MU-NLPC/Calc-aqua_rat huggingface dataset:
Chauncy, an English bulldog, received 1200 votes in the Mr. Bulldog USA competition, giving him approximately 30 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 70 percent of the total votes? Answers.
A) 56.14% B) 57.14% C) 58.14% D) 59.14% E) 60.14%

Solution: let the total vote is x.then 30% of x=(30/100)*x=1200,   or,x=(1200*100)/30;   or,x=4000;   now, 30% of votes already given...so other 70% of x votes=(70/100) *4000= 
(70/100) *4000 = 2_800
2800 votes. now other needed votes=(70-30)= 
(70-30) = 40
40% votes. so 40% votes of x=(40/100)*4000= 
(40/100)*4000 = 1_600
1600; now he have needed only % of votes=(100*1600)/2800=160000/2800= 
160000/2800 = 400/7 = around 57.142857
57.14285714%   ANSWER:57.14%
Answer: B
Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?	Select
A) 33277  B) 6888  C) 6000  D) 2777  E) 27812

Solution: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x   10 * 20 * 90 = 15 * 2 * x => x = 6000   Answer: 6000
Answer: C
The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is	Choose the correct answer.
A) 33 B) 28 C) 30 D) 88 E) 287

Solution: Explanation:   Let the three parts be A, B, C. Then,   A : B = 2 : 3 and B : 30 = 5 : 8 ==   A : B : 30 = 2 : 3 : = 10 : 15 : 24   B = = 30   Answer: 30) 30
Answer: C
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Choose the correct choice from the following answers: A) 11 a.m. B) 10 a.m. C) 12 a.m. D) 9 a.m. E) 8 a.m.

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer: Option 10 a.m.
Answer: B
If each number in the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is used exactly once, in how many ways can the numbers be arranged?	Choose the correct choice from the following choices.
A) 3,228,400	B) 3,328,500	C) 3,428,600	D) 3,528,700	E) 3,628,800

Solution: 10! = 3,628,800   The answer is 3,628,800.
Answer: E
Tom can hit a target 3times in 6 shots, Karan can hit the target 2 times in 6shots & Ashwini can hit 4 times in 4 shots.What is the probability that at least 2 shots hit the target ? Options
A) 1/2
B) 2/5
C) 2/3
D) 2/7
E) 3/7

Solution: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by   Karan hits tha target and Raja not hit the target.   or   Karan does not hit the target and Raja hits the target.   or.   Karan hits the target and Raja hits the target   = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6   = 24/36 = 2/3   2/3
Answer: C
Tough and Tricky questions: Absolute Values.
If |a| = 1/2 and |b| = 2/3, which of the following CANNOT be the result of a + b? Select
A) 7/6  B) -1/6  C) 1/6  D) 2/6  E) -7/6

Solution: |a| = 1/2   Absolute value of 'a' can have two values = 1/2 and -(1/2)   |b| = 2/3   Absolute value of 'b' can have two values = 2/3 and -(2/3)   Now different combinations of a + b are as follows:   a + b = (1/2) + (2/3) = 7/6   - a - b = -(1/2) - (2/3) = -7/6   a - b = (1/2) - (2/3) = -(1/6)   -a + b = -(1/2) + (2/3) = 1/6   Cross verifying with the given options, left over option is 2/6.
Answer: D
The sale price watches listed for Rs.4500 after successive discount is 10% and 20% is?
Choose one:
A) 3240 B) 3420 C) 4320 D) 4230 E) 3140

Solution: 4500*(90/100)*(80/100)   = 342   3240nswer: 3240
Answer: A
A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Choices
A) 20 years  B) 21 years  C) 22 years  D) 23 years  E) 24 years

Solution: Let present age of the son =x years   Then, present age the man =(x+24) years   Given that, in 2 years, man's age will be twice the age of his son   =(x+24)+2=2(x+2)   =x=22   Answer: Option 22 years
Answer: C
A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Choose the correct choice:
A) 15 B) 61 C) 21 D) 14 E) 12

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [385 * 3/55= 
385 * 3/55 = 21
21 sec   Answer: 21
Answer: C
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank? Choose the correct choice from the following answers.
A) 12 minutes
B) 18 minutes
C) 10 minutes
D) 15 minutes
E) 42 minutes

