MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following CANNOT be the least common multiple of two positive integers x and y  Choose the most appropriate option
A) xy	B) x	C) x - xy	D) y	E) x + y

Solution: The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - xy is less than x, it cannot be the LCM of a x and y.   Answer: x - xy
Answer: C
I chose a number and divide it by 8. Then I subtracted 160 from the result and got 12. What was the number I chose?  Answers.
A) 1376	B) 1800	C) 1400	D) 2500	E) 100

Solution: Let x be the number I chose, then   x/8−160=12   x/8=172   x=1376   1376nswer is 1376.
Answer: A
Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss
Pick one.
A) 75  B) 65  C) 45  D) 25  E) 35

Solution: Explanation:   Let the origianl salary = Rs. 100   It will be 150% of (50% of 100)   = (150/100) * (50/100) * 100= 
(150/100) * (50/100) * 100 = 75
75   So New salary is 75, It means his loss is 25%   Answer: Option 25
Answer: D
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months? Pick.
A) $1500 B) $1750 C) $2000 D) $2500 E) $3000

Solution: Solution:   r = Rate = 8% compounded quarterly.. = 2% per quarter   t = 6 months = 2 quarters   So A = P (1+0.02)^2   => A = P * 1.0404   Substitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).   For 2500, interest is 101...   Hence, $2500
Answer: D
Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 2:3. The first number is:
Choose the correct option
A) A)27
B) B)98
C) C)34
D) D)35
E) E)62

Solution: (3x-9):(5x-9) = 2:3   x = 9 => 3x = 27   27nswer:27
Answer: A
The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
Choices.
A) 151
B) 149
C) 152
D) 148
E) None of the above

Solution: Corrected mean = 150×30−135+165/30   = 4500−135+165/30   =4530/30= 
4530/30 = 151
151   151nswer 151
Answer: A
A set of data consists of the following 7 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers? Options.
A) -1 and 9 B) 4 and 4 C) 3 and 5 D) 2 and 6 E) 0 and 8

Solution: If you are in for some calculations , this is how I got to it   mean = 4   sd = \sqrt{8} = 2.8   Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8)= 
(4 - 2.8) = 1.2
1.2 , and one value above SD is (4 + 2.8)= 
(4 + 2.8) = 6.8
6.8   This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.   Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.   1. -1 , 9   distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2   2. 4 , 4   distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8   3. 3 , 5   Distance is - 1.8 and 1.8   4. 2 , 6   Distance is - 0.8 and 0.8   5. 0 , 8   Distnace is - 1.2 and 1.2   Hence from above , we see that adding 3 and 5 , results in a value that would change the SD to the least. Hence 3 and 5
Answer: C
If A + B means A is the brother of B; A - B means A is the sister of B and A x B means A is the father of B. Which of the following means that C is the son of M?	Choose the correct answer
A) M - N x C + F  B) F - C + N x M  C) N + M - F x C  D) M x N - C + F  E) none

Solution: M is the father of N and N is the sister of C.C is brother of F..   so,N and c and F are siblings.   ANSWER:M x N - C + F
Answer: D
Louie takes out a three-month loan of $1000. The lender charges him 20% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?  Choose the correct choice
A) A)333  B) B)383  C) C)402  D) D)438  E) E)478

Solution: Here's the calculation for that case, assume monthly payment is X.   After 1st month: (1000)(1.2)-X = 1200-X   After 2nd month: (1200-X)(1.2)-X = 1440-2.21X   After 3rd month: (1440-2.21X)(1.2)-X = 1584-3.31X   Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:   1584-3.31X = 0   X = 1584/3.31 = 478.54   Answer 478
Answer: E
Calculate the area of a triangle, if the sides of are 39 cm, 36 cm and 15 cm, what is its area?
Choose the correct choice.
A) 570 cm2	B) 370 cm2	C) 170 cm2	D) 271 cm2	E) 270 cm2

