MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain gallery is hanging a series of 6 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE Choose the correct option
A) 240 B) 200 C) 122 D) 48 E) 16

Solution: We need to consider them separately because the question specifies:   1. Panel paintings have to be placed only at 2nd and 6th place.   2. Implies that Canvas has to be placed 1,3,4,5th place.   So we have two separatebucketsto consider.   So panels can be ordered in 2!   Canvas can be ordered in 4!   since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 2! x 4! = 48   48
Answer: D
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream? Choices.
A) 76 kmph  B) 17 kmph  C) 14 kmph  D) 18 kmph  E) 10 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer: 14 kmph
Answer: C
The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 588 feet squared, what is the difference between the length and the width of the roof?
Options:
A) 28.  B) 40.  C) 42.  D) 44.  E) 46.

Solution: Answer is A: 28   Let w be the width , so length is 3w. Therefore : w*3w = 588, solving for, w = 14 , so 3w-w = 2w = 2*14= 
2*14 = 28
28
Answer: A
A cubical tank is filled with water to a level of 3 feet. If the water in the tank occupies 75 cubic feet, to what fraction of its capacity is the tank filled with water? Select the correct option
A) 1/2
B) 2/3
C) 3/4
D) 2/5
E) 3/5

Solution: The volume of water in the tank is H*L*B = 75 cubic feet.   Since H = 3, then L*B = 25 and L = B = 5.   Since the tank is cubical, the capacity of the tank is   5*5*5= 
  5*5*5 = 125
125.   The ratio of the water in the tank to the capacity is 75/125= 3/5   The answer is 3/5.
Answer: E
If x, 6, 7, 8 are there and the range and median of them are the same, what is the value of x?	Choose the correct choice from the following:
A) 0	B) 1	C) 2	D) 3	E) 7

Solution: Try taking the values of x as you suggested and then see if the median and the range are equal.   Once you do that, you will get the answer yourself.   Tried substituting values starting with 6, 7, 8...   only x = 7 satisfies the condition.   7
Answer: E
What value will replace the question mark in the following equation ? 5172.49 + 378.352 + ? = 9318.678  Choices.
A) 3767.836
B) 3677.863
C) 3767.863
D) 3767.683
E) None of them

Solution: Let 5172.49 + 378.352 + x = 9318.678   Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836   3767.836nswer is 3767.836.
Answer: A
If n is a prime number greater than 11, what is the remainder when n^2 is divided by 12 ?  Choices.
A) 0  B) 1  C) 2  D) 3  E) 5

Solution: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 11, square it and see what would be the remainder upon division of it by 12.   n=17 --> n^2=289 --> remainder upon division 289 by 12 is 1.   Answer: 1.
Answer: B
A and B together can do a piece of work in 6 days and A alone can do it in 12 days. In how many days can B alone can do it?
Choose the correct choice from the following answers:
A) 11 days
B) 15 days
C) 12 days
D) 21 days
E) 22 days

Solution: Explanation:   A and B can do work 1/6 in 1 day   A alone can do 1/12 work in 1 day   B alone can do (1/6 -1/12) =1/12 work in 1 day   => complete work can be done in 12 days by B   Answer: Option 12 days
Answer: C
In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 115 hats in this group, how many of these hats are not blue?
Pick one.
A) 28 B) 42 C) 48 D) 64 E) 80

Solution: B:G:P = 7:4:12 --> total of 23 parts.   Not blue = (G + P)/(total)*92 = 16/23*115= 
16/23*115 = 80
80.   Answer: 80.
Answer: E
What is the smallest positive perfect square that is divisible by 9, 21, and 49? Choose one: A) 225 B) 324 C) 441 D) 529 E) 900

Solution: The number needs to be divisible by 3^2, 3*7, and 7^2.   The smallest such perfect square is 3^2*7^2 = 441   The answer is 441.
Answer: C
32 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?  Choose the most appropriate option
A) 66 B) 26 C) 42 D) 27 E) 14

