MU-NLPC/Calc-aqua_rat huggingface dataset:
if x and y are different integers and x^2=xy, which of the following must be true?	Pick one
A) x=0  B) x=6  C) x=3  D) x=2  E) x=1

Solution: (1) when x is 0, above eqn is satisfied regardless of y - true   (2) when x is not zero, the eqn is not satified   eg whn x = 2, 2*2 is not equal to 2 * 0 - false   (3) when x = -y, clearly product xy is negative.   but x^2 is positive - doesnt satify eqn   x=0nswer x=0
Answer: A
A is the average (arithmetic mean) of the first 7 positive multiples of 7 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?	Select:
A) 4	B) 12	C) 14	D) 21	E) 28

Solution: If A^2 - B^2 = 0, then let's assume that A = B.   A must equal the 4th positive multiple of 4, thus A = 28, which also equals B.   B is the second positive multiple of n, thus n = 28/2= 
28/2 = 14
14.   The answer is 14.
Answer: C
Two trains 160 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose one:
A) 10.7  B) 10.9  C) 10.52  D) 11.52  E) 18.82

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 160 + 160= 
160 + 160 = 320
320 m.   Required time= 320 * 9/250= 
320 * 9/250 = 288/25 = around 11.52
11.52 sec.   Answer:11.52
Answer: D
Half of 7 percent written as decimal is
Choose the correct choice from the following choices.
A) 5	B) 0.5	C) 0.035	D) 0.025	E) None of these

Solution: Explanation:   It will be 1/2(7%) = 1/2(7/100) = 7/200= 
7/200 = 7/200 = around 0.035
0.035   Answer: Option 0.035
Answer: C
Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4048. What is the difference between Rohan’s and Sudhir’s share in the profit?  Choose the correct choice from the following options.
A) s.345
B) s.350
C) s.352
D) s.362
E) s.368

Solution: Suresh : Rohan : Sudhir   Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8   = 6 : 3: 2   The difference between Rohan’s and Sudhir’s share = 1 share   :.i.e. = Rs. 4048 × 1/11 = Rs.368.   s.368
Answer: E
Fathers age is 5 times his son's age. 4 years back the father was 9 times older than son.Find the fathers' present age.  Choose the correct choice:
A) 41	B) 40	C) 39	D) 45	E) 30

Solution: fathers age =x sons age =y   x=5y;x-4=9(y-4)   5y-4=9y-36   y=8 so x=40   ANSWER:40
Answer: B
If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 5n years to that after 4n years?	Choose the correct choice from the following answers
A) (1+k/100)^n	B) (1+k)^n	C) (1+kn/100)	D) (1+n/100)^k	E) (1+kn)

Solution: Amount after 5n years will be = x ( 1 + k/100)^5n   Amount after 4n years will be = x ( 1 + k/100)^4n   So, required ratio will be -   { x ( 1 + k/100)^5n } / {x ( 1 + k/100)^4n } = (1+k/100)^n   Hence answer will be a. (1+k/100)^n   (1+k/100)^n
Answer: A
An employer has 9 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
Options:
A) a) 1,490 B) b) 132 C) c) 504 D) d) 60 E) e) 23

Solution: 9C3 * 4C2 = 504. Answer c) 504.
Answer: C
If 80% of a number is equal to four-third of another number, what is the ratio of first number to the second number?	Choose one
A) 5:3 B) 1:4 C) 3:7 D) 6:11 E) 2:3

Solution: Let 80% of 5:3 = 4/3 B   then 805:3/100 = 4B/3   45:3/5 = 4B/3   5:3/B = 5/3   5:3:B = 5:3   5:3nswer is 5:3
Answer: A
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 85 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
Choose one:
A) 81
B) 159
C) 166
D) 285
E) 324

Solution: I solve it using the tough luck technique:   According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.   80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80   Now, we need to be certain that out of the books we picked, there are either at least 85 physics books or 80 chemistry books   What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.   We picked:   50 Botany Books   65 Zoology Books   50 Geology Books   Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!   Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick   79*2+1 books   Because, we could have picked the books in following order;   1st book picked: Physics   2nd book picked: Chemistry   3rd book picked: Physics   Thus, Total= 50+65+50+79*2+1=165+1+158= 
165+1+158 = 324
324   Ans:324
Answer: E
At a certain company, each employee has a salary grade s that is at least 1 and at most 6. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 6 receives how many more dollars per hour than an employee with a salary grade of 1?
Options:
A) $0.50
B) $1.00
C) $1.25
D) $1.50
E) $1.75

