MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit?	Options
A) 310	B) 320	C) 330	D) 340	E) 350

Solution: Ratio of the initial capital of A and B = 4 : 5   Hence we can take the initial capitals of A and B as 4x and 5x respectively   Ratio in which profit will be divided   =((4x)3)+(3/4)×(4x)7 :((5x)3)+4/5×(5x)7   =(12+21):(15+28)   =33:43   A's share =760×33/76=330   Answer is 330.
Answer: C
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km. Answers.
A) 16 B) 18 C) 24 D) 19 E) 12

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 3x/(x/8) = 24 kmph   Answer: 24
Answer: C
If the product of the integers from 1 to n is divisible by 686, what is the least possible value of n?	Pick one.
A) 7
B) 14
C) 21
D) 28
E) 35

Solution: 686 = 7 x 7 x 7 x 2   N must include at least 7, 2*7, and 3*7.   The answer is 21.
Answer: C
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:	Choose the correct choice from the following options:
A) 10
B) 15
C) 26
D) 87
E) 30

Solution: Explanation:   Let the total number of shots be x. Then,   Shots fired by A =5/8 x   Shots fired by B =3/8 x   Killing shots by A=1/3 of 5/8x=5/24x   Shots missed by B=1/2 of3/8x=3/16x   3/16x=27   x=(27x16/3)=144   Birds killed by A=5/24x=(5/24x144)=30   Answer is 30
Answer: E
Due to construction, the speed limit along an 5-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?	Choose the correct choice from the following answers.
A) 3.12 B) 8 C) 10 D) 15 E) 24

Solution: Old time in minutes to cross 5 miles stretch = 5*60/55 = 5*12/11 = 5.45   New time in minutes to cross 5 miles stretch = 5*60/35 = 5*12/7 = 8.57   Time difference = 3.12   3.12ns:3.12
Answer: A
If two integers between –5 and 3, inclusive, are chosen at random, which of the following is most likely to be true? Choose the correct choice from the following
A) The sum of the two integers is even B) The sum of the two integers is odd C) The product of the two integers is even D) The product of the two integers is odd. E) The product of the two integers is negative

Solution: 1. The sum of the two integers is even and 2 sum of two integers odd   for sum to be odd -- 5c1*4c1/9c2 = 20/36 thus for even 1-(20/36) = 16/36   3,4 product of two integers even/odd --   for integers to be odd ---- 5c2/9c2 = 52/72 for even 1-52/72 = 20/72   5 for product to be negative -- 0 will not be taken into account. Hence 8 numbers is the set.   5c1 * 3c1/ 8c2 = 15/28   thus comparison is between b 20/36, c 52/72 e 15/28   C is greatest since 52 is much closer to 72 hence much greater than 1/2. 20/36 and 15/28 are much closer to 1/2 though.   Thus The product of the two integers is even.
Answer: C
6x − 12 = 6y
6y + 6x = 18
Which of the following is the number of solutions to the system of equations shown above?
Choose the correct choice from the following.
A) More than three
B) Exactly three
C) Exactly two
D) Exactly one
E) None

Solution: 6x − 12 = 6y   => 6x - 6y = 12   => x- y =2 -- 1   6y + 6x = 18   =>x + y = 3 -- 2   From equation 1 and 2 , we get   2x = 5   => x=2.5   y=.5   Therefore , the given system will have Exactly one solution   Answer : Exactly two
Answer: C
The price of 3 pants and 6 t-shirts is Rs. 1500. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ?
Pick one.
A) 700	B) 300	C) 250	D) 550	E) 800

Solution: Let the price of a pant and a t-shirt be Rs. x and Rs. y respectively.   Then, 3x + 6y = 1500 .... (i)   and x + 12y = 1500 .... (ii)   Divide equation (i) by 3, we get the below equation.   = x + 2y = 500. --- (iii)   Now subtract (iii) from (ii)   x + 12y = 1500 (-)   x + 2y = 500   ----------------   10y = 1000   ----------------   cost of 8 t-shirts = 8*100= 
8*100 = 800
800   Answer : 800
Answer: E
There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
A. 17 B. 29 C. 23 D. 31	Choose the correct choice:
A) 17  B) 29  C) 23  D) 31  E) 33

