MU-NLPC/Calc-aqua_rat huggingface dataset:
City A to city B, Andrew drove for 1hr at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?	Choose one:  A) 57  B) 57.5  C) 61  D) 61.5  E) 62.5

Solution: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,   Average Speed=(Total DistanceTotal Time)=2304=57.5   57.5
Answer: B
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area Q of that hemisphere?	Choose the correct choice from the following.
A) 6/π B) 9/π C) 6 D) 9 E) 12

Solution: Given Area of the base of a hemisphere is 3 = PI * R^2   Thus R = Sqrt ( 3 / PI ) .   Surface area of whole sphere = 4*PI*R^2 .   = 4 * PI * 3 / PI   = 12 .   Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2= 
12 / 2 = 6
6 ( curved part , not including the flat rounded base ) .   But the total surface area= 6 + Area of the base of a hemisphere .   = 6 + 3= 
6 + 3 = 9
9.   Answer is 9 !!
Answer: D
On dividing 15 by a number, the quotient is 4 and the remainder is 3. Find the divisor?  Options:	A) 3	B) 6	C) 9	D) 12	E) 15

Solution: d = (D-R)/Q   = (15 - 3)/4   = 12/4= 
12/4 = 3
3   3)
Answer: A
In how many different ways can 9 people be seated in a room with 11 chairs? Pick one:
A) 40,320
B) 181,440
C) 403,200
D) 1,814,400
E) 19,958,400

Solution: Order doesn't matter   With 11 chairs and only 9 to seat   9!- Number of ways the 9 can seat on the chair   11C2 - Number of ways the 2 empty sits can be vary with the 9 seated   9! * 11C2 = 19,958,400 Answer - 19,958,400
Answer: E
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? Choose the correct option.
A) 7297
B) 2977
C) 2871
D) 6725
E) 2981

Solution: Explanation:   CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer: 6725
Answer: D
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold n bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2n
II. y > n
III. y > 3  Choose the correct choice from the following answers
A) I only  B) II only  C) I and II  D) II and III  E) I, II, and III

Solution: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -   0 Bikes - $20   6 Bikes - $56   12 Bikes - $128   More than 12 bikes - 128 + 18*(n-12) where n is the total number of bikes sold (when n>12).   XN = cycles sold last week   NS = Salary last week.   Y = cycles sole this week   YS = Salary this week.   given YS>2NS   lets test all statements with N=0;   NS = 20   YS >40   True when Y = 4   satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C   lets test all statements with N=1;   NS = 26   YS>52   True when Y=6   Still satisfies all the statements - Nothing achieved   lets test all statements with N=6;   NS = 56   YS>112   True when Y = 11   This proves statement i wrong, hence eliminate E so we are left with   Answer II and III
Answer: D
x is the product of each integer from 1 to 100, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Choose the correct choice from the following answers.
A) 5
B) 6
C) 8
D) 10
E) 12

Solution: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:   n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n   x = 1*2*3....*100 = 100!   No. of trailing zeros in 100! = 100/5 + 100/5^2 = 20+4= 
20+4 = 24
24   100^k= 10^2k → k = 24/2= 
24/2 = 12
12   12
Answer: E
To mail a package, the rate is 30 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?	Choose the correct option:  A) Combined, with a saving of 20 cents  B) Separately, with a saving of 5 cents  C) Combined, with a saving of 25 cents  D) Separately, with a saving of 15 cents  E) Combined, with a saving of 22 cents

Solution: 4 pounds cost = 30+3*5= 
30+3*5 = 45
45   6 pounds cost= 30+5*5= 
30+5*5 = 55
55   Total= 100   10 pounds cost = 30+ 9*5= 
30+ 9*5 = 75
75 dif. 25   Answer : Combined, with a saving of 25 cents
Answer: C
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different W arrangements of plays can be run, if the same play can’t be run more than once?	Choose the correct choice from the following
A) 24  B) 125  C) 243  D) 504  E) 729

