MU-NLPC/Calc-aqua_rat huggingface dataset:
How many 2-inch by 3-inch rectangular tiles are required to tile this shaded region?	Answers:
A) Less than 10	B) 10—100	C) 101—1,000	D) 1,001—1,500	E) 1,500+

Solution: convert all feet into inches as we are looking into tiles which are in inches   so total area of garden = 6*12*12*12   shaded region = 12*12(6*12-2*3) = 12*12*2*3(12-1)   no of 2"*3" tiles required =12∗12∗12∗2∗3∗11/2∗3=12∗12∗11=1584>1500   so ans is 1500+   ANSW1,500+R:1,500+
Answer: E
An offshore company sells two products, L and M. Last year, seventy percent of the units sold were product L, and the price of product L was 25 percent greater than the price of product M. Approximately what percent of the total revenue the company received last year was from the sale of product L? Pick one:
A) 15%	B) 25%	C) 35%	D) 65%	E) 74%

Solution: Percentage of total units that is product L = 70 %   Price of product L = 25 percent greater than price of product M.   Now , we can consider this as a weighted average scenario .   If the price of both the products L and M was equal , then contribution of product L to total sales would be = 70%   But since , price of product L is greater than M , then contribution of product L to total sales will be greater than 70%   The only option is 74%   Answer 74%
Answer: E
The difference between a two-digit number and the number obtained by interchanging the digits is 9. What is the difference between the two digits of the number?  Choose the correct choice from the following:  A) 8  B) 2  C) 7  D) Cannot be determined  E) None of these

Solution: Suppose the two-digit number be 10x + y.   Then we have been given   l0x + y – (10y + x) = 9   ⇒ 9x – 9y = 9   ⇒ x – y = 1   Hence, the required difference = 1   Note that if the difference between a two-digit number and the number obtained by interchanging the digits is D, then the difference between the two digits of the number = D⁄9   Answer None of these
Answer: E
If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many digits does this integer consists of?	Choices.
A) 150	B) 339	C) 342 integers	D) 359	E) 362

Solution: 1-digit integers   Number of 1-digit integers (1 to 9) = 9 - 1 + 1= 
9 - 1 + 1 = 9
9   Number of digits used= (9)(1) = 9   2-digit integers   Number of 2-digit integers (10 to 99) = 99 - 10 + 1= 
99 - 10 + 1 = 90
90   Number of digits used= (90)(2) = 180   3-digit integers   Number of 3-digit integers (100 to 150) = 150 - 100 + 1= 
150 - 100 + 1 = 51
51   Number of digits used= (51)(3) = 153   TOTAL # of digits uses = 9 + 180 + 153= 
9 + 180 + 153 = 342
342   Answer: 342 integers
Answer: C
Instead of multiplying a number by 5, the number is divided by 5. What is the percentage of error obtained ?
Choose the correct answer.
A) 98%
B) 97%
C) 96%
D) 99%
E) 95%

Solution: let the number be x   the right number is 5x   the wrong number is x/5   error is(5x-x/5)=24x/5   percentage of error is((24x/5)/5x)*100=96%   ANSWER:96% ((24 /5)/5 )*100= 
 ((24 /5)/5 )*100 = 96
96%   ANSWER:96%
Answer: C
The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers? Answers
A) 323 B) 377 C) 344 D) 239 E) 112

Solution: Explanation:   Let the four numbers be x, x + 2, x + 4 and x + 6.   => x + x + 2 + x + 4 + x + 6 = 36   => 4x + 12 = 36 => x = 6   The numbers are 6, 8, 10 and 12.   Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144= 
36 + 64 + 100 + 144 = 344
344.   Answer: 344
Answer: C
What is the greatest prime factor of 4^18 - 2^30?  Select the correct option
A) 2
B) 3
C) 5
D) 7
E) 11

Solution: 4^18 - 2^30   =(2^2)^18 - 2^30   = 2^36 - 2^30   = 2^30 (2^6 -1)   = 2^30 * (64-1)   = 2^30 * 63   = 2^30 * 7 * 9   = 2^30 * 3^2 * 7   The greatest prime factor is 7.   The answer is 7.
Answer: D
the twonumbers (23__)^32 and (12__)^ 33 has 6 in the last digit what is the missing digit ?  Answers.
A) 4  B) 5  C) six (6)  D) 7  E) 8