Solution: (7429/12673) = 17/29 Fourth Number is 29   ANSWER:29
Answer: B
Four pipes fill a cistern in 15,20,30 and 60 hours.The first was opened at 6 am,the second at 8 am,third at 10 am and fourth at noon.When will the reservoir be full? Choose the correct choice from the following answers:
A) 1PM B) 2PM C) 3PM D) 4PM E) 5PM

Solution: If the cistern was filled after x hrs from 6 AM, Then   x/15 + (x-2)/20 + (x-4)/30 +(x-6)/60 =1   solving , we get   x=8 hrs   2PM   ANSWER:2PM
Answer: B
John and David were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 40 days of the festival, while David performed on 5 fewer days than John performed. If David gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?	Choose the correct answer:  A) 10Y  B) 12Y  C) 15Y  D) 18Y  E) 24Y

Solution: Both of them were given X $ each   David to adjust Y $ in advance to John   So David now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same   So Rate of David= Rate of John   Also , David works for 35 days and John works for full 40 days   (X-Y) / 35 = (X+Y) / 40   Solving 40x-40y=35x+35y =>5x=75y => x=75/5= 
75/5 = 15
15Y   Answer : 15Y
Answer: C
A man can row 11 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man? Choose the correct option.
A) 6.24 km B) 6 km C) 5.76 km D) 5.66 km E) 10.87 km

Solution: M = 11   S = 1.2   DS = 12.2   US = 9.8   x/12.2 + x/9.8 = 1   x = 5.43   D = 5.43 * 2 = 10.87   ANSW10.87 kmR:10.87 km
Answer: E
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Choose the correct choice from the following options
A) 22
B) 88
C) 12
D) 87
E) 29

Solution: D = 250 m + 250 m = 500 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 500 * 3/125= 
500 * 3/125 = 12
12 sec   Answer: 12
Answer: C
The salaries of A,B and C are in the ratio 2:3:5. If the increments of 15%,10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
Select the correct option.
A) 11:23:55	B) 23:33:60	C) 15:45:66	D) 23:59:77	E) 15:63:71

Solution: Let A = 2k   23:33:60 =3k   C = 5k   A's new salary = 115/00 of 2k = 23/10 k   23:33:60's new salary = 110/100 of 3k = 110/100 * 3k = 33/10 k   C's new salary = 120/100 of 5k = 120/100 * 5= 
120/100 * 5 = 6
6k   New ratio= 23k/10 : 33k/10 : 6k = 23:33:60   Answer is 23:33:60
Answer: B
A 6% stock yields 8%.The market value of the stock is : Select
A) Rs. 48	B) Rs. 75	C) Rs. 96	D) Rs. 133.33	E) None

Solution: Solution   For an income of Rs. 8, investment = Rs. 100.   For an income of Rs. 6, investment = Rs.(100/8x6) = Rs. 75.   ∴ Market value of Rs.100 stock = Rs. 75.   Answer Rs. 75
Answer: B
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ? Select:
A) 32
B) 76
C) 29
D) 27
E) 11

Solution: Explanation:   The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.   The first 24 of these words will start with A.   Then the 25th word will start will CA _ _ _.   The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.   The next word starts with CH and then A, i.e., CHA _ _.   The first of the words will be CHAMS. The next word will be CHASM.   Therefore, the rank of CH32SM will be   24+6+2= 
  24+6+2 = 32
32   32nswer: 32) 32
Answer: A
If 10^(c-1)< 0.000125 <10^c, what is the value of an integer c?
Select the correct option:
A) -4  B) -3  C) -2  D) 3  E) 4

Solution: -> Multiply 10^6- > (10^6){10^(c-1)}<125<(10^6)(10^c) -> 125 is bigger than 100   -> (10^6)(10^(c-1))=100 -> 10^(6+c-1)=10^2, c+5=2 -> c=-3   Thus, the answer is -3
Answer: B
The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is  Choose one.
A) 88  B) 28  C) 55  D) 25  E) 71

