36_000
36000   Answer:36000
Answer: E
A train 1200 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Choose the correct choice from the following answers:
A) 2898
B) 277
C) 500
D) 100
E) 435

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (1200 + x)/60 = 65/3   x = 100 m.   Answer: 100
Answer: D
If 1 pound of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture? Select:
A) (x + 2y)/5 B) (x + 2y)/(x + y) C) (x + 2y)/(xy) D) 5(x + 2y) E) x + 2y

Solution: Total Cost = Weight(in pounds) * Price/pound;   To find Total cost/pound, Divide by total pounds.   Cost of Dried apricots = x;   Cost of prunes = 2y;   Cost per pound = (x + 2y)/5;   (x + 2y)/5ns is ((x + 2y)/5).
Answer: A
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?	Pick:	A) 12	B) 72	C) 48	D) 99	E) 11

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.75 + 1.25= 
1.75 + 1.25 = 3
3 km= 3000 m.   Required time = 3000 * 3/125= 
3000 * 3/125 = 72
72 sec.   Answer: 72
Answer: B
Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 1010000 and 10100000 ? Pick one.
A) 10  B) 11  C) 101  D) 1011  E) 10001

Solution: Binary Divison can provide a quick answer if you are comfortable with it.   as option E is the biggest binary number we try with it first :   100010000/ 101 =10000   1000100000/ 101 =100000   so answer is option is 101
Answer: C
An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,160, what was the total number of pairs of contact lenses that she sold?	Pick
A) 11 B) 13 C) 15 D) 17 E) 19

Solution: (x+5)*150 +x*85=2160   =>x=6   total lens=6+(6+5)= 
6+(6+5) = 17
17   Answer 17
Answer: D
One pump drains one-half of a pond in 2 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?  Choose the most appropriate option.
A) 1.3 hour  B) 1.2 hour  C) 3 hours  D) 5 hours  E) 6 hours

Solution: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.   We have the 1st pump working rate/hour = 1/2 : 2 = 1/4   Working rate of 2 pumps: 1/2 : 1/2 = 1.   Working rate of 2nd pump: 1 -1/4 = 3/4 --> Time taken for the 2nd pump to finish: 1 : 3/4 = 4/3 = 1.3 hours.   1.3 hour
Answer: A
Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 14 inches on a side and costs $10, and a large pizza that measures 21 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
Choose the correct option:
A) 5 square inches B) 10 square inches C) 49 square inches D) 25 square inches E) 350 square inches

Solution: In the first case each can buy one pizza of $10 and one pizza of $20.   In square inches that would be (14*14=196) for the small pizza and (21*21=441) for the large pizza. In total sq inches that would be  (196+441)*2= 
 (196+441)*2 = 1_274
1274 sq inches.   In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be   3*441= 
  3*441 = 1_323
1323 sq inches.   Hence, the difference is 49 square inches more (1323-1274).   The correct answer is 49 square inches
Answer: C
Find a sum for 1st 7 prime number's?  Choose the correct choice from the following options:  A) 25  B) 28  C) 58  D) 34  E) 36

Solution: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17)= 
(2 + 3 + 5 + 7 + 11 + 13 + 17) = 58
58   Note: 1 is not a prime number   Option 58
Answer: C
If x is a positive number and 2 the square root of x is equal to x/2, then x =	Choose the correct choice from the following choices.
A) 1/16 B) 4 C) 1 D) 2 E) 8

Solution: 2 of sqrt(x) = x/2, which means that sqrt(x) = x   or x = x^2 -> divide by x   1= x   x=1   1.
Answer: C
A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 4 more Blu-ray movies, that ratio would change to 13:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?	Choose the correct choice:
A) 22
B) 28
C) 77
D) 99
E) 234

Solution: if u can just keep an eye on the options   99 is the only multiple of 9 in options given .. SO you can mark it wid in seconds.   Now coming to the process m(D) = 7x and b(D) = 2x   now from the next line the new eqn becomes 7x/ (2x + 6) = 11/4   Solving it 28x = 26x + 52   x =11   which means m (d) = 182 and b(d) =52   SO total initially is m(d) + b(d) = 234   234
Answer: E
If seven persons sit in a row, then the probability that three particular persons are always together is? Choose one.
A) 1/5 B) 1/4 C) 1/9 D) 1/6 E) 1/7

Solution: Seven persons can be arranged in a row in 7! ways.   Treat the three persons to sit together as one unit then there five persons and they can be arranged in 5! ways.   Again three persons can be arranged among them selves in 3! ways.   Favourable outcomes = 3!5!   Required probability = 3!5!/7! = 1/7   Answer:1/7
Answer: E
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?	Choose one
A) 18 B) 16 C) 12 D) 10 E) 14