Solution: it should be 6   as last digit in all powers of nos with unit digit 6 is 6.   ANSWER:six (6)
Answer: C
Find the area of a parallelogram with base 48 cm and height 36 cm?  Choose the correct choice from the following options:
A) 1730 cm2
B) 1728 cm2
C) 1870 cm2
D) 1890 cm2
E) 668 cm2

Solution: Area of a parallelogram = base * height   = 48 * 36= 
48 * 36 = 1_728
1728 cm2   Answer: 1728 cm2
Answer: B
In how many ways can 5 boys and 2 girls bearranged at a table if 2 girls are never together?
Choose the correct choice from the following answers
A) 345  B) 379  C) 420  D) 430  E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
Find the number of different meals of 4 items that you can get from the given menu of 6 items and no need to choose different items. Choose one: A) 120 B) 126 C) 5040 D) 15 E) 18

Solution: total item : 6   we can select : 4   thus -> 6C4 which = 6C2   :: 6*5/ 2*1= 
6*5/ 2*1 = 15
15   ANSWER:15
Answer: D
Calculate 469111 x 9999 = ? Pick
A) 4586970843  B) 4686970743  C) 4691100843  D) 4586870843  E) 4690640889

Solution: Answer   469111 x 9999 = 469111 x (10000-1)   = 4691110000 - 469111= 
4691110000 - 469111 = 4_690_640_889
4690640889.   Option: 4690640889
Answer: E
The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 24 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ? Choose the correct choice from the following answers
A) 13	B) 14	C) 15	D) 16	E) 18

Solution: a must be an integer as it is the number shoots at a rate of 24sec/shoot   3*60 + 24a = 10*60   24a = 420   a = 17   The total number of shoots -->1 +17 = 18 and   19th shoot will be taken at 612 seconds which is above 10 minutes   ANSW18R: 18-- 1 +17= 
-- 1 +17 = 18
18 and   19th shoot will be taken at 612 seconds which is above 10 minutes   ANSW18R: 18
Answer: E
A survey was taken among 100 brainiacs. Of those surveyed, twice as many brainiacs likerebus teasers as math teasers. If 18 brainiacs like both rebus teasers and math teasers and 4like neither kind of teaser, how many brainiacs like math teasers but not rebus teasers?
Choose one:
A) 17
B) 18
C) 19
D) 20
E) 21

Solution: let X brainiacs like ONLY rebus teasers and Y brainiacs like ONLY math teasers .   NOW,X+Y=100-18-4= 
100-18-4 = 78
78.   ALSO GIVEN THAT,X+18=2(Y+18)   X=2Y+18.   78-Y=2Y+18   3Y=60   Y=20   SO 20 brainiacs like math teasers but not rebus teasers   ANSWER:20
Answer: D
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 9020, then what will be the share of Sameer in the profit?
Choose the correct choice from the following choices
A) s.3080	B) s.2380	C) s.2329	D) s.2329	E) s.2312

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 9020 * 14/41   = Rs.3080.   s.3080nswer: s.3080
Answer: A
A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 88 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
Answers
A) 20
B) 30
C) 40
D) 60
E) 72

Solution: Total distance = 88   Distance = Speed * Time   Walking speed = s1 = 8   Walking time = t1   Bike speed = s2 = 16   Time traveled in bike = t2   d1 + d2 = 88   s1t1 + s2t2 = 88   8*t1 + 16*t2 = 88   t1 + 2*t2 = 11 ----- (1)   Given: t1 + t2 = 8 ----- (2)   (1) - (2) --> t2 = 3 and t1 = 8 - 3= 
8 - 3 = 5
5   Walking distance= s1*t1 = 8*5= 
8*5 = 40
40   Answer: 40
Answer: C
The sum of all the integers k such that −26 < k < 24 is Choose the correct option.
A) 0  B) −2  C) −25  D) −49  E) −51