Solution: Number of W ways to choose the first play: 9   Second play: 8   Third:7   9*8*7= 504.504
Answer: D
On a game show, a contestant is given three keys, each of which opens exactly one of the three identical boxes.The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $4, the second $400, and the third $4000. What is the probability that a contestant will win more than $4000?  Choose the correct choice from the following options: A) 2/6 B) 1/6 C) 1/8 D) 1/3 E) 1/2

Solution: Let's call the boxes that contain $4, $400, and $4000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.   We want to know the probability of winning more than $4000. Notice that if the distribution of keys is:   Box A = Key B   Box B = Key A   Box C = Key C   then the contestant wins exactly $4000, not more than $4000. The only configuration that leads to winning more than $1000 is:   Box A = Key A   Box B = Key B   Box C = Key C   i.e., getting all three keys correct. That's the only way to be more than $4000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?   Well, for a set of three items, the number of possible permutations is 3! = 3*2*1= 
3*2*1 = 6
6.   Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is   Probability= 1/6   Answer: 1/6
Answer: B
How many bricks, each measuring 5 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 2 cm?
Select.
A) 5600 B) 6000 C) 2909 D) 7200 E) 8600

Solution: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 600 x 2)/(5 x 11 x 6) = 2909.   Answer: Option 2909
Answer: C
If x =- |x| , then which one of the following statements could be true?
I. x = 1
II. x < 0
III. x > 0
Options:
A) None	B) I only	C) II only	D) I and II	E) II and III

Solution: Answer copied from NOVA guide   Statement I could be true because + 1 = −(+1) = −(1) = -1 .   Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].   Now, if one side of an equation is always negative, then the other side must always be negative,   otherwise the opposite sides of the equation would not be equal.   Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:   Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.   Hence, x cannot be positive. The answer is (II only).
Answer: C
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?	Choose the correct option:
A) 37.5
B) 25.7
C) 30.5
D) 22.5
E) 20.5

Solution: 100 * 100= 
100 * 100 = 10_000
10000   110 * 125= 
110 * 125 = 13_750
13750   -----------   3750   10000 ------ 3750   100 ------- ?=> 37.5%   37.5NSWER 37.5
Answer: A
In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 10 feet between each tree. How many trees can be planted if the road is 166 feet long? Choose the most appropriate option
A) 8 B) 9 C) 10 D) 11 E) 16

Solution: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T   To maximize the number of trees, the number of 10 feet spaces between trees should be 1 less than total number of trees.   For example, If there are 3 trees, then there should be 2 spaces between them.   So the number of 10 feet spaces will be T-1. Then, the length of sidewalk required for 10 feet spaces will be 10*(T-1)   It is given that total lenght of sidewalk is 166 feet.   or 10(T-1)+T = 166   or 10T-10+T = 166   or T=16   Answer:- 16
Answer: E
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? Choose the most appropriate option.
A) 16
B) 17
C) 18
D) 19
E) 20

Solution: Explanation:   Average of 20 numbers = 0.   Sum of 20 numbers (0 x 20) = 0.   It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).   Answer 19
Answer: D
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th terms in the sequence?
Options:	A) 2^18	B) 3(2^17)	C) 7(2^16)	D) 3(2^15)	E) 7(2^15)

Solution: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...   so 16th term will be 2^15   17th term 2^16   adding all three   we get   2^15+(2^15)*2   so answer is 2^15(1+2)=>3(2^15)   answer 3(2^15)
Answer: D
A train 110 m long is running with a speed of 84 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?	Choose the correct option:
A) 7 sec
B) 6 sec
C) 8 sec
D) 4.4 sec
E) 2 sec

