MU-NLPC/Calc-aqua_rat huggingface dataset:
which number need to add to 859622 to get a number exactly divisible by 456?
Choices:
A) 547896 B) 243545 C) 445321 D) 354568 E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
What is the total number of integers between 100 and 250 that are divisible by 5?
Choose the correct option.
A) 27
B) 28
C) 29
D) 30
E) 25

Solution: 105, 110, 115, ..., 240,245   This is an equally spaced list; you can use the formula:   n = (largest - smallest) / ('space') + 1 = (245 - 105) / (5) + 1 = 140/5 + 1 = 28 + 1= 
28 + 1 = 29
29   Answer is 29
Answer: C
Evaluate permutation
4P4
Choose the correct choice from the following choices:
A) 22 B) 23 C) 24 D) 25 E) None of these

Solution: Explanation:   nPn=n!   4P4=4∗3∗2∗1=24   Option 24
Answer: C
The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? Choose the correct choice from the following choices: A) 3:9 B) 3:6 C) 3:1 D) 3:4 E) 3:2

Solution: Let the present ages of A and B be 5x and 3x years respectively.   Then, (5x - 4)/(3x + 4) = 1/1   2x = 8 => x = 4   Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1   Answer: 3:1
Answer: C
The ratio between the sale price and the cost price of an article is 10:7. What is the ratio between the profit and the cost price of that article? Select
A) 2:9 B) 2:5 C) 3:7 D) 2:0 E) 2:1

Solution: Let C.P. = Rs. 7x and S.P. = Rs. 10x.   Then, Gain = Rs. 3x   Required ratio =3x : 7x = 3:7   Answer:3:7
Answer: C
A man purchases some eggs for Rs.500. 15% of the eggs break during transportation. What profit percentage should he take on the remaining to get an overall profit of 20%?  Choose the correct choice:
A) 37.5  B) 41.17  C) 21.17  D) 45.17  E) 46.18

Solution: Explanation:   The eggs remaining = 85%   CP of 85% eggs = 85x500/100 = Rs.425   Overall profit = 500 + 20% of 500 -CP of 85% eggs.   Rs.600 – Rs.425 = Rs.175.   :. Overall profit percent = 175x100/425 = 41.17%.   Answer: Option 41.17
Answer: B
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Choose one:	A) Rs. 150	B) Rs. 300	C) Rs. 250	D) Rs. 200	E) Rs. 220

Solution: Explanation:   Let the amount paid to X per week =x   and the amount paid to Y per week =y   12y/10+y=550   22y/10=550   y=5500/22=500/2= 
500/2 = 250
250   ANSWER IS Rs. 250
Answer: C
How many three digit numbers X greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once? Choose the correct choice from the following
A) 72	B) 48	C) 120	D) 96	E) 76

Solution: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.   ABC three digit numbers greater than 300 - total of  4*5*4= 
 4*5*4 = 80
80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.   Between 300 and 330 there are   1*2*4= 
  1*2*4 = 8
8 numbers with the given property: A= 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.   Total possible choice  80 - 8= 
 80 - 8 = 72
72=X   72nswer: 72.
Answer: A
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds. What is the length of the goods train?
Choose the correct choice from the following answers:
A) 230 m
B) 350 m
C) 260 m
D) 270 m
E) None of these

Solution: Explanation:   Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.   Time = 30 sec.   Let the length of the train be x metres.   Then,[ (x+250)/30 ]= 20   => x + 250 = 600   => x = 350. Answer: 350 m
Answer: B
A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Select:
A) 107 kmph	B) 138 kmph	C) 121 kmph	D) 108 kmph	E) 103 kmph

Solution: 108 kmph   108 kmph   S = 180/6 * 18/5= 
180/6 * 18/5 = 108
108 kmph
Answer: D
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.19404/- in 3 years at the same rate of interest. Find the rate percentage? Choose the correct choice from the following answers:
A) 5%	B) 7%	C) 9%	D) 10%	E) 12%

Solution: Explanation:   The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.   S.I = 19404/- - 17640/- = Rs. 1764/-   Rate of interest = (1764/17640) × (100/1)   =>10%   Answer: Option 10%
Answer: D
How many digits 2^1000 has?  Choose the correct choice.
A) 31
B) 35
C) 50
D) 99
E) 310