Solution: The triangle with sides 39 cm, 36 cm and 15 is right angled, where the hypotenuse is 39 cm.   Area of the triangle = 1/2 * 36 * 15= 
1/2 * 36 * 15 = 270
270 cm2   Answer: 270 cm2
Answer: E
A person can swim in still water at 12 km/h. If the speed of water 10 km/h, how many hours will the man take to swim back against the current for 12km?  Choose the correct choice from the following options:
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: M = 12   S = 10   US = 12 - 10= 
12 - 10 = 2
2   6= 12   T = 12/2= 
12/2 = 6
6 Answer:6
Answer: D
Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive? Choose the most appropriate option: A) 65000 B) 67000 C) 70000 D) 72000 E) 75000

Solution: Ratio of the profits of Kamal and Kiran   =25000×12:60000×8   =25×12:60×8   =5×3:12×2   =5:4×2   =5:8   Let the total profit =x   Then Kamal received 10x/100=x/10 as commission for managing the business.   Remaining profit =x−x/10=9x/10 which is shared in the ratio 5:8   Total amount received by Kamal =(x/10)+(9x/10)×(5/13)   ⇒(x/10)+(9x/10)×(5/13)=58000   ⇒x+9x(5/13)=580000   ⇒x(1+(45/13))=580000   ⇒x(58/13)=580000   ⇒x(1/13)=10000   ⇒x=130000   Kiran's share = 130000−58000=72000   Answer is 72000.
Answer: D
When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass?  Select the correct option
A) 10	B) 9	C) 13	D) 7	E) 5

Solution: B = 9   2/3x= 30   x=45   for 90% approval we need 41 garments approved.   already approved = 28   we need 13 more.   Answer : 13
Answer: C
According to a recent student poll, 4/6 out of 24 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking? Pick one
A) 1/14	B) 4/49	C) 2/7	D) 62/69	E) 13/14

Solution: 16 students are interested, 8 are not interested   Prob = 1 - 8C2/24C2 = 1 - (8*7/(24*23))=1 - 7/69 = 62/69   Answer : 62/69
Answer: D
If 35% of the 840 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?	Choose the correct answer.
A) 546  B) 550  C) 555  D) 532  E) 515

Solution: We know 35 % people study biology,therefore the no of people not studying = 100 - 35= 
100 - 35 = 65
65%   > Therefore the people not studying biology out of a total 840 people are= 65 % of 840   >   (65/100)*840= 
  (65/100)*840 = 546
546 people   546
Answer: A
The current in a river is 5 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?  Choose the correct option:
A) 69 miles
B) 88 miles
C) 93,75 miles
D) 100 miles
E) 112 miles

Solution: Upstream Speed = 20-5= 
20-5 = 15
15 mph   Downstream Speed= 20+5= 
20+5 = 25
25 mph   D/15 + D/25= 10 hours   Solving for D we get D=93,75   Answer: 93,75 miles
Answer: C
X is the least common multiple of 96,196,300, which number below is not factor of X?	Choose the correct choice from the following answers
A) 600
B) 700
C) 900
D) 2100
E) 4900

Solution: Factors:   96=2^5, 3^1   196=2^2, 7^2   300= 2^2, 3^1, 5^2   So, I get LCM= 2^5, 3^1, 5^2, 7^2   A. 600=2^3, 3^1, 5^2   B. 700=2^2, 5^2, 7^1   C. 900=2^2, 3^2, 5^2   D. 2100=2^2, 3^1, 5^2, 7^1   E. 4900=2^2, 5^2, 7^2   answer is 900
Answer: C
The sum of three consecutive multiples of 3 is 81. What is the largest number?
Choose one.
A) 24
B) 28
C) 30
D) 32
E) 35

Solution: Let the numbers be 3x, 3x + 3 and 3x + 6.   Then,   3x + (3x + 3) + (3x + 6) = 81   9x = 72   x = 8   Largest number = 3x + 6 = 30.   Answer : 30
Answer: C
How many three letter words are formed using the letters of the word MARRIAGE? Choose the correct choice from the following answers
A) 326
B) 429
C) 226
D) 336
E) 280

Solution: The number of letters in the given word is eight.   The number of three letter words that can be formed using these four letters is 8P3   = 8 * 7* 6= 
8 * 7* 6 = 336
336.   Answer: 336
Answer: D
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?  Pick:	A) 227	B) 2689	C) 342	D) 787	E) 191