Solution: Since k defines a range between −26 < k < 24 we can set 0 as the reference point for the negative values and positive values.   The negative values will range from -25 to 0 whereas the positive values will range from 0-23.   We can conclude that for all but -25 and -24 the number pairs will add to 0. So we have left -25 - 24 = -49.   Answer −49.
Answer: D
A rectangular-shaped carpet that measures x feet by y feet is priced at $42. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)  Choose the correct choice from the following choices:
A) xy/360  B) 9xy/40  C) 40xy/9  D) 378xy  E) 378/(xy)

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 42 / (xy/9) = 378/(xy).   The answer is 378/(xy).
Answer: E
What is the Value given by the equation (-2+a)^2=(a-2)^2?  Choose one
A) Indefinite	B) Two	C) Three	D) One	E) None

Solution: (-2+a)^2=(a-2)^2   Both the equations in RHS and LHS are equal   So it give the Value One   Option One is answer
Answer: D
A customer purchased a package of ground beef at a cost of $1.80 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 20 percent less than the package of ground beef. What was the cost per pound of the steak?
Choices:
A) $2.05	B) $2.15	C) $2.25	D) $2.35	E) $2.45

Solution: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.80.   Let x be the price per pound for the steak.   Then 0.8x = 180   x = 180/0.8 = $2.25   The answer is $2.25.
Answer: C
The password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and characters can be repeated. Given these rules, how many different passwords are possible?
Choose the correct choice from the following choices:  A) 2^9  B) 2^14  C) 2^18  D) 2^40  E) 2^48

Solution: 26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have;    26+26+10+1+1= 
 26+26+10+1+1 = 64
64, or 2^6 possibilities per character of the password.   Total number of possible combinations: (2^6)^8= 2^48   ANSW2^48R:2^48
Answer: E
Find 16th term in the series 7, 13, 19, 25, ...	Choose the correct option.
A) 97
B) 98
C) 99
D) 100
E) 101

Solution: SOLUTION:   a = 7   d = 13 – 7 = 6   16th term, t16 = a + (n-1)d = 7 + (16 – 1)6 = 7 + 90= 
7 + 90 = 97
97   97NSWER IS 97
Answer: A
If the wheel is 14 cm then the number of revolutions to cover a distance of 1672 cm is? Select the correct option: A) 22 B) 28 C) 19 D) 12 E) 88

Solution: 2 * 22/7 * 14 * x = 1672 => x = 19   Answer: 19
Answer: C
During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?  Answers
A) x/8 B) x/5 C) 2x/3 D) 3x/4 E) 4x/5

Solution: Let y be the number of total burgers.   veggie = y/6 , non veggie = 5y/6   1/4 of the rest of the burgers sold were double-meat   => 5y/6 * 1 = double meat = x   => y/6 = x/5 = veggie   Hence x/5
Answer: B
A can run 3 km distance in 2 min , while B can run this distance in 2 min 30 sec. By how much distance can A beat B?  Select: A) 900 m B) 600 m C) 120 m D) 180 m E) 190 m

Solution: A takes time 2 minutes=120sec   600 m takes time 2.30 minutes=150sec   diffrence= 150-120= 
150-120 = 30
30sec   now we are to find distance covered in 30 sec by 600 m   150sec=3000m   1sec=20 m   30sec=20x30=600m   ANSWER:600 m
Answer: B
Joe invested one half of his savings in a bond that paid simple interest for 2 years and received $450 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?	Pick
A) 5%	B) 10%	C) 12%	D) 15%	E) 68%

Solution: First divide $450/2years to get 225$/yr non-compounding interest.   Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$225= $380.   To find the difference in interest gained, $380-$225= $155 increase in interest after the first year through compounding.   From this information we can set up the equation $225 * X% = $155=68% giving us answer choice 68%.
Answer: E
How many positive integers less than 9,000 are there in which the sum of the digits equals 5?  Choose the correct option
A) 56	B) 57	C) 58	D) 59	E) 60

Solution: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.   Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).   So, for example:   XX|X|X|X = 2111   ||XXX|XX = 0032   etc.   There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.   56
Answer: A
If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r + s?  Choose the correct choice from the following
A) 8
B) 2
C) − 2
D) − 3
E) − 5