Solution: Part filled by A in 1 min. = 1/20   Part filled by B in 1 min. = 1/30   part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.   Both the pipes can fill the tank in 12 minutes.   12 minutesnswer:12 minutes
Answer: A
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Choose the correct choice from the following choices.
A) 287 m B) 350 m C) 187 m D) 197 m E) 186 m

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x   = 350 m.   Answer: 350 m
Answer: B
A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? Choose the most appropriate option.
A) 20% B) 45% C) 44% D) 48% E) 49%

Solution: g% = 20 + 20 + (20*20)/100= 
20 + 20 + (20*20)/100 = 44
44%   ANSWER:44%
Answer: C
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2700 sq m, then what is the breadth of the rectangular plot?
Select the correct option.
A) 11  B) 17  C) 18  D) 101  E) 30

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 2700   3b2 = 2700   b2 = 900 = 30 (b > 0)   b = 30 m.   Answer: 30
Answer: E
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Choose the correct choice from the following answers:
A) 227
B) 350
C) 771
D) 176
E) 125

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer: 350
Answer: B
10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 6514, how much was it in the beginning?
Choices.
A) 8545 B) 8770 C) 8515 D) 7999 E) 7989

Solution: X * (90/100) * (85/100) = 6514   X = 8515   Answer: 8515
Answer: C
Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999 ?
Pick one:
A) Rs.45,000
B) Rs.50,000
C) Rs.70,000
D) Rs.75,000
E) None of these

Solution: Solution   Shekhar : Rajeev : Jatin   = (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1.   ∴ Rajeev’s share = Rs.(15000x2/6) = Rs. 50,000. Answer Rs.50,000
Answer: B
If a > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - a) = Choose the correct answer:
A) 1/4 B) 1/3 C) 1/2 D) 3/4 E) 1

Solution: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have a-x=2t. So y-x=-t, y-a=-3t. ---> (y - x)/(y - a) = 1/3.   The answer is (1/3).
Answer: B
If 5 machines can produce 20 units in 10 hours, how long would it take 10 to produce 60 units?
Pick
A) 9
B) 10
C) 15
D) 25
E) 30

Solution: 5 machines would produce 60 units in 30 hours. Increasing the amount of machines by 2 would mean dividing 30 hours by 2.   30/2= 
30/2 = 15
15   Answer : 15
Answer: C
Sami's investment portfolio consists of three stocks: an airline, a bank, and a computer company. In the month of February, the price of the airline's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Sami owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order airline, bank, and computer company respectively?	Choose the correct choice from the following answers
A) $55, $85, $40
B) $60, $60, $60
C) $65, $55, $90
D) none of these
E) $25, $60, $70

Solution: Since Sami owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased.   Answer is none of these.
Answer: D
What is the total surface area in square meters of a rectangular solid whose length is 8 meters, width is 7 meters, and depth is 4 meters?  Choose the correct choice from the following
A) 132 m2	B) 145 m2	C) 165 m2	D) 152 m2	E) 120 m2

Solution: Surface 132 m2rea of a cuboid = 2(lb+bh+lh) = 2(8*7+7*4+8*4)=2(56+28+32)=2*116=132 m2   132 m2nswer : 132 m2
Answer: A
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Select the correct option
A) 828
B) 788
C) 378
D) 750
E) 288

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min.   = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60   = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer: 750
Answer: D
Find the number of numbers from 1 to 100 which are not divisible by any one of 2,3,5,7. Choose the correct answer
A) 16	B) 17	C) 18	D) 19	E) 21

Solution: All Prime Numbers between 1 to 100 - (4)= 25-4= 
25-4 = 21
> 21   ANSW21R:21
Answer: E
B and C started a business by investing Rs.3300/- and Rs.8800/- respectively. Find the C’s share out of a total profit of Rs.2200:  Choose the correct choice from the following.
A) 500
B) 600
C) 700
D) 800
E) 900

Solution: 600 = Rs.3300/-   C = Rs.8800/-   600 share 3 parts & C share 8 parts   Total 11 parts -----> Rs.2200/-   ----> 1 part -------> Rs.200/-   C share = 3 parts -----> Rs.600/-   600
Answer: B
On dividing 23 by a number, the quotient is 5 and the remainder is 3. Find the divisor. Answers:
A) 1  B) 2  C) 4  D) 6  E) 7

