MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:	Pick:	A) 45 km/hr	B) 55 km/hr	C) 35 km/hr	D) 50 km/hr	E) 56 km/hr

Solution: Speed of the train relative to man =125/10	m/sec   25/2	m/sec.   25/2	x 18/15	km/hr   = 45 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.   x - 5 = 45 x = 50 km/hr. Answer : 50 km/hr
Answer: D
What is the probability of getting a number less than 4 when a die is rolled? Pick:
A) 2
B) 1
C) 3/2
D) 2/3
E) 1/2

Solution: Total number of outcomes possible when a die is rolled=6   That is any one face out of the 6 faces is n(s)=6   e=getting a number less than 4={1,2,3}.   Hence,n(e)=3   p(e)=n(e)/n(s)   =3/6=1/2   Answer:option 1/2
Answer: E
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is	Choose the most appropriate option.
A) 1/20	B) 1/26	C) 1/23	D) 1/50	E) 1/45

Solution: Total no of cases = 52   fav cases = 2   prob = 2/56 = 1/26   ANSWER 1/26
Answer: B
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 22nd term in the sequence? Choose the correct choice from the following choices:
A) 4
B) 7
C) 6
D) 8
E) 9

Solution: Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below   02,07,22,67, 202, 607, 1822, 5467...   Observe the last two digits of the sequence which have the cyclicity of 4 and the last two digits repeat in the order {02, 07, 22, 67}   Also 22th Term =4*5 +2   i.e. 35th Terms will have same Last two digits as 2 nd term of the sequence = 07   i.e. Sum of lat two digits of 2ndth Term = 0+7= 
0+7 = 7
7   7
Answer: B
Two trains start from stations A and B spaced 50 kms apart at the same time and speed. As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the first train. This is repeated till the trains collide. If the speed of the trains is 25 km/h and that of the bird is 100 km/h. How much did the bird travel till the collision. Select the correct option:
A) 100
B) 288
C) 127
D) 27
E) 2691

Solution: ince the trains is travelling at 25 kmph, at each other, the relative speed is 50 kmph.   Speed = 50 kmph   Distance = 50 km   Time to collision = distance / speed = 1 hr   Speed of bird = 100 kmph   Time flying = 1 hr (the bird is flying till the trains collide)   Distance travelled = speed × time = 100 km   100nswer:100
Answer: A
S1 = 6 S2 = 9 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?  Select:  A) 14  B) 12  C) 13  D) 16  E) 15

Solution: term 16 = 3*16+4= 
3*16+4 = 52
52   Answer : 16
Answer: D
The distance between Delhi and Mathura is 215 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? Pick one:
A) 10.50 a.m.  B) 00.20 p.m.  C) 10.30 a.m.  D) 11.40 a.m.  E) 1.40 p.m.

Solution: D = 215 â€“ 20 = 195   RS = 20 + 25= 
20 + 25 = 45
45   T= 195/45 = 4 1/3 hours   8 a.m. + 4 hrs 20 min = 00.20 p.m.   ANSWER:00.20 p.m.
Answer: B
A, B and C can do a work in 9 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work? Answers.
A) 3 3/23
B) 3 3/28
C) 2 2/0
D) 2 2/2
E) 2 2/1

Solution: Work done by all three of them in one day = 1/9 + 1/8 + 1/12 = 23/72.   The number of days required = 72/23 = 3 3/23 days.   3 3/23nswer:3 3/23
Answer: A
If an integer "k" is divisible by 2,5 and 13.what is the next largest number that is divisible by all the three given numbers?	Choose the correct option
A) k+13 B) k+130 C) 2k D) 2k+13 E) 2k+65

Solution: LCM of 2,5,13 is 130   so k=130   2k also the correct answer,but we need to find next largest number   therefore ans is k+130   ANSWER:k+130
Answer: B
If the number of boys in a class are 8 times the number of girls. If the number of people in the class are 45, how many girls are in the class?  Choose the most appropriate option.
A) A - 5  B) B - 6  C) C - 7  D) D - 8  E) E - 9

Solution: Let the number of girls = x and the number of boys = 8x Then, total number of students = x + 8x = 9x = 45Hence, x = 45/9= 
45/9 = 5
5 i.e., the total number of girls in the class are 5. A - 5nswer is A - 5.
Answer: A
Eric throws 2 dice,and his score is the sum of the values shown.Sandra throws one dice and her score is the square of the value shown. what is the probabilty that Sandras score will be strictly higher than Erics score??	Options.
A) 117/216
B) 127/126
C) 137/126
D) 147/126
E) 157/126