Solution: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.   The roots here are -r and -s.   -r - s = -(-2)/1 = r + s = -2   (-r)*(-s) = -15/1 = rs   So one of r and s is -5 and the other is 3. So r + s could be -2.   Answer (− 2)
Answer: C
In how many ways a group of 5 men and 2 women can be made out of total of 7 men and 3 women?	Select:	A) 63	B) 56	C) 25	D) 72	E) 59

Solution: Required number of ways = 7C5 * 3C2 = 7C2 * 3C1 = 3*7*6/2= 
3*7*6/2 = 63
63   63nswer is 63
Answer: A
A certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 ½ years. Find the sum and rate of interests. Choose the correct choice from the following:  A) 13%  B) 12%  C) 25%  D) 18%  E) 52%

Solution: S.I. for 1 ½ years = Rs.(1164-1008) = Rs.156.   S.l. for 2 years = Rs.(156*(2/3)*2)=Rs.208   Principal = Rs. (1008 - 208) = Rs. 800.   Now, P = 800, T = 2 and S.l. = 208.   Rate =(100* 208)/(800*2)= 
(100* 208)/(800*2) = 13
13%   13%nswer is 13%.
Answer: A
For integers x and y, if 91x = 8y, which of the following must be true?
I. x > y
II. y/7 is an integer
III. The cube root of x is an integer	Options
A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: Statement 1: y>x   When y=x=0, equation holds but y is not greater than x   When x=-8 and y=-91, equation again holds but x>y   TRUE   Statement 2: y/7 is an integer   Since x and y are integers, 91x and 8y must also be integers.   It is given that 91x=8y   or 13*7*x = 8 y   or 13x = 8y/7   To balance the equation, y/7 must be an integer   TRUE   Statement 3: The cube root of x is an integer   x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3   So, x may or may not be a cube root.   NOT TRUE   Answer:-I and II
Answer: D
An elevator starts with 5 pasengers and stops at 8 different floors of the house. Find out the probability of all the 5 passengers alighting at different floors.	Choose the most appropriate option.
A) 90 / 512 B) 105 / 512 C) 15/512 D) 30/512 E) 48/512

Solution: Explanation :   Probability   => No. of arrangements with restriction / No. of arrangements without restriction .   => nPr / nr.   => 8P5 / 85 .   => 105 / 512.   Required probability is 105 / 512.   Answer : 105 / 512
Answer: B
if remainder is 8 , quotient is 43 and dividend is 997 then what is divisor ?  Choose the correct choice from the following options:  A) 21  B) 20  C) 23  D) 27  E) 31

Solution: we know   dividend = divisor * quotient + remainder===> 997 = divisor * 43 + 8 =====> 989/43 = divisor ===> divisor = 23   Ans - 23
Answer: C
5, 10, 13, 26, 29, 58, 61, (....)
Choose the most appropriate option:
A) 128	B) 122	C) 64	D) 125	E) 140

Solution: 5 × 2 = 10   10 + 3= 
10 + 3 = 13
13   13 × 2= 26   26 + 3= 
26 + 3 = 29
29   29 × 2= 58   58 + 3= 
58 + 3 = 61
61   61 × 2= 122   Answer is 122
Answer: B
Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,268
III. 5,555,554,673
Answers
A) I​ only  B) I and II​  C) II and III  D) II Only  E) I​ and III

Solution: III. is not divisible by 2 since the last digit is odd so we eliminate option C and E, we are left with option A, B and D   Among option I and II lets check the divisibility of 3   I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3   II. is not divisible by 3 since sum of the digits is not divisible by 3   Thus among the given options only (A) holds true.   I​ onlynswer: I​ only
Answer: A
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :  Pick
A) Rs. 120	B) Rs. 121	C) Rs. 124.75	D) Rs. 130.75	E) Rs. 167

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
If each data point in a certain set Q is increased by a factor of 8, what happens with the set's standard deviation? Choices:
A) Doesn't Change
B) Decreases by Factor 8
C) Increases by Factor 8
D) Increases by 8
E) Can't be determined

Solution: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 8, the standard deviation will increase proportionately, giving us answer choice Increases by Factor 8.
Answer: C
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/4 the number of cans that Karen collected and 1/9 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
Pick:
A) 1/5	B) 1/3	C) 2/5	D) 1/2	E) 1/9