Solution: 2^10 = 1.024 * 10^3 => 2^1000 = (1.024)^100 * 10^300   therefore 310 digits would be my best guess   310
Answer: E
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:  Choose the correct choice from the following options.
A) 10 B) 18 C) 36 D) 72 E) 84

Solution: Explanation:   Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x =	(120 + 120) /12   2x = 20   x = 10.   Speed of each train = 10 m/sec = 10 x	18/5 km/hr = 36 km/hr.   ANSWER IS 36
Answer: C
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7/10 of its present?  Select the correct option:
A) 61.5 B) 60.5 C) 63.5 D) 35.71429 E) 64.5

Solution: Let capacity of 1 bucket = x   Capacity of the tank = 25x   New capacity of the bucket = 7x/10   Hence, number of buckets needed = 25x/(7x/10)=(25×10)/7=35.71429   Answer is 35.71429.
Answer: D
If p#q denotes the least common multiple of p and q, then E=((12#16)#(18#24)) = ?	Choose the correct option.
A) 216
B) 180
C) 144
D) 108
E) 72

Solution: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB   The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4= 
12*16/4 = 48
48.   The greatest common factor of 18 and 24 is 6. So, 18#24= 18*24/6= 
18*24/6 = 72
72   Finally, the greatest common factor of 48 and 72 is 24. So, E=((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72= 
2*72 = 144
144   The correct answer is 144.
Answer: C
One fourth of a solution that was 15% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? Choices:	A) 34%	B) 24%	C) 22%	D) 16%	E) 8.5%

Solution: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.   3 parts of 15% + 1 part of x (unknown) % = 4 parts of 16%   => x% = 64%-45% = 16%   ans 16% it is.
Answer: D
The 41 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?  Choose one:
A) 4
B) 7
C) 8
D) 9
E) 10

Solution: The formula is Total = A+7+C - sum of exactly two + 2*all three + neither   21+18+19-x-2*5=41   solving for x you get 7   Answer 7
Answer: B
Sam deposited $12,000 to open a new savings account that earned eight percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Sam account one year after the account was opened?	Choose one.
A) $13,128  B) $12,763  C) $12,968  D) $12,942  E) $12,865

Solution: Approach #1:   8 percent annual interest compounded semi-annually --> 2.5% in 6 moths.   For the first 6 moths interest was 4% of $12,000, so $480;   For the next 6 moths interest was 4% of $12,000,plus8% earned on previous interest of $480, so $480+$8=$488;   Total interest for one year was $480+$488  480+ 8= 
  480+ 8 = 488
$488;   Total interest for one year was $480+$488=$968, hence balance after one year was $12,000+ $968 480+ 488= 
 480+ 488 = 968
$968, hence balance after one year was $12,000+ $968=$12,968.   Answer: $12,968.
Answer: C
A shopkeeper expects a gain of 22½% on his cost price. If in a week, his sale was of Rs.392, what was his profit?	Answers: A) Rs.18.20 B) Rs.70 C) Rs.72 D) Rs.88.25 E) None

Solution: Solution   C.P	= Rs.(100/122.50x392)   = Rs.(1000/1225×392)   = Rs.320.   Therefore, Profit	= Rs.(392-320)   = Rs.72.   Answer Rs.72
Answer: C
If a and y are different prime numbers less than ten, what must be true about the sum of a and y?	Choose the correct option:	A) the sum is even	B) the sum is odd	C) the sum is less than ten	D) the sum is greater than ten	E) the sum is less than 13

Solution: This has to be solved by checking for each option:   Prime numbers less that 10 = 2, 3, 5, 7   A. the sum is even   May or may not be true. a = 3, y, = 5 -> True.   a = 2, y = 3 - True   B. the sum is odd   May or may not be true. a = 3, y, = 5 -> False.   a = 2, y = 3 - True   C. the sum is less than ten   May or may not be true a= 5, y = 7, Sum = 12   a = 2, y = 3. Sum = 5   D. the sum is greater than ten   May or may not be true a= 5, y = 7, Sum = 12   a = 2, y = 3. Sum = 5   E. the sum is less than 13   This will always be true.   Maximum sum = 7 + 5= 
7 + 5 = 12
12.   This is always less than 13.   Correct Option: the sum is less than 13
Answer: E
If a^2 is divisible by 240 what is the least possible value of integer a?	Choose the correct choice from the following choices.
A) 120
B) 30
C) 90
D) 60
E) 12