Solution: :   Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.   Answer: 12
Answer: C
If p is not equal to zero, and p+1/p = 5, then what is the value of p^4 + (1/p)^4? Pick one: A) 527 B) 247 C) 547 D) 527 E) 537

Solution: p + 1/p=5   we square both sides so we have p^2 + 1/p^2 +2 = 25   or p^2 + 1/p^2= 23   squaring again we have p^4 + 1/p^4 + 2 = 529   or p^4 + 1/p^4 = 527   answer =527 (527)
Answer: D
Doug bought bananas on sale for 5% off the original price and another 10% off the discounted price. If the final price was $5, what was the price before the first discount?	Choose the correct option.
A) $5.15
B) $5.35
C) $5.85
D) $6.14
E) $4.85

Solution: let x be the price before the first discount. The price after the first discount is x - 5%x The second discount was 10%, after which the final price was $5 (x - 5%x) - 10%(x - 5%x) = 5 Solve for x x = $5.85correct answer $5.85
Answer: C
Sequence W consists of 16 consecutive integers. If -6 is the least integer in sequence W, what is the range of the positive integers in sequence W?
Answers.
A) 16 B) 15 C) 9 D) 8 E) 7

Solution: Since set W consists of 16 consecutive integers and -6 is the least integer then set W is consecutive integers from -6 to 9, inclusive: 9-(-6)+1= 
9-(-6)+1 = 16
16.   The range of positive integers in sequence W is 9-1= 
9-1 = 8
8.   Answer: 8.
Answer: D
What is the product of all positive factors of 24?
Choose one:
A) 351776 B) 331476 C) 331776 D) 332976 E) 331776

Solution: Positive factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.   So product of all positive factors: 24*12*8*6*4*3*2= 
24*12*8*6*4*3*2 = 331_776
331776   Answer: 331776
Answer: E
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?  Pick:
A) 3	B) 4	C) 5	D) 8	E) 2

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer: 3
Answer: A
For any real number x, the operatoris defined as:
(x) = x(4 − x)
If p + 1 =(p + 1), then p = Choices
A) −4 B) 0 C) 1 D) 2 E) 3

Solution: (x) = x(4 − x)   (p + 1) = (p + 1)(4 - p - 1) = (3-p)(p+1)   We are given that p + 1 =(p + 1)   Therefore (3-p)(p+1) = (p + 1)   Or (p + 1) + (3-p)(p+1) = 0   (p + 1)(p-3) = 0   p = -1,p=3   Option 3
Answer: E
Three cards are randomly selected, one at a time (without return), from a standard deck of 52 cards. What is the probability that the last two of the three cards are spades? (Answer in lowest terms).
Choose the correct answer: A) 18/750 B) 19/750 C) 18/850 D) 39/850 E) 39/750

Solution: A standard deck has 52 cards of which 13/52 are spades, so the probability of not getting a spade is P(NS) = (52-13)/4 on the first selected card.   Because selection is (without return), the P(S) has changed for following selections. Now, there are 51 cards and number spades is dependent upon whether first card was a spade, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:   Formula = P(A\B) = P(A and B)/P(B).   P(A\B) = (39/52)(13/51)(12/50) = 6084/132600 = 39/850   Answer: 39/850
Answer: D
A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?  Choose the correct choice from the following options
A) 7	B) 6	C) 5	D) 2 pineapples	E) 3

Solution: Explanation:   The equation for this problem can be made as:   5x + 7y =38   Where x is the number of watermelons and y is the number of pineapples.   Now test for 2, 3 and 4:   For y = 2   5x + 14 =38   x is not an integer   For y = 3   5x = 17   X not an integer   For y =4   X = 2   So 4 pineapples and 2 watermelons can be bought by 38 Rs.   ANSWER:2 pineapples
Answer: D
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest?	Choose one
A) The average (arithmetic mean) of set S  B) The median of set S  C) The mode of set S  D) The range of set S  E) The standard deviation of set S

Solution: A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is   749/7= 
  749/7 = 107
107.   B) The list is of 7 numbers and median is 105.   C) Mode is number of repetition of a number in the list , here it is 100.   D) Range= Max value - min value = 124 -99= 
124 -99 = 25
25.   E) SD= square root of (sum of ( mean of series - number)^2 ) / n => < 100   IMO option The average (arithmetic mean) of set S is correct answer..
Answer: A
If f(x)= 2x^2- 3x+5 and g(y)= 2y-4, then g(f(x)) Choices
A) 7x^2+45x+9	B) 9x^2-15x+4	C) 4x^2-6x+6	D) 8x^2-9x+6	E) 9x^2+79x+78

Solution: g(f(x)) = 2(f(x)) -4   =2(2x^2-3x+5)-4   =4x^2-6x+10-4   =4x^2-6x+6   the answer is 4x^2-6x+6
Answer: C
Jack and Dick work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Dick will both be chosen?  Choose the correct choice from the following options
A) A)1/3 B) B)1/4 C) C)1/15 D) D)3/8 E) E)2/3

