MU-NLPC/Calc-aqua_rat huggingface dataset:
Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?	Choose the most appropriate option
A) 28/243  B) 31/243  C) 35/729  D) 83/729  E) 101/729

Solution: The number of ways to select w, x, and y is:   9*9*9= 
  9*9*9 = 729
729   The number of ways to choose three different numbers from the set is 9C3=84.   There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.   The probability that w < x < y is 84/729 = 28/243   The answer is 28/243.
Answer: A
A boat moves down stream at the rate of 1 km in 6 minutes and
upstream at the rate of 1 km in 10 minutes. The speed of current is
Pick:
A) 2 kmph  B) 3 kmph  C) 4 kmph  D) 5 kmph  E) 6 kmph

Solution: If speed(in kmph) of the boat=b and current=c, then   In downstream time taken(in hrs.)=1/(b+c)=6/60=1/10 or b+c=10 ---(i) &   In upstream time taken(in hrs.)=1/(b-c)=10/60=1/6 or b-c=6 ---(ii)   From (i) & (ii), b=8, c=2   2 kmphNSWER:2 kmph
Answer: A
If a, b, w are integers, 33 = abw, and a < b < w, what is the smallest possible value of a? Choose the correct choice from the following options
A) -33 B) -3 C) 1 D) 3 E) 11

Solution: Given : a * b * w = 33.   33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.   Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).   We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.   -33 * -1 * 1= 
-33 * -1 * 1 = 33
33.   Correct answer is -33
Answer: A
If you multiply two integers together and
then add 4, the result is 40. Which of the
following could NOT be the sum of the
two numbers?	Pick
A) 12 B) 13 C) 15 D) 18 E) 20

Solution: Let the two integers equal x and y, and then create the following equation and simplify:   xy + 4 = 40   xy = 36   So x and y are a pair of integers that equal 36. Try adding all possible combinations of two   integers that multiply out to 36:   1 × 36 = 36 1 + 36 = 37   2 × 18 = 36 2 + 18 = 20   3 × 12 = 36 3 + 12 = 15   4 × 9 = 36 4 + 9 = 13   6 × 6 = 36 6 + 6 = 12   This list of sums includes 12, 13, 15, and 20, but not 18. Thus, no pair of integers both   satisfies the original equation and adds up to 18   correct answer 18)18
Answer: D
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio A of men to women?  Select: A) 5:2 B) 5:1 C) 4:3 D) 4:1 E) 3:1

Solution: (5:2) 5:2=184 x 5 + 170 x 2 = 1260.5:2
Answer: A
Find the arithmetic mean P of all roots of the following equation- see an attachment.	Choose the most appropriate option:
A) 2  B) 1  C) 0.5  D) -1/3  E) 0.3

Solution: arithmetic mean P your answer C and E are same, can you correct one of them please. thanks.0.5
Answer: C
The product of two numbers is 336 and the sum of their squares is 289. The sum of the number is?  Choose the correct choice: A) A)23 B) B)25 C) C)27 D) D)31 E) E)35

Solution: Let the numbers be x and y.   Then, xy = 336 and x2 + y2 = 289.   (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 336) = 961   x + y =31.   Option 31
Answer: D
Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 5 hours. How long would it take Taimour to paint the fence alone? Choose one.
A) 6 hours B) 8 hours C) 15 hours D) 24 hours E) 32 hours

Solution: I believe the answer is C. Please see below for explanation.   if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T   if working together they can do the job in 8 hours we can infer 1 = 2T+T * 5 => 1/15   Working alone Taimour can do the job in 1 = 1/15* hours => 15   Answer 15 hours
Answer: C
Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 35% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?  Choose the correct choice from the following options.
A) $20
B) $65
C) $50
D) $80
E) $100

Solution: Deargoodyear2013,   I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.   Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.   They had this same selling price, $100, before they made the change, and had a profit of 35%, so the manufacturing must have been $65. Answer = ($65).
Answer: B
There are 2 sections A and B in a class, consisting of 50 and 70 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class? Select
A) 50.78kg	B) 49.32kg	C) 61.67kg	D) 69.15kg	E) 70.89kg