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 32= 
7/16 * 32 = 14
14   Answer: 14
Answer: E
A box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective? Choose the correct choice from the following answers:	A) 17	B) 18	C) 54	D) 56	E) 864

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   5 is the biggest number that could divide all three, 35, 20 and 10.   Thus side of cube must be 5, and total number of cubes = 35/5 * 20/5*10/5= 
35/5 * 20/5*10/5 = 56
56   Ans 56 it is.
Answer: D
In an election, candidate Douglas won 64 percent of the total vote in Counties X and Y. He won 76 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?
Choose the correct choice from the following answers:
A) 10%	B) 25%	C) 30%	D) 35%	E) 40%

Solution: given voters in ratio 2:1   let X has 200 votersY has 100 voters   for X 76% voted means 76*200=152 votes   combined for XY has 300 voters and voted 64% so total votes =192   balance votes=192-152= 
192-152 = 40
40   As Y has 100 voters so 40 votes means 40% of votes required   Ans 40%
Answer: E
A line that passes through (–1, –4) and (4, k) has a slope = k. What is the value of k?	Choose one:
A) 3/4
B) 1
C) 4/3
D) 2
E) 7/2

Solution: Slope = (y2-y1)/(x2-x1)   => k = (k+4)/(4+1)   => 5k = k+4   => k =1   Ans 1 it is!
Answer: B
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? Choose the correct option: A) 520 B) 720 C) 890 D) 870 E) 1098

Solution: The word 'OPTICAL' contains 7 different letters.   When the vowels OIA are always together, they can be supposed to form one letter.   Then, we have to arrange the letters PTCL (OIA).   Now, 5 letters can be arranged in 5! = 120 ways.   The vowels (OIA) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   ANSWER 720 72
Answer: B
A train 325 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 45 sec. The speed of the train is? Options:
A) 12 km/hr
B) 13 km/hr
C) 14 km/hr
D) 15 km/hr
E) 16 km/hr

Solution: Speed of the train relative to man = 325/45 = 65/9 m/sec.   = 65/9 * 18/5= 
65/9 * 18/5 = 26
26 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 10) km/hr.   x - 10 = 26 => x = 16 km/hr.   Answer: 16 km/hr
Answer: E
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is? Select:
A) Rs.628
B) Rs.629
C) Rs.629
D) Rs.600
E) Rs.629

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1500   => 5 parts out of 15 parts is Rs. 1500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1500) = Rs.600'   Answer: Rs.600
Answer: D
For a race a distance of 224 meters can be covered by P in 14 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?	Choose the correct choice from the following choices
A) 232m	B) 288m	C) 324m	D) 231m	E) 236m

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/14= 
224/14 = 16
16m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken = 18 seconds   Therefore, Distance covered by P in that time= 16m/s x 18 seconds = 288 metres   ANSWER: 288m
Answer: B
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Pick.
A) 1	B) 4	C) 5	D) 6	E) 8

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: 4
Answer: B
The sum of 111 consecutive integers is 11211. What is the greatest integer in the set? Choose the correct answer:  A) 148  B) 150  C) 152  D) 154  E) 156

Solution: Let x be the first integer in the set, then x+110 is the largest integer.   The sum is: x+(x+1)+(x+2)+...+(x+110)   = 111x + 110*111/2   = 111(x+55)   Then x+55=101   x=46   The largest integer in the set is  46+110= 
 46+110 = 156
156   The answer is 156.
Answer: E
A baseball card decreased in value 30% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years? Choose the correct choice from the following:  A) 28%  B) 30%  C) 32%  D) 36%  E) 37%

Solution: Let the initial value of baseball card = 100   After first year , value of baseball card = (1- 30/100)* 100= 
(1- 30/100)* 100 = 70
70   After second year , value of baseball card=(1 - 10/100)* 70= 
(1 - 10/100)* 70 = 63
63   total percent decrease of the card's value over the two years= (100-63/100 *100%   =37%   Answer 37%
Answer: E
A person bought 10 bottles for 1 dollar. How many for a dollar must he sell to gain 100%?	Choose the correct option:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: C.P. of 10 bottles = $1   S.P. of 10 bottles = 200% of $1 =2   for $2 bottles sold = 10   for $1 bottles sold = 10/2= 
10/2 = 5
5   Answer is 5
Answer: E
A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is? Choose the correct option
A) 3	B) 2	C) 5	D) 7	E) 1