Solution: Total number of people = 6   Probability of selecting Jack first and then Dick is 1/6∗1/5=1/30   Probability of selecting Dick first and then Jack is 1/6∗1/5=1/30   Therefore probability of selecting Jack and Dick for the review is 1/30+1/30=1/15   Answer is 1/15
Answer: C
In how many a committee of 5 members can be selected from 6 men 5 ladies consisting of 3 men and 2 ladies  Choose the most appropriate option
A) 250
B) 150
C) 100
D) 50
E) 200

Solution: (3 men out of 6) and (2 ladies out of 5) are to be chosen   Required number of ways   =(6C3 * 5C2)   = 200   ANSW200R 200
Answer: E
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 3300 in all from both of them as interest. The rate of interest per annum is?  Choose the correct choice
A) 16%
B) 12%
C) 74%
D) 10%
E) 15%

Solution: Let the rate be R% p.a. Then,   (5000 * R * 2)/100 + (3000 * R * 4)/100 = 3300   100 R + 120 R = 3300   R = 15%   Answer:15%
Answer: E
Sripad has scored average of 60 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?	Choose the correct choice from the following:	A) 79	B) 64	C) 38	D) 27	E) 21

Solution: Assuming Sripad has scored the least marks in subject other than science,   Then the marks he could secure in other two are 58 each.   Since the average mark of all the 3 subject is 60.   i.e (58+58+x)/3 = 60   116 + x = 180   x = 64 marks.   Therefore, the maximum marks he can score in maths is 64.   Answer: 64
Answer: B
(a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression?	Choices: A) 8/2 B) 2/4 C) 1/8 D) 2/4 E) 4/6

Solution: (a/2)/(b/c)   = (a*c)/2b   The expression will have the largest value when numerator (a*c) is the largest.   = (2*4)/2*1   =8/2   8/2nswer 8/2
Answer: A
Find the unit's digit in (264)^102 + (264)^103 Choose the correct option
A) 0
B) 2
C) 5
D) 3
E) 4

Solution: Required unit's digit = unit's digit in (4)^102 + (4)^103.   Now, 4^2 gives unit digit 6.   (4)102 gives unjt digit 6.   (4)103 gives unit digit of the product (6 x 4) i.e., 4.   Hence, unit's digit in (264)m + (264)103 = unit's digit in (6 + 4) = 0.   0nswer is 0
Answer: A
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 40 m long and 16 1/2 m board? Pick:  A) 99  B) 132  C) 16  D) 10  E) 15

Solution: 40 * 33/2 = 5/2 * 2 * x => x   = 132   Answer:132
Answer: B
If x is an integer and (x)(x^2)(x^3)(x^4) is positive, which of the following could be negative? Choose the correct answer.
A) x^4  B) (x)(x^3)  C) (x)(x)  D) 3x^2  E) x + x^5

Solution: A) X^4 - always positive (or 0).   B) X(X^3) = X^4 - Again always positive (or 0).   C) (x)(x) = X^2 - Again always positive (or 0).   D) 3X^2 - again always positive (or 0)   E) x+x^5 - Could be -ve if x is -ve.   Answer x + x^5.
Answer: E
Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $8,500, what is the bonds face value?	Choose the correct choice from the following answers
A) $6,000 B) $6,800 C) $7,425 D) $7,500 E) $9,375

Solution: Interest = 0.05*face value = 0.04*8,500 --> face value = 0.04*8,500/0.05 = 6,800.   Answer: $6,800.
Answer: B
What will be the compound interest earned on an amount of Rs. 5000 in 2 years?
I.	The simple interest on the same amount at the same rate of interest in 5 years is Rs. 2000.
II.	The compound interest and the simple interest earned in one year is the same.
III.	The amount becomed more than double on compound interest in 10 years.  Choices:
A) I only
B) I and II only
C) II and III only
D) I and III only
E) None of these

Solution: EXPLANATION   P = Rs. 5000 & T = 2 years.   I. S.I. on Rs. 5000 in 5 years is Rs. 2000.   5000 x R x 5/ 100 = 2000 = R = 8   Thus I only gives the answer.   answer is (I only).
Answer: A
A polling company reports that there is a 20% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?  Choices:
A) 10	B) 8	C) 6	D) 4	E) 5

Solution: 20% - Candidate Elected   100%-60% = 40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   20% x 40% x 50%   0.2 x 0.4 x 0.5 100 -60= 
100 -60 = 40
40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   20% x 40% x 50%   0.2 x 0.4 x 0.5= 0.04 = 4%   Answer (4)
Answer: D
Two pipes A and B can fill a cistern in 22 and 44 minutes respectively, and a third pipe C can empty it in 48 minutes. How long will it take to fill the cistern if all the three are opened at the same time? Choose one
A) 18 1/9 min	B) 21 1/8 min	C) 21 3/25 min	D) 18 8/7 min	E) 19 3/7 min