Solution: Total weight of 50+70 students = 50*50 + 70*70= 
50*50 + 70*70 = 7_400
7400   Average weight of the class is= 7400/120 = 61.67 kg   Answer is 61.67kg
Answer: C
The sum of two consecutive numbers is 37. What are they?	Choose the correct choice from the following choices:
A) 18 and 19  B) 18 and 21  C) 18 and 23  D) 19 and 20  E) None

Solution: Two consecutive numbers are like 8 and 9, or 51 and 52.   Let x, then, be the first number. Then the number after it is x + 1.   The problem states that their sum is 37:   word problem = 37   2x = 37 − 1   = 36.   x = 36   2   = 18.   The two numbers are 18 and 19.   Option is 18 and 19
Answer: A
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/8. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?	Choose the correct choice.
A) 134	B) 146	C) 152	D) 162	E) 170

Solution: The probability of survival for each of the first 3 months of life is 1-1/8= 7/8, so of 200 newborn 200*7/8*7/8*7/8=~134 is expected to survive.   134nswer: 134.
Answer: A
In a class of 50 students, 20 play Tennis, 15 play Cricket and 11 play Football. 7 play both Tennis and Cricket, 4 play Cricket and Football and 5 play Tennis and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports? Choose the correct choice from the following options:
A) 10	B) 20	C) 25	D) 30	E) 40

Solution: {Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS   50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;   Those who play ONLY Hockey and Cricket are   7-2= 
  7-2 = 5
5;   Those who play ONLY Cricket and Football are  4-2= 
 4-2 = 2
2;   Those who play ONLY Hockey and Football are 5-2= 
5-2 = 3
3;   Hence, 5+2+3=10 students play exactly two of these sports.   {Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS   50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;   Those who play ONLY Hockey and Cricket are   7-2= 
  7-2 = 5
5;   Those who play ONLY Cricket and Football are  4-2= 
 4-2 = 2
2;   Those who play ONLY Hockey and Football are 5-2= 
5-2 = 3
3;   Hence, 5+2+3=10 students play exactly two of these sports.   10nswer 10
Answer: A
Bradley owns b video game cartridges. If Bradley’s total is one-ninth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b? Choices:
A) 37b / 4
B) 39b / 4
C) 41b / 4
D) 43b / 4
E) 45b / 4

Solution: b = Bradley’s total   9b = Andrew’s total   b/4 = 41b / 4harlie’s total   The total number of cartridges is:   b + 9b+ b/4 = (4b + 36b + b) / 4 = 41b / 4   The answer is 41b / 4.
Answer: C
According to a survey, at least 65% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?  Choose the correct choice: A) 15% B) 20% C) 25% D) 0% E) 35%

Solution: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.   80% like cherries and 20% don't like cherries.   Let's combine this with the people who like bananas.   20% don't like cherries but do like bananas.   55% like cherries and bananas.   25% like cherries but not bananas.   Now let's distribute the people who like apples.   20% like bananas and apples, but not cherries.   25% like cherries and apples, but not bananas.   20% like all three.   35% like cherries and bananas, but not apples.   The answer is 20%.
Answer: B
Find the two digit number, such that the ratio is 7/4 of original number to the number formed by reversing the digits.
Choose the correct choice from the following choices
A) 20	B) 21	C) 22	D) 23	E) 24

Solution: here ratio is 7/4.   so lets check one by one.   for 1 : 7*1/4*1 = 7/4   for 2 : 7*2/4*2 = 14/8 ,which doesn't satisfy the conditions.   for 3 : 7*3/4*3 = 21/12   ANSWER:21
Answer: B
A soccer team played 140 games and won 50 percent of them. How many games did it win?  Choose the correct choice from the following:  A) 140  B) 94  C) 104  D) 70  E) 80

Solution: 50% of 140 =x   0.50*140= 
0.50*140 = 70
x   70=x   answer :70
Answer: D
Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 2.5. What value is exactly 2 standard deviations less than the mean?  Choose the correct choice from the following options:	A) 8.5	B) 11	C) 11.5	D) 12	E) 12.5