Solution: 240 can be written as (2^4)*3*5.   For a^2 to be divisible by 240 it should contain at least 2^4 and 3 and 5 in its factors. We can leave out option E because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^ 2 will have 2 as the maximum power of 2, so we can leave out this option too.   Option D is the right answer if we follow the same method as we followed for other two previous options.   60 = (2^2)*3*5; 60^2 = (2^4)*(3^2)*(5^2). So it shows that 60^2 is divisible by 240 and hence the answer.   Answer : 60
Answer: D
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 420. What was Simran share in the profit?	Pick:
A) s 180  B) s 100  C) s 120  D) s 190  E) s 290

Solution: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Simran's share = Rs.420 x	3/7	= Rs. 180.   s 180NSWER :s 180
Answer: A
The salaries of A and B together amount to $4000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary? Select the correct option:
A) $1000
B) $1250
C) $2500
D) $3000
E) $1200

Solution: Let A's salary is x   B's salary = 4000-x   (100-95)% of x = (100-85)% of (4000-x)   x = $3000   Answer is $3000
Answer: D
Albert is 2 times Mary’s age but only 4 times as old as Betty. Mary is 16 years younger than Albert. How old is Betty? Choose the correct choice from the following options.
A) 8  B) 12  C) 10  D) 15  E) 18

Solution: given that A=2M=4B..AND M=A-16..   substituting the values M=16,A=32 AND B=8..   8nswer is 8
Answer: A
A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage Choose one:
A) 10% B) 15% C) 20% D) 25% E) 30%

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (810 ~ 900)/900 = 10% Loss   10%
Answer: A
Fresh grapes contain 70% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 30kgs of raisins?
Choose the correct choice from the following options
A) 75 kgs	B) 64kgs	C) 72 kgs	D) 65 kgs	E) 70 kgs

Solution: The weight of non-water in 30 kg of dried grapes (which is 100-25= 
100-25 = 75
75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-70= 
100-70 = 30
30% of whole weight),   so 30*0.75= x*0.3   --> x = 75.   75 kgsnswer: 75 kgs.
Answer: A
Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?  Options:
A) 1
B) 2
C) 4
D) 5
E) 6

Solution: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.   (4x + 8) = 5 (x + 8)   2   8x + 16 = 5x + 40   3x = 24   x = 8.   Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 
48/24 = 2
2.   2
Answer: B
If 5 less than x is 1 greater than y, then a number z that is 5 greater than x reduced by y is equal to  Answers.
A) 4  B) 9  C) 14  D) 11  E) y + 14

Solution: 11 it is....nice one....   11
Answer: D
In how many different ways can 5 females and 5 males form a circle such that the males and the females alternate?	Choose the correct choice:
A) 1400
B) 2800
C) 1200
D) 3000
E) 4012

Solution: circle 5 males can be arranged in 4!   gvn that the males and females alternate then 5 places for females   => female arranged in 5 !   tot no of ways = 4! * 5 ! = 24 * 120= 
24 * 120 = 2_880
2880   ANSWER 2800
Answer: B
Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age.
Pick: A) 14 B) 18 C) 20 D) 22 E) 24

Solution: Explanation:   Present age is 4x and 3x,   => 4x + 2 = 26 => x = 6   So Deepak age is = 3(6) = 18   Option 18
Answer: B
A and B invest money in the ratio 8:9 and they has loss of Rs.6900 at the end of year. what is the share of loss of B? Choose the correct option:
A) Rs.1600  B) Rs.1500  C) Rs.1400  D) Rs.1300  E) None of the above

Solution: et ratio of Rs.1600 and B be 8x & 9x   so net loss = 8x+9x= 6800   x=400   Rs.1600=3x=3(400)=1200   B= 4x=4(400)=1600   so, B= 1600   Rs.1600NSWER:Rs.1600
Answer: A
Two bullet train s 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:  Select
A) 15.8 sec.  B) 12.8 sec.  C) 11.88 sec.  D) 10.8 sec.  E) 08.8 sec.