Solution: sandra score can be like 1,4,9,16,25,36   eric score less then 1-->0   eric score less then 4=(1,1),(1,2)(2,1)-->3   eric score less then 9 are (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(5,1)(5,2)(5,3)(6,1)(6,2)-->26   eric score will always be less then 16--->36   eric score will always be less then 25--->36   eric score will always be less then 36--->36   total favorable outcomes=3+26+36+36+36= 
3+26+36+36+36 = 137
137   total possible outcomes=216(36*6)   probability=137/216   ANSWER:137/126
Answer: C
Two spies agreed to meet at a gas station between noon and 1pm, but they have both forgotten
the arranged time. Each arrives at a random time between noon and 1pm and stays for 6
minutes unless the other is there before the 6 minutes are up. Assuming all random times are
equally likely, what is the probability that they will meet within the hour (noon to 1pm)?
Answers:
A) 0.12  B) 0.15  C) 0.17  D) 0.19  E) 0.25

Solution: The probability that they do not meet is represented by the total of the areas of the   two outer triangles in the figure below, which is 0.81. So the probability of a meeting is 1 -   0.81 =0 .19.   correct answer 0.19
Answer: D
Raja's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
Select:
A) 5 B) 7 C) 8 D) 10 E) 12

Solution: Raja's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.   Hence only M is 8. Now we need to consider only S, (S n R) and R.   (M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.   30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.   22 = (12-x) + (5-x) + x + Neither.   Now the max value of x could be 5 and the min value of x could be 0.   When x is 5 (max), Neither is 10.   When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.   Answer 10 (10).
Answer: D
The sum of the present ages of a father and his son is 50 years. five years ago, father's age was five times the age of the son. After 5 years, son's age will be:  Select the correct option
A) 16
B) 16.2
C) 16.1
D) 16.66
E) 17

Solution: Let the present ages of son and father be x and (50 -x) years respectively.   Then, (50 - x) - 5 = 5(x - 5)   45 - x = 5x - 25   6x = 70   x = 70/6= 11.66 years   Son's age after 6 years = (x+ 5) = 16.66 years.   answer :16.66
Answer: D
A committee of two people is to be chosen from 4 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? Pick.
A) 16	B) 24	C) 26	D) 30	E) 32

Solution: One of the approaches:   Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 4 to send only onerepresentativesto the committee: 4C2=6.   But each of these 2 couples can send two persons (husband or wife): 2*2=2^2=4.   Total # of ways: 4C2*2^2=24.   Answer: 24.
Answer: B
There are 2 sections A and B in a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, Find the average of the whole class? Choose the correct option:
A) 35.29kg	B) 37.25kg	C) 42.45kg	D) 55.12kg	E) 29.78kg

Solution: Total weight of 36+44 students = 36*44 + 44*35 = 2980   Average weight of the class is = 2980/80= 
2980/80 = 149/4 = around 37.25
37.25 kg   Answer is 37.25kg
Answer: B
Of 25 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
Choose the correct choice from the following options:	A) 14	B) 10	C) 9	D) 7	E) 5

Solution: set A : people with more than 4 years exp   set 10 : people with degree   AU10 = total - (less than 4 exp and no degree)   AU10 = 25-3= 
25-3 = 22
22   AU10= A + 10 - Ai10   Ai10 = 18+14-22= 
18+14-22 = 10
10   Answer 10
Answer: B
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 5x boxes? Pick.
A) 3 minutes  B) 4 minutes  C) 5 minutes  D) 10 minutes  E) 12 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / Combine Rate = 5x/5x * 10 = 10 Min   Ans: 10 minutes5 /5  * 10= 
5 /5  * 10 = 10
10 Min   Ans: 10 minutes
Answer: D
In a business school case competition, the top three teams receive cash prizes of $1000, $ 2000, and $ 3000. while remaining teams are not ranked and do not receive any prizes, there are 6 participating teams, named A, B, C, D, E, F. If team A wins one of the prizes, team B wins also one of the prizes. How many outcomes of the competition are possible ? Choices
A) 18 B) 28 C) 36 D) 84 E) 120