Solution: 400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   Answer: 342
Answer: C
How long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length?
Choose the correct choice from the following answers:	A) 15.8 sec	B) 14.9 sec	C) 12.4 sec	D) 16.8 sec	E) 17.4 sec

Solution: 17.4 sec   17.4 sec   D = 120 + 170= 
120 + 170 = 290
290 m   S= 60 * 5/18 = 50/3   T = 290 * 3/50= 
290 * 3/50 = 87/5 = around 17.4
17.4 sec   Answer is 17.4 sec
Answer: E
One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 260cm when it touches the floor on third time. What is the value of the original height?
Pick one
A) 80cm B) 90cm C) 104cm D) 120cm E) 130cm

Solution: when Ball comes down, Then i have indicated the distance covered in green   when Ball goes up, Then i have indicated the distance covered in red   Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h   h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 260   2.5 h = 260   h = 104.   104cm is the answer.
Answer: C
A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long?  Choose the correct choice from the following.
A) 20 sec	B) 21	C) 22	D) 23	E) 24

Solution: Speed = 120/6= 
120/6 = 20
20 m/sec.   Required time= (120 + 360)/20= 
(120 + 360)/20 = 24
24 sec.   Answer:24
Answer: E
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?
Pick one.
A) 31( 5/7) B) 81( 5/7) C) 51( 5/7) D) 41( 5/7) E) 31( 3/7)

Solution: Explanation:   Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)   = (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.   31( 5/7)nswer: 31( 5/7)
Answer: A
The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ?
Choose one:
A) 440
B) 512
C) 550
D) 620
E) 750

Solution: Large numbers are made in two ways:   Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.   31*2= 
31*2 = 62
62 (large prime number)   2^6= 64 (many small prime numbers)   To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.   You are left with 620 which is 31*2*2*5 (sum greater than 32)   Answer 620
Answer: D
The age of father 8 years ago was twice the age of his son. eight years hence, father's age will be twice that of his son. The ratio of their present ages is:  Pick one:
A) 5 : 3
B) 7 : 3
C) 9 : 2
D) 7 : 2
E) 13 : 4

Solution: Let the ages of father and son 8 years ago be 2x and x years respectively.   Then, (2x + 8) + 8 = 2[(x + 8) + 8]   2x + 16 = 2x + 32   x = 16.   Required ratio = (2x + 8) : (x + 8) = 40 : 24 = 5:3   answer :5 : 3
Answer: A
Find out the wrong term in the series 1, 10, 100 100, 1000, 100000
Choose the correct choice
A) 100,000,000	B) 10,000	C) 100,000	D) 10,000,000	E) 100,000,000,000

Solution: Explanation:   Each number with in the series is the product of the two numbers that proceed it.   So, if (1 * 10 = 10) , then (1000 * 100000 = 100 000 000 ).   100000000 should replace 100000.   100,000,000nswer: 100,000,000 )100,000,000
Answer: A
If a sum of money trebles itself in 40 years,what is the rate of interest? Pick:	A) 5%	B) 6%	C) 4%	D) 3%	E) None of these

Solution: Explanation:   Let the sum of money be Rs.x   5%fter 40 years, this becomes 3x   Simple Interest = 3x - x = 2x   Simple Interest = PRT/100   2x = (x×R×40)/100   2 = (R×40)/100   200 = 40R   R = 5%   5%nswer: Option 5%
Answer: A
If the average (arithmetic mean) of 4x-5, 8x-6, and 9x+5 is 279, what is the value of x?	Choose one:
A) 18 B) 25 C) 27 D) 29 E) 31

Solution: AM of 4x-5, 8x-6, and 9x+5=4x-5+ 8x-6+9x+5 / 3 = 31x/3   Given that 31x/3 = 279   x = 837/31= 
837/31 = 27
27   x= 27   Answer is 27
Answer: C
Three medical experts, working together at the same constant rate, can write an anatomy textbook in 32 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 6 days?	Options
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: Each expert can write 1/96 of the book per day.   To complete the book in 6 days, we need 96/6= 
96/6 = 16
16 experts, thus 13 more experts are needed.   The answer is 13.
Answer: D
8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
Choose the correct option.
A) 11/13
B) 12/17
C) 15/39
D) 19/31
E) 21/35