Solution: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.   Distance covered in crossing each other = (140 + 190)= 
(140 + 190) = 330
330 m.   Required time= 330x9/250 = 54/5 = 11.88 sec.   ANSWER 11.88 sec.
Answer: C
A $77.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? Options:
A) 15%  B) 23%  C) 25%  D) 60%  E) 80%

Solution: Listed selling price of chair = 77.95 $   Discounted selling price of chair = 59.95 $   Discount = 77.95 - 59.95= 
77.95 - 59.95 = 18
18 $   % decrease in price of chair= (18/77.95) * 100% = 23 % approx   Answer 23%
Answer: B
In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability W at least one of the shirts he draws will be blue?
Choose the correct choice from the following answers
A) 25/153
B) 28/153
C) 5/17
D) 4/9
E) W=12/17

Solution: P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =W= 12/17.   Answer: W=12/17.
Answer: E
In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 5 hours a day, the number of men required is: Pick one:
A) 24
B) 5
C) 6
D) 8
E) 9

Solution: Explanation :   Let the required number of men be x.   Less days, More men (Indirect Proportion)   More working hrs per day, Less men (Indirect Proportion)   Days 8 : 10   Working Hrs 5 : 8 :: 12 : x   => 8 x 5 x x = 10 x 8 x 12   => x = 10 x 8 x 12 / (8 x 5)   => x = 24   24nswer : 24
Answer: A
The perimeter of a square is 72 m. Find the area of the square.  Options:
A) 161 mÂ².
B) 324 mÂ².
C) 166 mÂ².
D) 169 mÂ².
E) 273 mÂ².

Solution: Perimeter of square = 72 m   But perimeter of square = 4 Ã— side   Therefore, 4 Ã— side = 72 m   Therefore, side= 72/4= 
72/4 = 18
18m   Now, the area of the square= (side Ã— side)   Therefore, area of the square = 18 Ã— 18 mÂ² = 324 mÂ².   ANSWER : OPTION 324 mÂ².
Answer: B
The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?  Pick one:  A) 39  B) 28  C) 27  D) 80  E) 71

Solution: 1/2 * d (10 + 6) = 640   d = 80   Answer: 80
Answer: D
14, 35, 56, 63, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
Choose one.
A) 402
B) 259
C) 322
D) 686
E) 847

Solution: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7   clearly the answer is 402 because if we divide 402 by 7 we get a remainder of 57.42   Correct answer - 402
Answer: A
Two pipes can fill a tank in 30 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?  Choices
A) 5 Hours	B) 7 Hours	C) 8 Hours	D) 9 Hours	E) 15 Hours

Solution: In 1 hour it fill 1/30 + 1/12 - 1/20 = 1/15   So fill tank fill up in 15 Hours   ANSW15 HoursR:15 Hours
Answer: E
9log9(4) = ?  Choose the correct choice
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Exponential and log functions are inverse of each other. Hence   aloga(x) = x , for all x real and positive.   and therefore   9log9(4) = 4   correct answer 4
Answer: D
The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/8. What is the probability of Michael passing his driving test?  Select the correct option: A) 1/24. B) 1/2. C) 1/3. D) 2/3. E) 2/5

Solution: 1/4 *1/m= 1/8 , 1/m = 1/2   Answer 1/2.
Answer: B
A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts three hours after A. If B and K overtake A at the same instant, how many hours after A did K start?	Choose the correct choice from the following choices:	A) 3	B) 4.5	C) 6	D) d) 5.5	E) e) 5

Solution: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.   We know their rates are 30, 40 and 60.   Say the time taken by B is T hrs. Then A takes 3+T hrs. And we need to find the time taken by K.   Distance covered by A = Distance covered by B   30*(3+T) = 40*T   T = 9 hrs   Distance covered by B = Distance covered by K   40*T = 60*Time taken by K   Time taken by K = 40*9/60= 
40*9/60 = 6
6 hrs   Time taken by A= 3+T = 3+9= 
3+9 = 12
12 hrs   Time taken by K= 6 hrs   So K starts  12-6= 
 12-6 = 6
6 hrs after A. (answer 6)
Answer: C
Steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?	Pick.
A) 53.33 mph  B) 56.67 mph  C) 60 mph  D) 64 mph  E) 66.67 mph

Solution: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4= 
240/4 = 60
60   Answer: 60 mph
Answer: C
The present age of a father is 3 years more than five times the age of his son. Three years hence, father's age will be 17 years more than thrice the age of the son. Find the present age of the father.  Choose the most appropriate option:
A) 33  B) 38  C) 29  D) 40  E) 53