Solution: John = (1/4)Karen --> Karen = 4(John)   John = 1/9(Luke) --> Luke = 9(John)   Total = 36(John)   Karen/Total = 4/36 = 1/9   Answer: 1/9
Answer: E
the cost of a tv is rs.2400 which is 20% below the marked price.If it is sold at a discount of 16% on the marked price,then find its marked price,selling price and profit ? Pick:	A) 2520,120	B) 2520,110	C) 2520,130	D) 2420,120	E) 2620,120

Solution: Let the marked price be x   SP is 20% below x   Then x*80/100 = 2400   4x/5 = 2400   4x = 12000   x = 3000   For 16% discount on x, SP ll be   SP = 3000*84/100 => CP = 2520   Profit = 2520 - 2400= 
2520 - 2400 = 120
120   Marked Price : 3000   Selling Price : 2520   Profit : 120   2520,120NSWER:2520,120
Answer: A
If A father said to his elder son, "I was as old as you are at the present at the time of your birth". If the father's age is 25 years now, what was the son's age four years back?  Answers:
A) 7.5
B) 8.5
C) 9
D) 9.5
E) 10

Solution: Let son's present age be a years. Then,   (25−a)=a   ⇒2a=25   ⇒a=25/2= 
25/2 = 25/2 = around 12.5
12.5   Son's age 4 years back=12.5-4= 
12.5-4 = 8.5
8.5   ANSWER:8.5
Answer: B
The equation r = 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at r = -5, the equation for l is Choose the correct choice from the following answers:
A) + y + 15 = 0  B) - 3x - 11 = 0  C) + y - 16.5 = 0  D) - y - 7 = 0  E) + y + 13.5 = 0

Solution: Is option+ y - 16.5 = 0: -3r + y -6.5= 0=+ y - 16.5 = 0
Answer: C
SECTION-1 If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days? Choose the most appropriate option:
A) 22
B) 99
C) 787
D) 66
E) 11

Solution: Explanation:   If men is fixed,work is proportional to time. If work is fixed, then time is inversely proportional to men therefore, (M1*T1/W1)=(M2*T2/W2) From the above formula i.e (m1*t1/w1)=(m2*t2/w2) so (9*6*88/1)=(6*8*d/1) on solving, d=99 days.   Answer: 99
Answer: B
A train 300 m long passed a pole in 30 sec. How long will it take to pass a platform 650 m long?
Choose the correct answer:
A) 28 sec	B) 89 sec	C) 85 sec	D) 16 sec	E) 95 sec

Solution: Speed = 300/30= 
300/30 = 10
10 m/sec.   Required time= (300 + 650)/10= 
(300 + 650)/10 = 95
95 sec.   Answer:95 sec
Answer: E
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.30 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?  Choose the correct choice from the following choices
A) 160	B) 175	C) 180	D) 200	E) 210

Solution: Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   160 x 2.30 + X x 3.20 = 432   X = 20.   Hence, total hours of work = (160 + 20)= 
(160 + 20) = 180
180.   answer :180
Answer: C
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Choices.
A) 55 years B) 44 years C) 33 years D) Data inadequate E) None of these

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 48 => b + c = 96 --- (2)   From (1) and (2), we cannot find b.   Answer:Data inadequate
Answer: D
if xy+z=x(y+z) which of the following must be true?	Choose the correct choice from the following options.
A) x=2 or z=0
B) x=1 or z=0
C) x=1 or z=1
D) x=0 or z=0
E) x=0 or z=0

Solution: xy+z=xy+xz   z=xz   xz-z=0   z(x-1)=0   Means;   either z=0   OR   x-1=0 i.e. x=1   Answer x=1 or z=0
Answer: B
How much time will it take for an amount of Rs. 400 to yield Rs. 100 as interest at 5% per annum of simple interest?
Choose the correct choice from the following options
A) 5 years	B) 4 years	C) 7 years	D) 6 years	E) 2 years

Solution: Explanation:   Time = (100 x 100)/(400 x 5) years   = 5 years.   5 yearsnswer: 5 years
Answer: A
In a certain country 1/3 of 4 = 8. Assuming the same proportion, what would be the value of 1/8 of 4 ?	Answers:
A) 2	B) 6	C) 5	D) 4	E) 3

Solution: 3   3
Answer: E