Solution: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)   = 15/39   15/39
Answer: C
At what price must an article costing Rs.47.50 be marked in order that after deducting 7% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following answers:
A) 63.84
B) 62.6
C) 62.1
D) 62.7
E) 62.2

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(93/100)= 59.375   MP = 63.84   63.84nswer: 63.84
Answer: A
What is the remainder when 54617^(42788234) is divided by 5? Options.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: We need to find the units digit of the number.   The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.   Since 42788234 has the form 4a + 2, the units digit is 9.   Then the remainder when dividing by 5 is 4.   The answer is 4.
Answer: E
A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun four times, approximately what is the probability that the product of the four winning sectors’ integers will be even? Choose the correct choice from the following
A) 50% B) 67% C) 88% D) 94% E) 98%

Solution: The only way to have an odd product is if all 4 integers are odd.   P(odd product) = 1/2*1/2*1/2*1/2 = 1/16   P(even product) = 1 - 1/16 = 15/16 which is about 94%   The answer is 94%.
Answer: D
If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. ab > 0
II. ab is even
III. c is even Choose the correct choice from the following: A) I only B) II only C) I and II D) I and III E) I, II, and III

Solution: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even   So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.   II only.letter II only
Answer: B
In a throw of coin what is the probability of getting head. Pick one:	A) 1	B) 2	C) 1/2	D) 0	E) None of these

Solution: Explanation:   Total cases = [H,T] - 2   Favourable cases = [H] -1   So probability of geƫng head = 1/2   Answer: 1/2
Answer: C
A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If7 were to be added to each score, which of these three statistics would change?  Pick.
A) The mean only B) The median only C) The standard deviation only D) The mean and the standard deviation E) The mean and the median

Solution: The correct answer is The mean and the median.
Answer: E
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?  Choose the correct choice from the following answers.
A) |k + 0.03| > 2.5  B) |k — 0.03| <= 2.5  C) |k — 2.5| > 0.03  D) |k — 2.5| >= 0.06  E) |k — 2.5| <= 0.03

Solution: So, let's go through this step by step:   rejects any screw whose length is less than 2.44 + 0.03= 
2.44 + 0.03 = 2.47
2.47 or greater than   2.50 + 0.03= 
  2.50 + 0.03 = 2.53
2.53 will be rejected.   If k represents the length of a screw   In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:   2.47 ≤ K ≤ 2.53   You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.   Let's look at (|k — 2.5| <= 0.03):   |k — 2.5| <= 0.03   For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53   For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47   2.47 ≤ k ≤ 2.53   (|k — 2.5| <= 0.03)
Answer: E
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?	Choose the correct answer
A) A)2
B) B)5
C) C)7
D) D)5
E) E)1

Solution: 1xplanation:   |-----------20--------------------|   60 40   D = 20   RS = 60– 40 = 20   T = 20/10 = 1 hours   Answer: Option 1
Answer: E
Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many W kilometers per hour did Tammy walk on the second day?
Choose the correct choice from the following options.
A) 3 B) 3.5 C) 4 D) 4.5 E) 6

Solution: Ans: C   Total time = 14 hrs   Let time traveled during 1st day = x   Let time traveled during 2nd day = x-2   Total time =14   x+x-2 = 14   x=8   speed * time = distance   s*8 + (s+0.5)(8-2) = 52   solving s = 4.5   now speed for 2nd day is 0.5 less than the 1st day which is 4.5   Thus speed for 2nd day = 4   Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.   8s+6s+3=52   14s=49   s=3.5
Answer: C
If p > 1 and q = 2^(p −1), then 4^p = Choose one:
A) 16q^2
B) 4q^2
C) q^2
D) q^2/4
E) q^2/16