Solution: Speed of train relative to man = 84 + 6= 
84 + 6 = 90
90 km/hr.= 90 * 5/18= 
90 * 5/18 = 25
25 m/sec.   Time taken to pass the men= 110/25= 
110/25 = 22/5 = around 4.4
4.4 sec.   Answer:4.4 sec
Answer: D
In Anthony's toy bin there are 17 red blocks. There are 8 more yellow blocks than red blocks. There are also 4 more blue blocks than red blocks. How many blocks are there in all?	Answers
A) 22
B) 11
C) 29
D) 63
E) 34

Solution: Step 1: Find the number of yellow blocks.   17 + 8= 
17 + 8 = 25
25   Step 2: Find the number of blue blocks.   17 + 4= 
17 + 4 = 21
21   Step 3: Find the total number of red, yellow, and blue blocks.   17 + 25 + 21= 
17 + 25 + 21 = 63
63   There are 63 blocks in Anthony's toy bin.   Answer is 63.
Answer: D
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choose the correct choice: A) 150m B) 288m C) 278m D) 229m E) 267m

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150mnswer: 150m
Answer: A
Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?	Choose the correct choice from the following answers: A) 6 B) 6.5 C) 7.5 D) 8 E) 24

Solution: The proportion of Dye and sugar will remain constant.   Dye/Sugar = (4/9)/(5/9) = x/7.5   => 4/5 = x/7.5 => x = 4*7.5/5= 
4*7.5/5 = 6
6.   6nswer is 6.
Answer: A
The three digits of a number add up to 14. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?	Choose the correct choice from the following:
A) 40
B) 72
C) 78
D) 90
E) 125

Solution: Say the three-digit number is abc.   The leftmost digit is double the middle digit --> a=2b;   The number is divisible by 5 --> c is either 0 or 5;   The three digits of a number add up to 13 --> a+b+c=14   So, either a+b+c=2b+b+0=14 or a+b+c=2b+b+5=14. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=3 --> a=6 and c=5 --> a*b*c=90.   Answer: 90.
Answer: D
David deposited $5,000 to open a new savings account that earned six percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in David account one year after the account was opened? Options:	A) $5,306	B) $6,120	C) $5,136	D) $5,405	E) $5,500

Solution: Approach #1:   6 percent annual interest compounded semi-annually --> 3% in 6 moths.   For the first 6 moths interest was 3% of $5,000, so $150;   For the next 6 moths interest was 3% of $5,000,plus3% earned on previous interest of $150, so $150+$6=$156;   Total interest for one year was $150+$156  150+ 6= 
  150+ 6 = 156
$156;   Total interest for one year was $150+$156=$306, hence balance after one year was $5,000+ $306 150+ 156= 
 150+ 156 = 306
$306, hence balance after one year was $5,000+ $306=$5,306.   $5,306nswer: $5,306.
Answer: A
A train moves with a speed of 162 kmph. Its speed in metres per second is  Options.
A) 10.8
B) 18
C) 30
D) 38.8
E) 45

Solution: Solution   Speed	= 108 Kmph   = (162 x 5/18)m/sec   = 45 m/sec.   Answer 45
Answer: E
If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is	Choose the correct choice from the following choices.
A) a) 160
B) b) 289
C) c) 250
D) d) 313
E) e) 525

Solution: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.   There are 102 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 51st and 52nd numbers in the set). This means that numbers 51 and 52 in this set are 413 and 415. Because we know that number 51 is 413, we know that the smallest number is 50 odd numbers below this, which means that it is 50*2= 
50*2 = 100
100 below this (every odd number is every other number). Therefore   413-100= 
  413-100 = 313
313, answer choice d) 313
Answer: D
40 is what percent of 160?
Pick one: A) 35% B) 40% C) 45% D) 50% E) 25%

Solution: 40/160×100=25% ANSW25%R : 25%
Answer: E
Which of the following equations passes through the points (2,4) and (-3,-6)?
Select:
A) y = (1/2)x - 2  B) y = 2x  C) y = (-1/2)x + 2  D) y = 2x + 4  E) y = 2x - 4