Solution: Salary grade of 6 is p(6)=9.50+0.25(6–1)=9.50+0.25*5;   Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50;   p(6)-p(1)=9.50+0.25*5-9.50=1.25.   Answer: $1.25.
Answer: C
At a recent small town election for mayor a total of 971 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?	Select the correct option
A) 134	B) 178	C) 197	D) 166	E) 194

Solution: The number of votes the winning candidate received was   971 + 53 + 79 + 105	/4= 302.   The second received 302 – 53 = 249,   The fourth place received 302 – 105 = 197.   197
Answer: C
What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?	Choices: A) 2888 B) 2669 C) 2662 D) 2992 E) 9680

Solution: A= P{1 + R/100}n   => 8000{1 + 10/100}2 = Rs.9680.Answer: 9680
Answer: E
Given that there are 4 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team? Choose the correct choice from the following:
A) 15 B) 30 C) 48 D) 75 E) 90

Solution: 2 teams can be selected from 3 teams in 3482 ways = 3 ways   as the condition is that the 2 players should be from different teams   one player can be chosen from 1st team in 5 ways   similarly another player can be chosen from 2nd team in 5 ways   Total number of ways to choose the player = 4 * 4 * 3= 
4 * 4 * 3 = 48
48 ways   48orrect Answer - 48
Answer: C
9 people decided to split the Travel expenditures evenly. If the bill was $546,874 dollars, how much amount in dollars should be added to the bill to make it split evenly across everyone?	Answers
A) $546,872
B) $546,874
C) $546,876
D) $546,878
E) $546,870

Solution: This is equivalent to finding the first number that is divisible by 9 that occurs after 546,874.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 546,874 = 34 and 18 is divisible by 9.   Hence, we need to add 2 to this number for it to be divisible by 9   $546,876orrect Option: $546,876
Answer: C
The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 84 ounces of this substance?
Choices
A) 27 B) 36 C) 42 D) 64 E) 147

Solution: 112 ounces of a substance has a volume of 48 cubic inches   84 ounces of a substance has a volume of (48/112)*84= 
(48/112)*84 = 36
36 cubic inches   Answer 36
Answer: B
A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase E in sales?  Pick:
A) 2% B) 17% C) 20% D) 65% E) 83%

Solution: Last year's sales = $320 million;   This year's sales = $385 million;   Increase E = $65 million.   Now, 20% of $320 million is $64 million, which is very close to actual increase of $65 million.   Answer: 20%.
Answer: C
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder A of Y divided by 5?  Options.
A) A=1. B) A=2. C) 3. D) 4. E) 5.

Solution: X divided by 10 gives reminder of 2. X can be 2/12/22....   X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....   If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2   Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2   Hence the answer must be 2 (B)   Also....   x+y=5m+4 and x=10K+2   hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is A=2.
Answer: B
The mean of 50 observations was 36. It was found later that an observation 30 was wrongly taken as 23. The corrected new mean is :
Choose one:
A) 36.02	B) 36.14	C) 36.12	D) 36.11	E) 36.8

Solution: Explanation:   Correct Sum = (36 * 50 + 30 - 23) = 1825.   Correct mean = = 1807/50= 
1807/50 = 1_807/50 = around 36.14
36.14   Answer: 36.14) 36.14
Answer: B
Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent. Choose the correct choice from the following answers.
A) 12%  B) 20%  C) 15%  D) 36%  E) 51%

Solution: Let the s.p be Rs. X .then C.P = Rs.9x/10,Receipt=108% of rs.x=Rs 27x/25   Gain=Rs (27x/25*9x/10)=Rs(108x-90x/100)=Rs18x/100   Gain%=(18x/100*10/9x*100)%=20%   Ans: 20%(18 /100*10/9 *100)= 
(18 /100*10/9 *100) = 20
20%   Ans: 20%
Answer: B
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?	Options:
A) 15 B) 26 C) 34 D) 25 E) 26