Solution: The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*2.5=8.5.   8.5nswer: 8.5.
Answer: A
A ladies hostel had provision of food for 300 women for 45 days. After 10 days, 275 women left the hostel. The number of days for which the remaining food will last is:
Choose the correct choice from the following:
A) 420	B) 430	C) 450	D) 480	E) 425

Solution: Explanation :   After 10 days : 300 women had food for 35 days.   Suppose 25 women had food for x days.   Now, Less women, More days (Indirect Proportion)   25 : 300 :: 35 : x   => 25 x x = 300 x 35   => x = 300 x 35 / 25   => x = 420   420nswer : 420
Answer: A
An auction house charges a commission of 17% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
Choose the correct answer: A) $115,000 B) $160,000 C) $205,000 D) $240,000 E) $365,000

Solution: Say the price of the house was $x, then 0.17*50,000+0.1*(x-50,000)=24,000 --> x=$205,000 (17% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).   Answer: $205,000.
Answer: C
In a certain corporation, there are 300 male employees and 150 female employees. It is known that 10% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?  Choose the correct choice from the following.
A) 1/5	B) 5/15	C) 6/15	D) 3/10	E) 4/15

Solution: P(female) = 150/450 = 1/3   P(male with advanced degree) = 0.1*300/450 = 30/450 = 1/15   The sum of the probabilities is 6/15 = 2/5   The answer is 6/15.
Answer: C
At a speed of 40 miles per hour, a certain car uses 1 gallon of gasoline every 40 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour, the amount of gasoline used would be what fraction of a full tank?	Choose the correct option.
A) 3/25 B) 5/12 C) 7/12 D) 2/3 E) 25/36

Solution: Gas used = (5 hours)*(40 miles/hour)*(1 gallon/40 miles) = 5 gallons   Portion used = (5) / 12 = 5/12   Ans 5/12
Answer: B
If x ≠ 1 and if yx/(y - x) = 1, what is the value of y in terms of x? Choose the correct answer:
A) (1-x)/x B) (x - 1)/x C) x/(x + 1) D) (x + 1)/x E) x/(1-x)

Solution: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.   Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.   Final Answer:   x/(1-x)
Answer: E
A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 250 items for $150 each, what will her monthly salary be?
Choose the correct choice
A) $1,500 B) $1,800 C) $3,250 D) $2,500 E) $2,800

Solution: Ans : 1000+ 7.5 % * 150 * (250-50) = $ 3250   ANSWER:$3,250
Answer: C
What least number must be subtracted from 427751 so that remaining no.is divisible by 10  Pick
A) 3 B) 1 C) 6 D) 8 E) 9

Solution: Explanation:   On dividing 427751 by 10 we get the remainder 1, so 1 should be subtracted   Option 1
Answer: B
Which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?
Choose the correct answer:	A) x^2 + 5x + 6 > 0	B) |x + 2| > 4	C) 9x - 7 < 3x + 14	D) x^2 - 4x + 3 < 0	E) (B) and (D)

Solution: Factorizing x^2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.   This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.   Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x".   ANSWER : x^2 - 4x + 3 < 0
Answer: D
P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? Choose the correct choice from the following options: A) 16 days B) 17 days C) 19 days D) 14 days E) 10 days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.   Hence, P can do the work in 16 days.   16 daysnswer:16 days
Answer: A
Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings?	Choices.
A) 3600  B) 3607  C) 3608  D) 3602  E) 3603

Solution: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.   Income, 5x = 18000 => x = 3600   Savings = Income - expenditure = 5x - 4x = x   So, savings = Rs. 3600.   3600nswer:3600
Answer: A
There are 12 yes or no questions. How many ways can these be answered?  Choose the correct answer
A) 1254 B) 3624 C) 4578 D) 4096 E) 3265

Solution: Each of the questions can be answered in 2 ways (yes or no)   Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.   Ans: 4096
Answer: D
Simplify: 0.3*0.8+0.1*0.5	Choose the correct choice:
A) 0.52	B) 0.29	C) 0.48	D) 0.64	E) 0.46