Solution: Find slope first = (y1-y2)/(x1-x2) = (-6-4)/(-3-2)= 
(-6-4)/(-3-2) = 2
2   Using the point (2,4) in options   we get,   y= 2x as right answer.   Ans- y = 2x
Answer: B
Ratio between 2 numbers is 5 : 7 and their product is 560.what is the difference between 2 numbers?  Choose one:  A) 6  B) 7  C) 8  D) 9  E) 2

Solution: Explanation:   x/y = 5/7   x × y = 560 ⇒ x = 560/y   Substituting this value in first equation, we get 560/yy=57560/yy=57 ⇒560y2=57560y2=57 ⇒ y = 28   x = 20   So difference between the numbers could be   x – y = –8   y – x = 8   Answer: 8
Answer: C
Three 8 faced dice are thrown together. The probability that all the three show the same number on them is ?	Choices
A) 1/38
B) 1/48
C) 1/56
D) 1/64
E) 1/68

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555, 666, 777 and 888. Those are eight in number. Further the three dice can fall in 8 * 8 * 8= 
8 * 8 * 8 = 512
512 ways.   Hence the probability is 8/512= 1/64   Answer:1/64
Answer: D
The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?	Choose the correct choice
A) 240
B) 272
C) 295
D) 360
E) 252

Solution: Let the smaller number be x. Then larger number = (x + 1375).   x + 1375 = 6x + 15   5x = 1360   x = 272   Smaller number = 270.   ANSWER 272
Answer: B
Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ? Pick one
A) 1 : 1  B) 2 : 3  C) 5 : 2  D) 10 : 11  E) 7 : 9

Solution: Mixture A has a total of 7 + 5= 
7 + 5 = 12
12 parts. If in the final mixture this represents 6 parts, then the total number of parts in mixture B should be  (12/6)*3= 
 (12/6)*3 = 6
6.   So, we should take of mixture B a quantity with 3 and 6 parts, respectively.   This will give us in the final mixture (7 + 3) : (5 + 6), which means 10:11   Answer 10 : 11.
Answer: D
What is the sum of all the prime numbers greater than 10 but less than 40?
Choose the correct choice from the following answers.
A) 190
B) 189
C) 180
D) 199
E) 1981

Solution: Required sum = (11 +13 + 17 + 19 + 23+ 29 + 31 + 37)= 
(11 +13 + 17 + 19 + 23+ 29 + 31 + 37) = 180
180   Note: 1 is not a prime number   Answer 180
Answer: C
The fourth proportional to 5, 8, 15 is: Options
A) 9  B) 24  C) 18  D) 19  E) 20

Solution: Let the fourth proportional to 5, 8, 15 be x.   Then, 5 : 8 : 15 : x   5x = (8*15)   x = (8*15)/5= 
(8*15)/5 = 24
24   ANSWER 24
Answer: B
Two ants, Arthur and Lily, have discovered a picnic and are bringing crumbs back to the anthill. Lily makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of a crumbs to the anthill, how many crumbs will Lily bring to the anthill, in terms of a?
Choose the correct choice from the following:  A) a/2  B) a  C) 3a/2  D) 2a  E) 3a

Solution: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Lily carries 3 crumbs per trip. Also let Arthur make 2 trips and so Lily makes 4 trips.   Thus total crumbs carried by Arthur (a) = 2 x 2 = 4, total crumbs carried by Lily = 3 x 4 = 12. 12 is 3 times 4, so 3a
Answer: E
What will come in place of (a) in the following expression?
a - 996.21 + 498.05 = 215.50 – 425.01  Select.
A) 288.64 B) 888.6 C) 888.67 D) 83.65 E) 288.65

Solution: 288.65xplanation:   a - 996.21 + 498.05 = 215.50 - 425.01   a = 288.65   ANSW288.65R: 288.65
Answer: E
The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? Pick one:
A) 2 : 5 B) 1 : 5 C) 3 : 5 D) 4 : 5 E) None of these