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 184 – 150 = 34   34
Answer: C
Jacob marks his goods up by 75% and then offers a discount on the marked price. The profit that he makes after offering the discount is 40%. What % discount did Jacob offer?  Choose the correct choice from the following choices:
A) 15%
B) 20%
C) 25%
D) 35%
E) 75%

Solution: Solution:   let x is the cost price.   so profit 40% means final selling price = 1.40x   marked up price = 1.75x   let discount be r%   so   1.40x=1.75x(1 - r/100)   after solving the equation r= 20%   ANSWER:20%
Answer: B
Tim and Élan are 150 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan? Choose the correct choice from the following:
A) 30 miles.  B) 35 miles.  C) 45 miles.  D) 90 miles.  E) 100miles.

Solution: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.   Plugging in the answer choice Only Answer Choice 100miles. meet the 2:1(Tim:100miles.lan=100:50) ratio of maintaining total distance traveled 150 miles   SoCorrect answer 100miles.
Answer: E
If the integer n leaves a remainder of 4 when divided by 5, then what is the largest possible
remainder when 2n is divided by 15? Select the correct option.
A) 10  B) 11  C) 12  D) 13  E) 14

Solution: Since n leaves a remainder of 4 when divided by 5, it leaves a remainder of 4, 9, or   14 when divided by 15. Thus 2n leaves a remainder of 2 * 4= 
2 * 4 = 8
8, 2 * 9-15= 3, or  2 *14-15= 
 2 *14-15 = 13
13   when divided by 15, and the maximum remainder is 13 .   correct answer 13
Answer: D
The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?  Choices:  A) 1,010  B) 1,164  C) 1,240  D) 1,316  E) 2,109

Solution: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.   Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.   Plug values of n = 18 and c = 1/2 into the equation and simplify to get the answer 2109.   Option 2,109.
Answer: E
If the operation € is defined for all x and y by the equation x € y = 3*x*y, then 3 € (4 € 5) =
Answers:
A) 80 B) 120 C) 160 D) 540 E) 660

Solution: working inside out,   (4 € 5) = 3*4*5= 
3*4*5 = 60
60   3 € 60= 3*3*60= 
3*3*60 = 540
540   Hence, answer is 540
Answer: D
The probability that a number selected at random from the first 50 natural numbers is a composite number is -.
Answers
A) 16/11 B) 17/25 C) 15/15 D) 11/11 E) 14/11

Solution: The number of exhaustive events = 50C1 = 50.   We have 15 primes from 1 to 50.   Number of favorable cases are 34.   Required probability = 34/50 = 17/25   Answer: 17/25
Answer: B
Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 400 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?  Answers:
A) 1:40 PM
B) 1:50 PM
C) 2:00 PM
D) 2:10 PM
E) 2:20 PM

Solution: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.   Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 400+60t=80t-200 --> t=30.   1:30 PM + 30 minutes = 2:00 PM.   Answer: 2:00 PM.
Answer: C
What is the sum of all remainders obtained when the first 300 natural numbers are divided by 9?  Choose the correct choice from the following answers
A) 397 B) 401 C) 403 D) 405 E) 399

Solution: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.   1 divided by 9 gives the remainder of 1;   2 divided by 9 gives the remainder of 2;   ...   8 divided by 9 gives the remainder of 8;   9 divided by 9 gives the remainder of 0.   We'll have 11 such blocks, since  99/9= 
 99/9 = 11
11. The last will be:   91 divided by 9 gives the remainder of 1;   92 divided by 9 gives the remainder of 2;   ...   98 divided by 9 gives the remainder of 8;   99 divided by 9 gives the remainder of 0.   The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:   11(1+2+3+4+5+6+7+8+0)+1=405.   Answer: 405.
Answer: D
Evaluate 28% of 350 + 45% of 280 Select the correct option
A) 224
B) 242
C) 252
D) 262
E) 282

Solution: Explanation:   = (28/100) * 350 + (45/100) * 280   = 98 + 126= 
98 + 126 = 224
224   224nswer: Option 224
Answer: A
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x3)(x+14)(2X+5) = 0?  Choose the correct choice from the following answers:
A) 1/12 B) 1/6 C) 1/4 D) 1/3 E) 1/2