Solution: if team A wins one of the prizes, team B wins also one of the prizes". Consider following cases:   A wins one of the prizes, then B must also win one of the prizes, and in this case we can have 4 triplets: {ABC}, {ABD}, {ABE}, {ABF}. Each triplet can be arranged in 3!=6 ways. Hence in the case when A wins one of the prizes  4*6= 
 4*6 = 24
24 arrangements are possible.   A does NOT win one of the prizes, then three winners must be from other 5 teams. 3 winners out of 5 (B, C, D, E, F) teams can be chosen in C35=10C53=10 ways and each case (for example {CDE}) can be arranged in 3!=6 ways, hence in the case when A does NOT win one of the prizes 10*6= 
10*6 = 60
60 arrangements are possible.   Total= 24+60= 
24+60 = 84
84.   Answer: 84.
Answer: D
A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%  Choose the correct choice from the following options:  A) 4 kg  B) 5 kg  C) 8 kg  D) 30 kg  E) 7 kg

Solution: Water in the given mixture = 10*20/100= 
10*20/100 = 2
2 kg,   4 kgnd spirit= (20-2)= 
(20-2) = 18
18 kg   Let x kg of water added, Then, x+2/20+x *100==25   4x+8 =20+x, or x =4 kg   4 kgNSWER:4 kg
Answer: A
In a kickball competition of 9 teams, how many possible matches can each team play with each other? Choose the most appropriate option.
A) 9 B) 16 C) 24 D) 36 E) 54

Solution: Each team can play with each other in 9C2 ways   9C2 = 9*8 / 1*2 = 36   Option 36
Answer: D
Working alone, Mary can pave a driveway in 4 hours and Hillary can pave the same driveway in 3 hours. When they work together, Mary thrives on teamwork so her rate increases by 33.33%, but Hillary becomes distracted and her rate decreases by 50%. If they both work together, how many hours will it take to pave the driveway?  Choose the correct choice from the following.
A) 2 hours B) 4 hours C) 5 hours D) 6 hours E) 7 hours

Solution: Initial working rates:   Mary = 1/4 per hour   Hillary = 1/3 per hour   Rate when working together:   Mary = 1/4 + (1/3*1/4) = 1/3 per hour   Hillary = 1/3 - (1/2*1/3) = 1/6 per hour   Together they work 1/3 + 1/6= 1/2 per hour   So they will need 2 hours to complete the driveway. The correct answer is 2 hours.
Answer: A
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work? Choose the correct choice from the following options
A) 6  B) 7  C) 5  D) 9  E) 3

Solution: 3/12 + (3 + x)/16 = 1   x = 9 days   Answer: 9
Answer: D
The edge of a cube is 9a cm. Find its surface? Select
A) 153a2 cm2
B) 143a2 cm2
C) 233a2 cm2
D) 243a2 cm2
E) 253a2 cm2

Solution: 6a2 = 6 * 9a * 9a = 243a2   Answer:243a2 cm2
Answer: D
On Thursday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?	Choices
A) Monday  B) Wednesday  C) Thursday  D) Friday  E) Saturday

Solution: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3   Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 2 /1*(2-1)= 
2 /1*(2-1) = 2
2*1/1*1= 
2*1/1*1 = 2
2   Hat combinations= 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4   Total Combinations = Shirt Combos*Sweater Combos*Hat Combos    3*2*4= 
 3*2*4 = 24
24 combinations   24 / 7 (days of the week)= remainder of 3   Purchased on Thursday, 3rd day is Sunday. Next day, which he won't have a new combination for, is Monday. (Monday)
Answer: A
A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? Choose one
A) A)182	B) B)208	C) C)220	D) D)224	E) E)302

Solution: If x is the original number of employees, then after 13% reduction in employees number is .87x   but we are given .87x = 181   x = 208   So the original number of employees is 208   Correct Answer - 208
Answer: B
The sale price sarees listed for Rs.500 after successive discount is 10% and 5% is? Choose the correct choice:
A) 427.5	B) 879	C) 342	D) 762	E) 269

Solution: 500*(90/100)*(95/100)= 
500*(90/100)*(95/100) = 855/2 = around 427.5
427.5   427.5nswer: 427.5
Answer: A
John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?
Choose the correct choice:
A) No loss or gain
B) Gain of $400
C) Loss of $400
D) Gain of $800
E) Loss of $800