Solution: if the present age be x years.   father's will be (5x+3)years..   so, (5x+3+3)=3(x+3)+17   or, x=10   so the fathers present age =(5x+3)=(5*10+3)= 
(5*10+3) = 53
53years..   ANSW53R : OPTION 53
Answer: E
A large tank can filled by A and B in 30 minutes and 45 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?	Answers
A) 30min B) 20min C) 25min D) 40min E) 45min

Solution: Part filled by A+B in 1 minute = 1/30 + 1/45 = 1/45   Suppose the tank is filled in x minutes   Then, x/2(1/45 + 1/45) = 1   x/2 * 2/45 = 1   x = 45 min   Answer is 45min
Answer: E
What percent of 40 is 80?  Choose one:	A) 133 1⁄3	B) 75	C) 200	D) 33 1⁄3	E) 25

Solution: To find out the % of 80 in 40   Do 80/40 = 200%   Answer 200)
Answer: C
A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1640 had it been put at the rate of interest compounded annually?	Choose the correct choice from the following
A) 4.5	B) 3.5	C) 3	D) 2	E) 1.5

Solution: We can form equations as following:   Initial amount = P, Total amount after interest = T, Interest per year = I   T = P+I   Given T1 = P+2I = 1400T2 = P+ 5I = 2000   From this we get, P = 1000I = 200 $   Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)   consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.   To get a 240 $ compound interest the duration have to be > 1 year and < 2 years.   Only option fitting : Option 1.5.
Answer: E
Three numbers are in the ratio 4 : 5 : 6 and their average is 20 . The largest number is:
Pick:
A) 24
B) 32
C) 36
D) 42
E) 45

Solution: Explanation:   Let the numbers be 4x, 5x and 6x. Therefore,   (4x+5x+6x)/3 = 20   15x = 60   x = 4   Largest number = 6x = 24.   24NSWER 24
Answer: A
P has $42 more than what Q and R together would have had if both B and C had 1/8 of what P has. How much does P have? Select the correct option:
A) $44  B) $48  C) $52  D) $56  E) $60

Solution: P = (2/8)*P+42   (6/8)*P=42   P=56   The answer is $56.
Answer: D
Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way?  Choose the most appropriate option.
A) 350	B) 345	C) 320	D) 280	E) 240

Solution: Let us backsolve here.   The answer option has to be divisible by 7 to give us 1/2.   Let us try k=280 km. Time taken will be 3.5 hours and 4 hours.   Hence 280 is the answer.
Answer: D
If a2 + b2 + c2 = 250 and ab + bc + ca = 3, then a + b + c is Choose the correct choice from the following options
A) 4
B) 8
C) 16
D) 32
E) 64

Solution: by formula ,   (a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),   since, a^2 + b^2 + c^2 = 250 and ab + bc + ca = 3,   (a + b + c)^2 = 250 + 2(3)   = 256   = 16^2   therefore: a + b + c = 16   ANSWER:16
Answer: C
which of the following could be the perimeter of the triangle?If two sides of a triangle have lengths 6 and 12.
I. 30
II. 25
III. 18 Answers
A) I only
B) II only
C) II and III only
D) none
E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Therefore:   (12-6) < {third side} < (12+6).   6< {third side} < 18.   Perimeter = {third side} + 6 + 18= {third side} + 24.   30< {perimeter} < 42   Answer: none.
Answer: D
In what time will a railway train 120 m long moving at the rate of 70 kmph pass a telegraph post on its way?  Choose the correct choice from the following options:  A) 3 sec  B) 4 sec  C) 5 sec  D) 6 sec  E) 7 sec

Solution: T = 120/70 * 18/5 = 6 sec   ANSWER:6 sec
Answer: D
If n = 3^6 – 2^6 which of the following is NOT a factor of n? Choose the correct choice from the following options
A) 97 B) 7 C) 35 D) 5 E) 19

Solution: 3^6 - 2^6   = (3^3)^2 - (2^3)^2   =(3^3 + 2^3)(3^3 - 2^3)   =(27+8)(27-8)   =35*19   =7*5*19   Therefore, 97 is Not a factor of n.   97
Answer: A