Solution: x = -4   Prob = 1/12   1/12nswer - 1/12
Answer: A
Sarah made $45 more than Kara yesterday. Today, they each made the same amount of money as yesterday and it totaled $834. How much would Kara make in 5 days if she continues to make the same amount of money every day.
Choose the correct answer
A) $225 B) $879 C) $930 D) $2,085 E) None of the above

Solution: S-K=45   2(S+K)=834   Solving the 2 equations, you get, S=$231 and K=$186   So $186x5=$930   $930orrect Answer: $930
Answer: C
What will be the fraction of 20%	Choose the correct choice from the following.
A) 1/4	B) 1/5	C) 1/10	D) 1/11	E) None of above

Solution: Explanation:   It will 20*1/100 = 1/5   Option 1/5
Answer: B
Mary, Bernie, and Rose can complete a job, all working together, in 4 hours. Mary and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Rose, working alone, to complete the entire job?	Choose the correct choice from the following options:
A) 8 hours	B) 10 hours	C) 12 hours	D) 20 hours	E) 21 hours

Solution: If Mary, Bernie, and Rosecan complete a job in 4 hours, they can complete 1/4 of the job in an hour. Furthermore, if Mary and Bernie can complete the same job in 5 hours, they can do 1/5 of the entire job in an hour.   If the three of them can do 1/4 of a job in an hour, and without Colleen the other two can do 1/5 of a job in an hour, then the amount of the job Colleen can do in an hour is the difference of these results:   1/4 – 1/5 = 5/20 – 4/20 = 1/20.   Since Colleen can do 1/20 of the job in an hour, it will take her 20 hours to do the entire job by herself.   The correct answer is choice (20 hours).
Answer: D
Can you deduce the pattern and find the next number in the series?
6, 14, 26, 98, __?  Choose one:
A) 276  B) 277  C) 278  D) 279  E) None of these

Solution: Solution:   276   Explanation:   6 = 1^1 + 2^1 + 3^1   14 = 1^2 + 2^2 + 3^2   36 = 1^3 + 2^3 + 3^3   98 = 1^4 + 2^4 + 3^4   Thus the next number will be   1^5 + 2^5 + 3^5 = 276   276nswer 276
Answer: A
In an examination, 40% candidates failed in one subject and 30% failed in another subject while 10% failed in both the subjects. If 100 candidates appeared at the end of the examination how many passed in either subject but not in both?	Choose the correct option:
A) 50
B) 75
C) 60
D) 100
E) 40

Solution: Failed in 1st subject = 40*100/100= 
40*100/100 = 40
40   Failed in 2nd subject= 30*100/100= 
30*100/100 = 30
30   Failed in both= 10*100/100= 
10*100/100 = 10
10   Failed in 1st subject only= 40-10= 
40-10 = 30
30   Failed in 2nd subject only= 30-10= 
30-10 = 20
20   Passed in either subject but not in both= 30+20= 
30+20 = 50
50   50nswer is 50
Answer: A
At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ?
Choose the correct choice from the following choices:
A) Rs.7.50 per kg	B) Rs.8.20 per kg	C) Rs.8.85 per kg	D) Rs.9 per kg.	E) None

Solution: Explanation:   Total C.P of 200 kg of sugar   = Rs.(80×6.75+120×8)=Rs.1500   C.P of 1 kg = Rs.[1500/200]=Rs.7.50   Gain required = 20%   S.P of 1 kg = (120% of Rs.7.50)   = Rs.[120/100×7.50]=Rs.9 per kg.   Correct Option : Rs.9 per kg.
Answer: D
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/5 hours to fill the tank. The leak can drain all the water of the tank in? Choose the correct answer:
A) 17 hr	B) 19 hr	C) 22 hr	D) 24 hr	E) 26 hr

Solution: Work done by the tank in 1 hour   = (1/2 - 2 1/5)   = 1/22 Leak will empty the tank in 22 hrs.   Answer:22 hr
Answer: C
If 4 people are selected from a group of 9 married couples, what is the probability that none of them would be married to each other? Choose the correct choice from the following choices.
A) 1/33
B) 2/85
C) 1/3
D) 56/85
E) 11/85