Solution: Cost of the profitable stock: x=96/1.2= 
96/1.2 = 80
80, so profit from it  96-80= 
 96-80 = 16
16. Total profit   50*16= 
  50*16 = 800
800   Cost of the non-profitable stock: y=96/0.8= 
96/0.8 = 120
120, so loss from it 96-120=-24. Total loss 50*(-24)=-1200   Total loss: 800+(-1200)=-400.   Answer: Loss of $400.
Answer: C
Suppose son name is 120,his brother name is 150 and his mother name is 180.find out his father's name??? Options:	A) 190	B) 210	C) 230	D) 240	E) 250

Solution: since difference between all name is =30   so father's name will be  180+30= 
 180+30 = 210
210.   ANSWER:230
Answer: C
If A lends Rs.2500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
A. Rs.107.50 Choose the correct choice from the following answers
A) 112.5 B) 122.5 C) 132.5 D) 114.5 E) 212.5

Solution: (2500*1.5*3)/100= 
(2500*1.5*3)/100 = 112.5
> 112.50   112.5NSWER:112.5
Answer: A
Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 3. Find the larger integer.  Choose the correct choice from the following answers
A) 4	B) 24	C) 30	D) 72	E) 80

Solution: One option is to set up the equations and solve:   If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.   If adding 6 to the smaller integer makes the ratio 1 to 3, then 3(x+6)=y.   Substituting y=4x into the second equation yields 3x+18=4x.   So, x=18 (smaller integer) and, y=4x=72 (larger integer) so D is the correct answer.   Another option is to TEST the answer choices.   A) the larger number is 4   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 1   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (1), we get 7.   So, the new ratio is 7 to 4.   No good. We want a resulting ratio of 1 to 3   ELIMINATE A   B) the larger number is 24   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 6   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (6), we get 12   So, the new ratio is 12 to 24 which is 1 to 2.   No good. We want a resulting ratio of 1 to 3   ELIMINATE B   C) the larger number is 30   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 7.5 (which is not an integer)   Since both numbers are integers, the larger number cannot be 30.   ELIMINATE C   D) the larger number is 72   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 18   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (18), we get 24   So, the new ratio is 24 to 72. This is the same as the ratio of 1 to 3   Therefore (D) is correct   E) the larger number is 80   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 20   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (20), we get 26   So, the new ratio is 26 to 80 which is 13 to 40.   No good. We want a resulting ratio of 1 to 3   ELIMINATE E   Therefore 72 is the only correct choice.
Answer: D
The daily hotel rates for five hotels John was considering were $60, $125, $80, $70 and $x. If the median price was $5 lower than the average (arithmetic mean) price, which of the following could be $x?  Choose the correct answer:
A) $80
B) $85
C) $90
D) $95
E) $100

Solution: Look at the options available   Value of x seems to $80 < = $x < = $100   A. $80   B. $85   C. $90   D. $95   E. $100   So position of $x is fourth   $60 , $70 , $80 , $x , $125   Median = $80   Median price was $5 lower than the average, so average = $85   $60 + $70 + $80 + x + $125 = $425   $x = $90 = Answer = $90
Answer: C
A 440-liter solution of Kola is made from 88% water, 8% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar? Pick
A) 4.52%. B) 7.5%. C) 9.2%. D) 10.5%. E) 11%.

Solution: Denominator:   440+10+3.2+6.8= 
440+10+3.2+6.8 = 460
460   Numerator:   440(1-.88-.08)+3.2   440(0.04)+3.2   17.6+3.2   20.8   Ratio:   20.8/460=0.045   4.52%.nswer: 4.52%.
Answer: A
For every positive integer n, form the number n / s(n), where s(n) is the sum of the digits of n in base 10. What is the minimum value of n/s(n) for 10 <= n <= 99.	Choose one.
A) 1.2
B) 3.45
C) 1.9
D) 2
E) 4

Solution: possibility to sum of digits 10   i.e   (1.9),(2,8),(3,7),(4,6),(5,5)   we get s/s()n are 1.9,2.8,3.7,4.6,5.5   so the minimum possibility of s/s(n)=19/10= 
19/10 = 19/10 = around 1.9
1.9   ANSWER:1.9
Answer: C
In one hour,a boat goes 11 km along the stream and 5 km against the stream.The speed of the boat in still water is : Select:
A) 3  B) 5  C) 8  D) 9  E) 10