Solution: Given exp. = 0.3*0.8+(0.1*0.5) = 0.24+0.05= 
0.24+0.05 = 0.29
0.29   Answer is 0.29.
Answer: B
There is a train and car. The ratio btw the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480km in 8h. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 6h?  Pick.
A) 300 km  B) 400 km  C) 420 km  D) 430 km  E) 450 km

Solution: Sol. Speed of bus = 480/8= 
480/8 = 60
60km/ h   Speed of train= (60*4)/3= 
(60*4)/3 = 80
80 km / h   Speed of train : Speed of car= 16 : 15   Speed of car =80/16 * 15= 
80/16 * 15 = 75
75 km/ h   Distance covered by car in 6 hr= 75 × 6 = 450 km   450 km
Answer: E
John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination. How many miles did John drive?
Select the correct option
A) 235 miles. B) 245 miles. C) 225 miles. D) 265 miles. E) 275 miles.

Solution: The total distance D traveled by John is given by   D = 45 * 2 + 3 * 45= 
45 * 2 + 3 * 45 = 225
225 miles.   Answer 225 miles.
Answer: C
If k, (k+200), (k+350), and 15*K are all multiples of A, then A could equal which of the following ?
Choose the correct option:  A) 20  B) A=25  C) 75  D) 100  E) 150

Solution: {Multiple of A} - {Multiple of A} = {Multiple of A}.   (K+200) - k = 200 = {Multiple of A}.   (K+350) - k = 350 = {Multiple of A}.   Both 200 and 350 are multiples of only option B.   Answer: A=25.
Answer: B
79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately? Choices:
A) 10^7	B) 10^11	C) 10^9	D) 10^10	E) 10^8

Solution: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,071 bacteria each. How many bacteria are there approximately?   A. 10^7   B. 10^8   C. 10^9   D. 10^10   E. 10^11   -> Due to approximately, 79=80, 48=50, 25,071=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is 10^8.
Answer: E
The average of four positive integers is 67. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers? Options
A) 72  B) 78  C) 80  D) 82  E) 84

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 67 => A + B + C + D = 268 ---> (1)   A = 93, D = 39 and B - C = 28   (1) => B + C = 268 - (A + D) = 268 - 132= 
268 - 132 = 136
136.   B + B -28= 136   B = (136 + 28)/2= 
(136 + 28)/2 = 82
82   ANSWER:82
Answer: D
If 1+2+3+...+n=n (n+1), then
2 (1+3+5+....+99)=?  Pick:
A) 6000  B) 5000  C) 2500  D) 6500  E) None of these

Solution: Explanation :   To solve this use the formula of AP,   Sn= (n/2)(a+l) ................(1)   To find n, use   => Tn= a+(n-1)d   => 99=1+(n-1)2   => n=50   Use value of n in (1)   then,   Sn = (50/2)(1+99) = 2500   Ans:- 2(Sn) = 5000   Hence (5000) is correct   Answer : 5000
Answer: B
3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is: Choose the correct choice
A) 2/9  B) 1/9  C) 8/9  D) 7/9  E) 6/9

Solution: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house   there will be 1 case when x,y,z will buy house a   another when they buy house b   and another when they buy house c   so the prob that they buy same house is 3*1/27=1/9   ANSWER:1/9
Answer: B
Find the highest common factor of 36 and 84. Answers.
A) 4 years
B) 6
C) 7
D) 8
E) 12

Solution: 36 = 22 x 32   84 = 22 x 3 x 7   H.C.F. = 22 x 3 = 12.   Answer: Option 12
Answer: E
X, Y, Z working alone finish constructing a house in 4, 6 and 12 hrs. resp. X starts alone and works for 1 hr. He is then joined by Y and they work together for 1 hr. Finally Z joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
Choose the correct option
A) 11.30 am  B) 11.35 am.  C) 11.40 am.  D) 12 am  E) 11.20am