Solution: If we are to select 4 people from 9 couples WITHOUT any restriction, how many ways can we make the selection? 18!/4!14! = 3060   If we are to select 4 people from 9 couples WITH restriction that no married couple can both make it to the group, only a representative?   9!/4!5! = 126   But we know that to select a person from each couple, take 2 possibilities     126*2*2*2*2= 
  126*2*2*2*2 = 2_016
2016   Probability= 56/85esired/All Possibilities = 2016/3060 = 56/85   Answer: 56/85
Answer: D
65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?  Choose the correct choice from the following choices:	A) 64	B) 128	C) 151	D) 216	E) 256

Solution: 65 small cube will make a large cube with 4 cubes in each line i.e.   Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.   Total number of small cubes in new cube = 6^3 = 216   Extra cube required = 216 - 65= 
216 - 65 = 151
151   Hence, 151 is the answer.
Answer: C
What is the smallest five digit number that is divisible by 15, 24, 36, and 54?  Choose the correct choice from the following answers
A) 10320 B) 10800 C) 10030 D) 10380 E) 10460

Solution: 15 = 3 * 5   24 = 2^3 * 3   36 = 2^2 * 3^2   54 = 2 * 3^3   LCM = 2^3 * 3^3 * 5 = 1080   The smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800   The answer is 10800.
Answer: B
Find the sum of all 3-digit nos that can be formed by 1, 2 and 3  Choose the correct choice from the following options.
A) 5994 B) 5042 C) 6900 D) 7002 E) 3546

Solution: No of such 3-digit nos = 27 (which is Ok)   1st no = 111, Last no = 333 (these r also Ok)   Hence their average = (111 + 333)/2= 
(111 + 333)/2 = 222
222   (couldn't understand how this formula is applied. I thought this holds true for an 5994P series only)   So, Sum= Number of nos X 5994verage of the nos   = 27 X 222 = 5994 5994NS:5994
Answer: A
How many ways are there to select a subcommittee of 9 members from among a committee of 17?  Choose the correct choice from the following answers.
A) 22888 B) 24310 C) 28791 D) 27711 E) 12111

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,9)= 24,310   Answer: 24310)
Answer: B
A river 4m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is?  Choose the correct answer
A) 25000  B) 26000  C) 27000  D) 28000  E) 29000

Solution: Rate of water flow-6kmph--6000/60--100 m/min   depth of river--4m   width of river--65m   vol of water per min--100 *4*65---26000   Answer 26000
Answer: B
A boy runs 200 metres in 24 seconds. What is his speed?  Answers:
A) 20 km/hr	B) 24 km/hr	C) 30 km/hr	D) 32 km/hr	E) 34 km/hr

Solution: 200/24 * 18/5= 
200/24 * 18/5 = 30
30 km/hr   ANSWER:30 km/hr
Answer: C
If a person walks at 25 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
Answers:
A) 50 km B) 56 km C) 13.3 km D) 70 km E) 80 km

Solution: Let the actual distance travelled be x km.   x/10 = (x+20)/25   25x = 10x + 200   15x = 200   x = 13.3 km.   answer :13.3 km
Answer: C
If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. a^b + b^2
II. (a + b)^2
III. a + b	Choose one.
A) . I only B) II only C) III only D) I and II only E) I, II, and III

Solution: Factors of 30 are 1,2,3,6,5,10,15,30.   for options 1) & 3) consider a=2 and b=1 we find then 3 ,which is a factor   but for option 2) any values doesn't melts to any factor.   eg:-if we put a=3 and b=1 then (a+b)^2 =16 which is not a factor of 30   so Answer: II only.
Answer: B
If the sides of a triangle are 28 cm, 24 cm and 15 cm, what is its area?
Choose the correct choice from the following.
A) 180 cm2
B) 112 cm2
C) 776 cm2
D) 666 cm2
E) 886 cm2

Solution: The triangle with sides 28 cm, 24 cm and 15 cm is right angled, where the hypotenuse is 28 cm.   180 cm2rea of the triangle = 1/2 * 24 * 15= 
1/2 * 24 * 15 = 180
180 cm2   180 cm2nswer: 180 cm2
Answer: A
2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?  Pick one:  A) 6  B) 8  C) 10  D) 12  E) 14

Solution: 1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   8
Answer: B