Solution: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9   =( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9   = (4 * 110 + 55)/9 = 495 / 9= 
495 / 9 = 55
55   Answer: 55
Answer: C
If there is exactly one root of the equation 2x^2 + ax + b, where a and b are positive constants, what is b in terms of a? Choose one:
A) a/2  B) a  C) 3a/2  D) a^2/8  E) a^2/4

Solution: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1   Here b = a   c= b   a = 2   substituting these values in 1, we have   a^2 = 8b => b =a^2/8   Answer is a^2/8.
Answer: D
Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 40% Vermouth by volume. How many ounces of Gin must he add?  Choose the correct choice from the following:
A) 0
B) n/3
C) 3n/5
D) 5n/6
E) 8n/5

Solution: 4 ounces is vermouth   6 ounces of gin...   Total volume 10.   To make vermouth account for 40% of total volume the new volume must be....   x*0.4=4   x=10 ounces....   So now you see that he must add 0 ounces of gin...   Plug in 0 for n in the answer choices and look for answer 0   0
Answer: A
If n = 30! + 25, then n is divisible by which of the following?
I. 25
II. 27
III. 29 Pick one:  A) None  B) I only  C) II only  D) I and II  E) II and III

Solution: 25 divides 30! so 25 also divides 30! + 25.   27 and 29 divide 30! so they do not divide 30! + 25.   The answer is I only.
Answer: B
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Answers:
A) 288  B) 375  C) 267  D) 298  E) 121

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375   Answer: 375
Answer: B
Insert the missing number
2, 4, 8, 16, ..., 64, 128, 256  Select:
A) 36
B) 35
C) 32
D) 33
E) 38

Solution: series is 2* Previous Number.   ANSWER:32
Answer: C
Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer E between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? Choose the correct option: A) 12 B) 15 C) 17 D) E=18 E) 20

Solution: Since we are concerned with integers between 1 and 20, write down the primes till 40.   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37   (you should be very comfortable with the first few primes... )   2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)   2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)   2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)   2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)   2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.   Answer (E=18).
Answer: D
The price of 2 skirts and 4 shirts is Rs. 1600. With the same money one can buy 1 skirt and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? Answers:
A) Rs. 2300 B) Rs. 2400 C) Rs. 2420 D) Rs. 2460 E) Rs. 2480

Solution: Let the price of a skirt and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Rs. 2400
Answer: B
A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
Choose the correct choice:
A) 80 cm  B) 10 cm  C) 70 cm  D) 60 cm  E) 20 cm

Solution: The volume of a rectangular prism is given by   area of base ? height   The rate at which the tank is being filled is 1 liter per minute which we need to convert   1 liter = 1 dm3   But 1 dm = 10 cm. Hence   1 liter = (10 cm)3 = 1000 cm3   The height h of the water is related to the volume by   volume = area of base ? h   In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by   h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm   correct answer 10 cm
Answer: B
Wendy begins sanding a kitchen floor by herself and works for 3 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?	Choose the correct option:
A) 9/80 hours B) 3/20 hours C) 20/3 hours D) 80/9 hours E) 506/91 hours

Solution: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.   Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.   If wendy works for 3 hours and is then joined by Bruce to finish the work in 2 more hours,   3/W + 2/W+2/B = 1 (1 denotes the total amount of work)   5/W + 2/B =1 and given B =20 hours.   Thus W = 506/91 hours , 506/91 hours is the correct answer.
Answer: E
A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have? Choose the correct choice from the following answers.
A) 576 B) 800 C) 726 D) 484 E) 500

Solution: (4/15) * A = (2/5) * B   A / B = 3 / 2   Therefore A's share is = (1210 * (3/5))= 
(1210 * (3/5)) = 726
726   Ans - 726
Answer: C
How many randomly assembled people do u need to have a better than 50% probability that at least 1 of them was born in a leap year?  Choose the correct choice from the following choices:  A) 3  B) 9  C) 27  D) 54  E) 81