Solution: 1/22 + 1/44 - 1/48   =25/528   528/25 = 21 3/25   Answer:21 3/25 min
Answer: C
How many positive integers will divide evenly into 230? Pick
A) 4  B) 6  C) 8  D) 12  E) 16

Solution: The question is asking how many factors 230 has.   230 = 2*5*23   The number of factors is 2^3 = 8   The answer is 8.
Answer: C
Find the next number in the Sequence
8, 18, 48, 98, ?	Choose the correct choice from the following options:  A) 163  B) 368  C) 169  D) 162  E) 168

Solution: +10 =>18   +30 =>48   +50 =>98   +70 =>168   Answer is 168
Answer: E
If $0.40 is the commission for sales of $1,000, what percent of the sales amount is the commission? Choose one.
A) 4% B) 0.4% C) 0.04% D) 0.004% E) 0.0004%

Solution: % of sales amount of commission   = (0.04%ommission/Total Value) *100   = (0.4/1000) * 100= 
(0.4/1000) * 100 = 0.04
0.04%   The answer is 0.04%.
Answer: C
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Choose the correct option
A) 2.6
B) 2.0
C) 2.5
D) 2.1
E) 2.3

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5.Answer: 2.5
Answer: C
A problem in mathematics is given to three students A, B and C whose chances of solving it are 1/2, 3/4 and 1/4 respectively. What is the probability that the problem will be solved if all of them try independently.  Pick one.
A) 29/32 B) 30 C) 31/33 D) 31/35 E) 33

Solution: The probability that the problem is not solved by any of them:   (1 - P(A))*(1 - P(B))* (1 - P(C)) = (1 - 1/2)(1 - 3/4)(1 - 1/4) = 1/2*1/4*3/4 = 3/32   Hence, the probability that the problem will be solved is   1 - 3/32 = 29/32.   29/32)
Answer: A
Large number of people went to an party and they decided to make some fun at the bar.
The first person asks the barman for half a pint of beer.
The second person asks for a quarter pint of beer
The third person asks for one-eighth of beer and so on ...
How many pints of beer will the barman need to fulfill the people need of beer ? Select
A) 1  B) 3  C) 6  D) 2  E) 8

Solution: 1   Just 1
Answer: A
Mr. CRUISE invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $200,000. In one year, Fund X paid 48% and Fund Y paid 23%. The interest earned in Fund Y was exactly $100 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X? Options
A) 34,234.78  B) 56,566.24  C) 34,565.54  D) 48,343.45  E) 69,545.45

Solution: X+Y=200,000   0.23Y=0.48A+100   Take away decimals first: 23Y+48X+10,000   Isolate first equation to solve for X (your goal): Y=200,000-Y   Plug in for B:   23(200,000-X)=43X+10,000   4,600,000-23X=43X+10,000   4,590,000=66X   4,590,000/66=X   X=69,545.45=Answer Choice 69,545.45
Answer: E
What will come in place of the x in the following Number series? 1. 0, 6, 24, 60, 120, 210, x Choose the correct option.
A) 336 B) 430 C) 530 D) 560 E) 609

Solution: (336)   The given series is : 13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6,   So the missing term = 73 – 7 = 343 – 7 = 336
Answer: A
The distance traveled by Helicopter in one year approximately 750,000,000 miles.The distance traveled by helicopter in 15 years? Choose the correct answer:	A) 10<4>	B) 10<6>	C) 10<7>	D) 10<9>	E) 10<16>

Solution: The distance traveled by Helicopter in one year = 75,000,000 miles   The distance traveled by Helicopter in 15 years =75,000,000 miles * 15 years = 1125000000   = 1125*10<6> (exponent miles) Answer =10<6>
Answer: B
A does a work in 10days and B does the same work in 15days. In how many days they together will do the same work?
Select
A) 3	B) 5	C) 6	D) 8	E) 10

Solution: A+B can finish =AB/A+B = 10*15/(10+15)= 
10*15/(10+15) = 6
6days   Answer is 6
Answer: C
A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements?	Select.
A) 2^(2k-2)
B) 2^(2k) - 2
C) 2^(2k) -1
D) 2^(2k)
E) 2^(2k-1)

Solution: I used k=3, so then we have   5!/2!3! + 5!/4!1! + 5!/0!5!    10 + 5 + 1= 
 10 + 5 + 1 = 16
16   So our target is 16   Now replace in answer choices   2^(2k-2) gives us 2^4= 16   Hence 2^(2k-2) is the correct option   Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes   2^(2k-2)void 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties
Answer: A