Solution: If p > 1 and q = 2^(p −1), then 4^p   Given p>1, so let's assume p=2   q=2^(p-1) = 2^(2-1) = 2, so q=2   hence, 4^p = 4^2 = 16   only 1 ans. choice can satisfy this:   A) 16q^2 --> clearly > 16   B) 4q^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)   C) q^2 --> clearly < 16   D) q^2/4 --> clearly < 16   E) q^2/16 --> clearly < 16   Ans. 4q^2) 4q^2
Answer: B
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among five colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)	Select the correct option.
A) 7	B) 10	C) 15	D) 17	E) 20

Solution: 5152 = 10   The number of test subjects is  10 + 5= 
 10 + 5 = 15
15   The answer is 15.
Answer: C
The mass of the sun is approximately 2 × 10^25 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
Select the correct option.
A) 4.0 × 10^(−18) B) 2.5 × 10^12 C) 4.0 × 10^18 D) 2.5 × 10^19 E) 4.0 × 10^42

Solution: Mass of sun = x * Mass of moon   x = Mass of sun / Mass of moon = (2 × 10^25) / (8 × 10^12) = 2*2^-3*10^13 = 10^13/4 = 2.5*10^12   Ans. 2.5 × 10^12) 2.5 × 10^12
Answer: B
If C + D = 17 and C and D are positive integers, which of the following is a possible value for 3C + 2D?
Choose the correct choice from the following options:
A) 29
B) -29
C) 0
D) -19
E) 19

Solution: c + d = 11   3c + 2d = 2c + c + 2= 
+ 2 = 2
2(c+d) + c= 34+ c=c=-34   Now this reults in   c+d=17=-34+d=17=d=51   c=-34;d=51   3c + 2d=3(-34)+2(51)=-102+102= 
-102+102 = 0
0   3c + 2d= 0   Hence, 0 is the right answer.
Answer: C
In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students are there in the class ?
Select.
A) 84 B) 164 C) 97 D) 94 E) 74

Solution: total no. of students   = n(164 U T U C)= n(164)+n(T)+n(C)-n(164∩T)-n(164∩C)-n(C∩T)+n(164∩T∩C)   = n(164 U T U C)= 73+79+75-25-24-30+16   = n(164 U T U C)= 164   ANSWER:164
Answer: B
Two lorries each 350 m long are running in opposite directions on parallel tracks. Their speeds are 40km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the most appropriate option:
A) 77 sec
B) 36 sec
C) 48 sec
D) 55 sec
E) 45 sec

Solution: Relative speed = 40 + 30= 
40 + 30 = 70
70 km/hr.   70 * 5/18= 175/9 m/sec.   Distance covered = 350 + 350 = 200 m.   Required time = 700 * 9/175= 
700 * 9/175 = 36
36 sec.   Answer: 36 sec
Answer: B
In a simultaneous throw of pair of dice .find the probability of getting the total more than 7	Choose the correct choice from the following:
A) 5/2
B) 4/7
C) 4/3
D) 5/12
E) 2/7

Solution: Here n(S)=(6*6)= 
(6*6) = 36
36   let E=event of getting a total more than 7   ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}   P(E)=n(E)/n(S)=15/36=5/12.   Ans: 5/12
Answer: D
A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hour?  Choose the correct choice from the following choices:  A) 7 km/hr  B) 7.2 km/hr  C) 8 km/hr  D) 9 km/hr  E) 11 km/hr

Solution: Speed = 600	m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr (see important formulas section)   = 2 x	18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in?	Choices:
A) 8 days  B) 10 days  C) 18 days  D) 20 days  E) 25 days

Solution: That is, half the work done = 5 × 15 × ½   Then, 5 × 15 × ½ = 3 × ? ×1/2   i.e. 5 × 15 = 3 × ?   therefore, ? (No. days required) = 5 × 15/3 = 25 days.   25 days)
Answer: E
A firm is comprised of partners and associates in a ratio of 2:63. If 50 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm? Choose one
A) 5
B) 10
C) 12
D) 20
E) 25

Solution: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.   68-63= 
68-63 = 5
5 which is 1/10 of the increase in 50 associates.   The ratio changed from 20:630 to 20:680.   Thus the number of partners is 20.   The answer is 20.
Answer: D