Solution: Prob[at least one of them was born in a leap year] > 50%   Since P(A) = 1 - P(A')   1 - Prob[none of them was born in a leap year] > 1/2   Prob[none] - 1 < -1/2   Prob[none] < 1/2   Assume that there are n people.   Prob[none] = (3/4)^n   (3/4)^n < 1/2   3^n < (4^n)/2   3^n < (2^2n)/2   3^n < 2^(2n-1)   If n = 3, 3^3 < 2^5 is true   3 is the answer
Answer: A
A company has found that when x units of a product are manufactured and sold, its revenue is given by x 2 + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars? (HINT: profit = revenue - costs)  Choose one.
A) 192  B) 193  C) 194.  D) 195  E) 196

Solution: Let us use profit = revenue - costs to find a formula for the profit P   P = ( x 2 + 100 x ) - ( 240 x + 500 )   Substitute P in the above equation by 10,000 dollars to obtain   10000 = x 2 - 140 x - 500   Write the equation in standard form and solve for x   x 2 - 140 x - 10500 = 0   Solve the above equation for x   x = 194.10 and x = -54.01   The number of units to produce must be positive, so   x = 194.   As an exercise, check that for the above value of x the profit is approximately (because of the rounding) equal to 10,000.   Answer 194.
Answer: C
If |5x-20| = 100, then find the sum of the values of x?
Choose the correct choice from the following answers
A) 1
B) -2
C) 8
D) -3
E) 4

Solution: |5x-20| = 100   5x-20 = 100 or 5x-20 = -100   5x = 120 or 5x = -80   x = 24 or x = -16   sum = 24-16= 
24-16 = 8
8   Answer is 8
Answer: C
The average weight of 25 boys sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys? Select the correct option.
A) 150 B) 154 C) 176 D) 182 E) 192

Solution: 25x + 46 = 26(x – 5)   x = 176   176
Answer: C
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?
Choose the correct answer:
A) 4/9	B) 5/9	C) 2/9	D) 3/8	E) 5/3

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer:5/9
Answer: B
Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756  Choose the correct choice:
A) 15 B) 16 C) 34 D) 424 E) 2124

Solution: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1= 
15 *1 + 1 = 16
16.   3rd term= (2nd term) * 2 + 2 = 16 * 2 + 2= 
16 * 2 + 2 = 34
34   4th term= (3th term) *3 + 3 = 34 * 3 + 3= 
34 * 3 + 3 = 105
105   5th term= (4th term) * 4 + 4 = 105 * 4 + 4= 
105 * 4 + 4 = 424
424   6th term= (5th term) * 5 + 5 = 424 * 5 + 5= 
424 * 5 + 5 = 2_125
2125   6th term should 2125 instead of 2124.   2124
Answer: E
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? Choose the correct choice from the following options
A) 29	B) 86	C) 25	D) 18	E) 12

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 28   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   86 + 86 -28= 
86 + 86 -28 = 144
144   86= (144 + 28)/2= 
(144 + 28)/2 = 86
86   Answer:86
Answer: B
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 36,000, what will be the amount A receives?	Answers
A) 15120  B) 14500  C) 14900  D) 14300  E) 14000

Solution: Total amount invested = 50000   Assume that investment of C =x.   Then investment of B =5000+x,   Investment of 15120 =4000+5000+x=9000+x   x+5000+x+9000+x=50000   ⇒3x+14000=50000   ⇒3x=50000–14000=36000   ⇒x=36000/3= 
36000/3 = 12_000
12000   Investment of C=x=12000   Investment of B =5000+x=17000   Investment of 15120 =9000+x=21000   Ratio of the investment of 15120, B and C   =21000:17000:12000   =21:17:12   Share of 15120 = Total profit ×21/50   =36000×21/50=15,120   15120nswer is 15120.
Answer: A
There are 60 slots around a circle,numbered 1 to 60. A man starts fromthe first slot and jumps to the 5th slot.From there he jumps to the 9th slot andso on. In which slot will he land in his 2200th jump?
Select the correct option:	A) 1	B) 5	C) 41	D) 45	E) 46