Solution: Solution   Speed in still water =1/2(11+5) kmph = 8 kmph.Answer 8
Answer: C
The cost price of a radio is Rs.1680 and it was sold for Rs.1450, find the loss %? Answers.
A) 18
B) 13
C) 15
D) 18
E) 41

Solution: 1680 ---- 230   100 ---- ? => 13%   Answer: 13
Answer: B
Out of 15 students in a class, 10 are wearing blue shirts, 2 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?  Choose the most appropriate option:
A) 10/21
B) 20/31
C) 30/41
D) 40/51
E) 50/61

Solution: Total possible ways to choose 4 students out of 15 = 15C4 = 1365   The number of ways to choose 4 students with no green shirts = 13C4 = 715   P(no green shirts) = 715/1365 = 11/21   P(at least 1 green shirt) = 1 - 11/21 = 10/21   The answer is 10/21.
Answer: A
Cole drove from home to work at an average speed of 80 kmh. He then returned home at an average speed of 120 kmh. If the round trip took a total of 3 hours, how many minutes did it take Cole to drive to work?	Choose the correct choice from the following options
A) 66 B) 70 C) 72 D) 85 E) 108

Solution: First round distance travelled (say) = d   Speed = 80 k/h   Time taken, T2 = d/80 hr   Second round distance traveled = d (same distance)   Speed = 120 k/h   Time taken, T2 = d/120 hr   Total time taken = 3 hrs   Therefore , 3 = d/80 + d/120   LCM of 80 and 120 = 240   3= d/80 + d/120   => 3 = 3d/240 + 2d/240   => d = 240 * 2/ 5 Km   Therefore, T1= d/80   => T1 = (240 *3) / (5 x 80)   => T1 = (9 x 60) / 5 -- in minutes   => T1 = 108 minutes.   108
Answer: E
On a sum of money, the S.I. for 2 years is $600, while the C.I. is $612, the rate of interest being the same in both the cases. The rate of interest is?	Choose the correct choice from the following options.
A) 3% B) 4% C) 5% D) 6% E) 7%

Solution: Difference in C.I. and S.I for 2 years = $612 - $600 = $12   S.I for one year 612 -  600= 
612 -  600 = 12
$12   S.I for one year= $300   S.I. on $300 for 1 year = $12   Rate = (100 * 12)/(300)= 
(100 * 12)/(300) = 4
4%   The answer is 4%.
Answer: B
The sum of number of boys and girls in a school is 300. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?	Choose the correct choice.
A) 50 B) 40 C) 60 D) 100 E) 75

Solution: We have x+x% of 300 = 300   x + x/100 * 300 = 300   4 * x = 300   x = 75   Answer is 75
Answer: E
John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.8 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push? Choose one: A) 13 seconds B) 17 seconds C) 26 seconds D) 34 seconds E) 42.5 seconds

Solution: Let t be the time that John spent for his final push.   Thus, per the question,   4.2t = 3.8t+15+2 ---> 0.4t = 17 ---> t = 42.5 seconds.   42.5 seconds is the correct answer.
Answer: E
In a box of 8 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?  Choose the correct choice from the following answers
A) 6/11	B) 8/15	C) 9/20	D) 11/25	E) 15/28

Solution: P(neither pen is defective) = 6/8*5/7 = 15/28   The answer is 15/28.
Answer: E
The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?
Pick one:
A) 315	B) 321	C) 330	D) 415	E) 424

Solution: a+(a+1)+(a+2)=3a+3+( +1)+( +2)= 
+( +1)+( +2) = 3
3a+3=312   (a+3)+(a+4)+(a+5)=(3a+3)+9=312+9= 
312+9 = 321
321   Answer: 321.
Answer: B
If 20x = 49y, which of the following must be true?
I. x > y
II. x^2 > y^2
III. x/7 is an integer Select:
A) I only
B) II only
C) III only
D) I and III
E) None

Solution: For x = 1,y = 20/49 and x>y. However, for x=-49,y = -20 and y>x. I is clearly not the right answer.   For y=0, x=0. Thus, even II doesn't hold good.   x/7 = 7y/20. For y=0, x/7 is an integer, however for y=1, it is not.   None of the options are (must be)true   ANSWNoneR:None
Answer: E