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2   => h1/h2 = 2/5   i.e. h1 : h2 = 2 : 5   2 : 5NSWER:2 : 5
Answer: A
In how many different ways can 3 identical bowls of beef ramen noodles and 3 identical bowls of pork ramen noodles be distributed among 6 women such that each woman receives a bowl?
Options
A) 442  B) 4011  C) 94  D) 151  E) 20

Solution: Approach 1:   1st Woman: 6 has options   2nd Woman: 5 has options…   Therefore, for all women: 6 x 5 x 4 x 3 x 2 = 720 arrangements.   Since the beef bowls are identical, we divide by 3!; Since the pork bowls are identical, we divide by another 3!   So: in all, 720/[ 3! X 3! ] = 20 ways.   (e.g. Answer: 20)
Answer: E
Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age  Select: A) 77 B) 30 C) 66 D) 55 E) 44

Solution: Let the age of younger person is x,   Then elder person age is (x+16)   => 3(x-6) = (x+16-6) [6 years before]   => 3x-18 = x+10   => x = 14.   So other person age is x + 16 = 30   Answer:30
Answer: B
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? Answers:
A) 2.5 sec
B) 4.25 sec
C) 5 sec
D) 12.5 sec
E) 6 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secNSWER:2.5 sec
Answer: A
Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?  Select:
A) 5  B) 6  C) 9  D) 24  E) 26

Solution: Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are   0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1= 
  0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5
5 cases...5
Answer: A
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
A. 27.5% Choose the most appropriate option.
A) 1 1/2  B) 1 1/6  C) 1 1/8  D) 1 1/1  E) 1 1/4

Solution: 3/20 * 2 + (2 + x)/5 = 1   x = 1 1/2 days   Answer:1 1/6
Answer: B
A chemist mixes one liter of pure water with x liters of a 45% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x? Choose the correct choice from the following choices: A) 1/4 B) 1/3 C) 1/2 D) 1 E) 3

Solution: 1/2oncentration of salt in pure solution = 0   1/2oncentration of salt in salt solution = 45%   1/2oncentration of salt in the mixed solution = 15%   The pure solution and the salt solution is mixed in the ratio of --> (45 - 15)/(15 - 0) = 2/1   1/x --  (45 - 15)/(15 - 0)= 
--  (45 - 15)/(15 - 0) = 2
2/1   1/x= 2/1   x = 1/2   Answer: 1/2
Answer: C
At Joes Steakhouse the hourly wage for a chef is 22% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?	Pick one.
A) $1.40
B) $2.40
C) $3.315
D) $4.40
E) $5.40

Solution: Manager wages per hour = $8.50   Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25   $3.315hef wages per hour = 22% greater than Dishwasher wages   --> 22% of $4.25 = (22*($4.25)) /100   --> ($93.5)/100   --> $0.935   Therefore,   $3.315hef wages per hour = $4.25 + $0.935 ==> $5.185   Difference of wages between manager and chef = $8.50 - $5.185 ==> $3.315   ANSWER:$3.315
Answer: C
An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1400 sculptures are not on display, how many pieces of art does the gallery have?  Choose the correct answer
A) 360
B) 3150
C) 540
D) 640
E) 720

Solution: Too many words and redundant info there.   (i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.   (ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.   (iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.   1400 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1400 --> {not on display} = 2100.   According to (i) 2/3*{total} = 2100 --> {total} = 3150.   Answer: 3150.
Answer: B
If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+4) III. (y+1)^(x-1) + 1	Pick: A) I only B) II only C) III only D) I,III only E) All options are applicable

Solution: let x= 5, y= 3   I. 5^5 = > Odd   II. 5*7 = > Odd   III. 4^4 +1 = > Odd   Answer : All options are applicable
Answer: E