Solution: Explanation:   S.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1)= 
(100 * 40)/(800 * 1) = 5
5%   Answer:5
Answer: C
What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for three years, compounding done annually?
Choices.
A) 9688  B) 9687  C) 9685  D) 9682  E) 10648

Solution: A= P{1 + R/100}n   => 8000{1 + 10/100}3 = Rs.10648   Answer:10648
Answer: E
How many seconds does a train 120 meters long, traveling at 54 km/h, take to completely cross a bridge of 180 meters in length?	Options
A) 18	B) 20	C) 22	D) 24	E) 26

Solution: 54 km/h = 54000/3600= 
54000/3600 = 15
15 m/s   Time= 300 / 15= 
300 / 15 = 20
20 seconds   The answer is 20.
Answer: B
If x + 5 > 2 and x - 3 < 6, the value of x must be between which of the following pairs of numbers?
Choose the correct choice from the following answers:
A) -3 and 10
B) -3 and 9
C) 2 and 7
D) 3 and 4
E) 3 and 10

Solution: Let’s isolate x in each inequality.   x + 5 > 2   x > -3   Next we simplify x – 3 < 7.   x – 3 < 6   x < 9   We know that x is greater than -3 and less than 9.   The answer is -3 and 9.
Answer: B
In a stable there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable? Choose the correct choice from the following answers
A) 8 men and 14 horses.
B) 7 men and 14 horses.
C) 6 men and 14 horses.
D) 5 men and 14 horses.
E) 4 men and 14 horses.

Solution: 8 men and 14 horses.   Let M = men and H = horses. We can come up with 2 equations.   M + H = 22   2M + 4H= 72   Solving the 2 equations will give 8 men and 14 horses.   8 men and 14 horses.nswer 8 men and 14 horses.
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	Choose the most appropriate option
A) 120 metres  B) 180 metres  C) 324 metres  D) 150 metres  E) 120 meters

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.   ANSWER:150 metres
Answer: D
How many of the positive factors of 19 are not factors of 29?  Select:  A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Factors of 19 - 1, 19   factors of 29- 1, 29   Comparing both, we have three factors of 19 which are not factors of 29- 19,   The answer is 1
Answer: B
A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform?
Choose the correct choice from the following options:  A) 150  B) 145  C) 165  D) 162  E) 152

Solution: D = 130 + x   T = 20   S = 130+x/15 * 18/5 = 70 kmph.   => (130+x) * 18 = 5250   => 130 + x = 292 => x= 162 m   Answer: 162
Answer: D
A shopkeeper forced to sell at cost price, uses a 850 grams weight for a kilogram. What is his gain percent?  Pick one.
A) 17.65%	B) 9%	C) 11.11%	D) 12 %	E) None of these

Solution: Shopkeeper sells 850g instead of 1000g.   So, his gain = 1000 - 850= 
1000 - 850 = 150
150g.   Thus, %Gain= (150 *100)/850 = 17.65%.   answer : OPTION 17.65%
Answer: A
A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $72, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.) Choose one:
A) 55
B) 84
C) 63
D) 75
E) 70

Solution: LET 63= 63HAIR ; T =TABLE   263+1T = 0.6 (163 + 2T) OR 63( 2-0.6) = 1.2T -1T OR 1.463 = 0.2 T THEREFORE 63= 0.2/1.4 T = 1/7 T   I63 +1T =72 OR 1/7T + 1T =60 THEREFORE T= 72*7/8= 
72*7/8 = 63
63   63
Answer: C
Raja sold two cycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both cycles?  Choose one.
A) 2000	B) 6700	C) 3400	D) 7800	E) 4500