Solution: every 15th jump, he comes back to 1st position   so, 2200/15 = Remainder 10   Hence 10th position is 41st slot   ANSWER:41
Answer: C
The age of the daughter is same as the digit in the mother's age, but in reverse order. In thirteen years mother will be twice as old as daughter will be then. what is the difference in their current age ? Choose the correct choice from the following answers:
A) 15	B) 23	C) 27	D) 46	E) 32

Solution: daughter's age= 10x+y   so mother's age= 10y+x..   after 13 years , 10x+y+13=2*(10y+x+13)....   so 13+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=4... so ages are 41 and 14 and ans as found correctly by u is 27..27
Answer: C
What is the solution of the equations x - y = 5 and 5(x + y)-1 = 2 ?	Pick one:
A) x = 3.75, y = 1.25 B) x = 1, y = 0.1 C) x = 2, y = 1.1 D) x = 1.2, y = 0.3 E) None

Solution: x = 3.75, y = 1.25nswer   x - y = 5 ...(i)   and 11(x + y)-1=2   ⇒ 5/ (x + y) = 2   ⇒ 2(x + y) =5   ⇒ x + y = 5/2 ...(ii)   On solving Eqs.(i) and (ii),we get   x = 3.75   and y = 1.25   Correct Option: x = 3.75, y = 1.25
Answer: A
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in?  Choose the correct answer
A) 144 min	B) 250 min	C) 196 min	D) 100 min	E) 112 min

Solution: Let the slower pipe alone fill the tank in x minutes   Then, faster pipe will fill it in x/3 minutes   1/x + 3/x = 1/36   4/x = 1/36   x = 144 min   144 minnswer is 144 min
Answer: A
Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $33. What was the percentage profit? Choose the correct choice from the following answers:
A) 5% B) 6% C) 8% D) 10% E) 12%

Solution: A dozen toys cost $360, so each toy cost $30.   selling price / cost price = 33/30= 
33/30 = 11/10 = around 1.1
1.1   The percentage profit is 10%.   The answer is 10%.
Answer: D
How many pairs of letters are there in the word 'CASTRAPHONE' which have as many letters between
them in the word as in the alphabet?  Choose the correct answer.
A) 8	B) 7	C) 6	D) 4	E) 3

Solution: Looking into the alphabets there are four such pairs namely ON,EH,ST,TO.   Answer: 4
Answer: D
If a wooden bar of length 45 feet is cut into two pieces, what is the length of the shorter piece if the longer bar is 15 feet longer than the shorter bar?
Choose the correct choice from the following answers
A) 7  B) 10  C) 13  D) 16  E) 15

Solution: Since, 45 is the total length. Shorter is any one from answers.   Try Back solving from D answer, i.e. 16. 16+(16+15) = 47 > 45   Hence, Select next smaller no. : 15 +(15+15)= 
15 +(15+15) = 45
45. So, 15 is the answer   Answer is 15
Answer: E
A train speeds past a pole in 12 seconds and a platform 160 m long in 17 seconds. Its length is?  Options:  A) 384  B) 360  C) 324  D) 390  E) 395

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 12 => y = x/12   x + 160 / 17 = x / 12   x = 384 m.   384nswer:384
Answer: A
Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked three 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?  Pick one:
A) 280
B) 300
C) 240
D) 350
E) 400

Solution: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.   Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).   Jill has worked for 3 days -> 80*3=240.   This matches answer choice 240.
Answer: C
Three integers are at random chosen between 0 and 9 inclusive. What is the probability E that each number is different ?
Choose the correct choice:
A) A.18/25
B) B.4/5
C) C.81/100
D) D.9/10
E) E.1

Solution: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10   Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8   Probability E= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25   A.18/25nswer: A.18/25
Answer: A
A larger hose connected to a swimming pool can fill the pool in 6 hours. A smaller hose can fill the pool in 12 hours. How many hours will it take for both of them to fill the pool? Choose one
A) 3  B) 7 1/2  C) 5 3/5  D) 8  E) 4

Solution: Work hrs=AB/(A+B)= 72/18= 
72/18 = 4
4   Answer is 4
Answer: E