Solution: Let the total work be 12 units   Efficiency of X = 3 units/ hour   Efficiency of Y = 2 units/ hour   Efficiency of Z = 1 units/ hour   So, X completes 3 units of work by 10 am   So, X and Y completes 5 units of work by 11 am   Work left is 4 units ( 12 - 3 - 5 ) and combined efficiency of X, Y and Z is 6 units   So, time required to complete 4 units will be 4/6 => 4/6*60= 
4/6*60 = 40
40 minutes...   So they will require 40 minutes after 11 am to complete the remaining work...   Hence answer will be (11.40 am.) 11:40 am
Answer: C
Sandy bought 65 books for $1280 from one shop and 55 books for $880 from another shop. What is the average price that Sandy paid per book?
Choose the correct answer
A) $12  B) $14  C) $16  D) $18  E) $20

Solution: average price per book = (1280 + 880) / (65 + 55) = 2160 / 120= 
2160 / 120 = 18
$18   The answer is $18.
Answer: D
If the sum of a number and its square is 182, what is the number?  Choose the correct answer.
A) 15	B) 26	C) 28	D) 91	E) None of these

Solution: Let the number = x   Then, x2 + x = 182   or, x2 + x – 182 = 0   or, x + 14x – 13x – 182 = 0   or, x(x + 14) – 13(x + 14) = 0   or, (x – 13)(x + 14) = 0   or, x = 13 (negative value is neglected)   Answer None of these
Answer: E
The number which exceeds 16% of it by 42 is : Choose the correct choice from the following options
A) 50
B) 52
C) 58
D) 60
E) 62

Solution: Solution   Solution   Let the number be x.   x-16% of x =42   x-16/100x =42   x-4/25x=42   21/25x=42   x=(42x25/21)= 50   50nswer 50
Answer: A
Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?  Choose the most appropriate option.
A) 19 11/17%  B) 15 11/17%  C) 18 11/17%  D) 17 11/17%  E) 10 11/17%

Solution: 850 --- 150   150 --- ? =>   =150/850 *100   =17 11/17%   Answer: 17 11/17%
Answer: D
At the beginning of 2011, Albert invests $15,000 at 10% simple annual interest, $6,000 at 7% simple annual interest, and $x at 8% simple annual interest. If, by the end of 2011, Albert receives interest totaling 9% of the sum of his three investments, then the ratio of $x to the sum of his two other investments is  Choose the most appropriate option: A) 1 : 3 B) 1 : 4 C) 1 : 6 D) 1 : 7 E) 1 : 8

Solution: Total interest earned = (10/100)*15000 + (7/100)*6000 + (8/100)*x = (192,000+8x)/100   Also, Total interest earned = (9/100)*(15000 + 6000 + x) = (9/100)*(21000 + x)   i.e. (9/100)*(21000 + x) = (192,000+8x)/100   i.e. 189,000 + 9x = 192,000+8x   i.e. x = 3000   Required ratio = x / (15000 +6000) = 3000 / 21000 = 1/7   Answer: option 1 : 7
Answer: D
A single pipe of diameter x has to be replaced by six pipes of diameters 10 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is:  Pick one:  A) 13 cm  B) 18 cm  C) 24.5 cm  D) 24 cm  E) 25 cm

Solution: Volume of water flowing through 1 pipe of dia x = Volume discharged by 6 pipes of dia 6 cms   As speed is same, area of cross sections should be same.   Area of bigger pipe of dia x = Total area of 6 smaller pipes   pi*R^2 = 6 * pi* 5^2   R = 12.25 cm   Dia = 24.5 cm   ANSWER:24.5 cm
Answer: C
The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?  Choices:
A) 178.26 B) 178.29 C) 178.2 D) 178.23 E) 178.21

Solution: Calculated average height of 35 boys = 180 cm.   Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm   = 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm   = 180 cm - 1.71 cm = 178.29 cm.   Answer:178.29
Answer: B
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 of Y divided by 5?  Choose the correct choice from the following options:
A) 1.
B) 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 (2.)
Answer: B