Solution: 2000   (10*10)/100= 
(10*10)/100 = 1
1%loss   100 --- 99   ? --- 1980=> Rs.2000
Answer: A
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 50 per square m? Select
A) s.43000  B) s.50000  C) s.57000  D) s.60000  E) s.47500

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 50 * 950   = Rs.47500   s.47500
Answer: E
90 percent of the members of a study group are women, and 60 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
Choose the correct choice.
A) 0.34
B) 0.44
C) 0.54
D) 0.64
E) 0.74

Solution: Say there are 100 people in that group, then there would be 0.9*0.60*100= 
0.9*0.60*100 = 54
54 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=54/100.   Answer: 0.54
Answer: C
In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?  Choose the correct choice from the following choices:
A) 100
B) 110
C) 179
D) 205
E) 219

Solution: Number of ways to select four children is 10C4 = 210   Number of ways to choose only girls is 5C4 = 5   Number of ways that at least one boy is selected is  210 - 5= 
 210 - 5 = 205
205   The answer is 205.
Answer: D
Ms. Lopez deposits $ 140 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year? Select.
A) $118.00 B) $120.00 C) $169.40 D) $122.00 E) $140.00

Solution: Using Formula - A = P(1+r/n)^nt   Given   P=140   n=2   t=1   r=0.2   Substituting value in formula   A = 140(1+0.2/2)^2   A= 169.40$=$169.40
Answer: C
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Choose the correct choice.
A) 19:1
B) 19:4
C) 19:8
D) 19:5
E) 19:2

Solution: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4= 
19/4 = 19/4 = around 4.75
4.75 litres   As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 4.75 : 1.25 = 19:5.   Answer: 19:5
Answer: D
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options: A) 45% B) 57% C) 34% D) 90% E) 49%

Solution: B   57%   Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400.   Required percentage= (11628/20400 x 100)% = 57%.
Answer: B
How many numbers between 100 and 630 are divisible by 2, 3, and 7 together? Choose the correct choice from the following options.
A) 112 B) 77 C) 267 D) 13 E) 99

Solution: Explanation:   As the division is by 2, 3, 7 together, the numbers are to be divisible by:  2*3*7= 
 2*3*7 = 42
42   The limits are 100 and 600   The first number divisible is 42*3= 
42*3 = 126
126   To find out the last number divisible by 42 within 630:   630/42= 13   Hence, 42*15 = 630 is the last number divisible by 42 within 630   Hence, total numbers divisible by 2, 3, 7 together are (15 â€“ 2) = 13   ANSWER: 13
Answer: D
Jack and Jill collect ladybugs. Jack only collects the ones with 2 spots,
and Jill only collects the ones with 7 spots. Jack has 5 more ladybugs
than Jill. The total number of spots found on all of their ladybugs is 100.
How many ladybugs do they have in their combined collection?  Choose the correct choice from the following answers.
A) 17
B) 21
C) 23
D) 25
E) 35

Solution: If x is the number of ladybugs that Jack has and y is the number of ladybugs that Jill has, then   x − y = 5 and 2x + 7y = 100. Multiplying the first of these equations by 5 and the second by 2   and adding gives 9(x + y) = 225. Hence, x + y = 25.   correct answer 25
Answer: D
Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days?	Choose the correct choice from the following choices:
A) 1/8	B) 1/3	C) 1/6	D) 1/2	E) 5/3

Solution: A's one day's work = 1/30   B's one day's work = 1/60   (A + B)'s one day's work = 1/30 + 1/60 = 1/20   The part of the work completed in 10 days = 10 (1/20) = 1/2.   Answer:1/2
Answer: D
A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $200 before any discount?
Select the correct option: A) $112.00 B) $145.60 C) $163.80 D) $182.00 E) $100.00

Solution: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).   We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....   We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):   30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...   The final price of an item that originally cost $200 would be.....   ($200)(.7)(.8) =   ($200)(.56)=112   Final $112.00nswer:   $112.00
Answer: A
If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week?	Pick one.
A) $374	B) $382	C) $345	D) $392	E) $399

Solution: (348/116)115 =345   In this case long division does not take much time.   (348/116)= 
(348/116) = 3
3   3*115= 
3*115 = 345
345(300+45)   Answer $345
Answer: C
If a * b = a + b/ab , find the value of 5 * (5 * -2) :
Choices
A) -3  B) -10  C) -1.66  D) 3/5  E) -12

Solution: (5 * -2) = (5 x (-2))/(5 + (-2)) = -10/3   So, 5 * (5 * -2) = 5 * (-10/3) = (5 * (-10/3))/(5 + (-10/3))   = (-50/3) * (3/5)   = -10.   ANSWER:-10
Answer: B
If x>y>0, which of the following must be true:
I. x^2>y^2
II. x^3 > y^3
III. x<y
Options:
A) I and II
B) II only
C) III only
D) II and III
E) I, II and III

Solution: I and IIssuming x and y to be integers   X=3,Y=2   X^2=3^2=9   Y^2=2^2=4   So I is true   Now lets look at option III because if option 3 is true E is the answer or else I and II   I and IIs per question X>Y>0 Hence |X| >Y   So OI and II=I and II
Answer: A
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last? Choose the most appropriate option:
A) 5 days B) 10 days C) 11 days D) 20 days E) 25 days

Solution: Work done by X in 4 days =1/20	x 4 = 1/5   Remaining work = (1 -1/5) = 4/5   (X + Y)'s 1 day's work = 1/20+1/12 = 8/60 = 2/15   Now,	2/15 work is done by X and Y in 1 day.   So,4/5work will be done by X and Y in	15/2	x 4/5= 6 days.   Hence, total time taken = (6 + 4)= 
(6 + 4) = 10
10 days.   ANSWER:10 days
Answer: B
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Pick:	A) 28,029	B) 28,199	C) 28,299	D) 28,000	E) 28,029

Solution: Explanation:   3:1   2:1   ------   6:1   1 ----- 4000   7 ----- ? => Rs.28,000   Answer: 28,000
Answer: D
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $200. Find the original price of petrol?
Pick:
A) $11
B) $5
C) $45
D) $400
E) $4.4

Solution: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 200/45=$4.4   Answer: $4.4.
Answer: E
What is the units digit of 23^3 * 17^2 * 39^2?  Options: A) 9 B) 7 C) 5 D) 3 E) 1

Solution: The units digit of 23^3 is the units digit of   3*3*3= 
  3*3*3 = 27
27 which is 7.   The units digit of 17^2 is the units digit of   7*7= 
  7*7 = 49
49 which is 9.   The units digit of 39^2 is the units digit of   9*9= 
  9*9 = 81
81 which is 1.   The units digit of  7*9*1= 
 7*9*1 = 63
63 is 3.   The answer is 3.
Answer: D
Find the odd man out. 362, 482, 551, 263, 344, 284 Choose the correct choice from the following options
A) 362	B) 482	C) 551	D) 344	E) 284

Solution: Explanation :   In all numbers except 344, the product of first and third digits is the middle digit.   Answer : Option 344
Answer: D
The ratio, by weight, of coffee to sugar to water in a pot of coffee is 3:1:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?  Choose the correct answer:
A) 35
B) 40
C) 45
D) 50
E) 55

Solution: The new ratio of coffee to sugar is 1.5:1   The new ratio of coffee to water is 6:15.   The new ratio of coffee to sugar to water is 6:4:15.   If there are 12 grams of sugar, then there are  (15/4)*12= 
 (15/4)*12 = 45
45 grams of water.   The answer is 45.
Answer: C
In a group of 27 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish? Choose the correct choice from the following:	A) 7	B) 6	C) 9	D) 4	E) 6

Solution: A   7   Add 7 + 10 + 4 to get 21.   Then subtract 21 from the total students ⇒ 27 – 21 = 6.   Answer is 6
Answer: E