Solution: d = (D-R)/Q   = (23 - 3)/5   = 20/5= 
20/5 = 4
4   4
Answer: C
There are 160 horses and 340 sheep on a certain farm. If 20% of the horses and 35% of the sheep are eight years old or older, what percent of the horses and sheep on the farm are under the age of eight? Pick one:
A) 15.6% B) 30.2% C) 55% D) 56% E) 69.8%

Solution: 2 horses are eight years or older, thus 128 are younger.   119 sheeps are eight years or older, thus 221 are younger.   Total sheeps and horses younger than eight: 349   Total sheeps and horses 500.   349/500 is very close to 350/500 which is 70%. Considering the error chose E.   Answer 69.8%.
Answer: E
If a + b - c =-2d, and if a - b + c = 2e, then a =  Select the correct option: A) 2(d + e) B) d – e C) (d + e)/2 D) d-2e E) e-d

Solution: Add both equations:   a + b - c =-2d   a - b + c = 2e   a+b-c+a-b+c=-2d+2e   2a=2e-2d   a=e-d   Ans:e-d
Answer: E
How many integers between 324,700 and 387,600 have tens digit 1 and units digit 3?  Choose the correct choice from the following answers:	A) 438	B) 629	C) 780	D) 879	E) 924

Solution: The integers are:   324,713   324,813   etc...   387,513   The number of integers is   3876 - 3247= 
  3876 - 3247 = 629
629   The answer is 629.
Answer: B
A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choose the correct option:
A) 126 Kmph
B) 136 Kmph
C) 172 Kmph
D) 128 Kmph
E) 19 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 700/20= 
700/20 = 35
35 M/Sec   Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 126 Kmph   126 Kmphnswer: 126 Kmph
Answer: A
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 9, what is the least possible value of n?
Choose one: A) 7 B) 6 C) 9 D) 12 E) 7

Solution: We need at least 2 factors of three, which means n must be at least 6, so 6 is the correct answer.
Answer: B
16 +17+18+19=70. How many such 4 consecutive numbers are there less than 1000 when added gives a sum which is divisible by 10?  Choose the correct choice from the following options:	A) 100	B) 200	C) 300	D) 400	E) 500

Solution: since 1+2+3+4= 
1+2+3+4 = 10
10 & 6+7+8+9= 
6+7+8+9 = 30
30   any combination with these no be will give u desirable result...   so total no in 100 will be 20 & that's why in in 1000,it will be 200   ANSWER:200
Answer: B
Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin  Choose the correct choice from the following answers.
A) 23.5 B) 24.5 C) 12.5 D) 14.5 E) 16.5

Solution: Explanation:   If Rahul age is x, then Sachin age is x-7,   so (x-7)/x = 7/9   => 9x-63 = 7x   => 2x = 63   => x = 31.5   So Sachin age is   31.5 - 7= 
  31.5 - 7 = 24.5
24.5   Answer: Option 24.5
Answer: B
Find the number of factors Q of 180 that are in the form (4*k + 2), where k is a non-negative integer?  Pick: A) 1 B) 2 C) 3 D) 4 E) Q=6

Solution: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 Q (=2^2*3^2*5) = 18. So listing the factors gives us:   1, 180   2, 90   3, 60   4, 45   5, 36   6, 30   9, 20   10, 18   12, 15   As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with   2,4,6,10,12,18,20,30,36,60,90,180   For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.   For checking any particular factor whether they conform to the form 4k+2---> do the following   4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.   Q=6 is thus the correct answer.
Answer: E
Find the reminder when 333666777888999 divided by 3 or 9 or 11
Answers.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: the sum of the digits is 3+3+3+6+6+6+7+7+7+8+8+8+9+9+9= 
3+3+3+6+6+6+7+7+7+8+8+8+9+9+9 = 99
99, which is a multiple of 3 & 9, hence divisible by 3 & 9. hence the remainder is 0.   the difference of the sum of even place digits and odd place digits is   (3+3+6+7+7+8+9+9)-(3+6+6+7+8+8+9)= 
  (3+3+6+7+7+8+9+9)-(3+6+6+7+8+8+9) = 5
5. hence not divisible by 11. so, the remainder is the difference, which is 5.   ANSWER:5
Answer: D
Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 192 as interest at the end of the loan period, what was the rate of interest?	Pick:
A) 3.6  B) 6  C) 4  D) Cannot be determined  E) None of these

Solution: Let rate = R% and time = R years.   Then,1200 x R x R/100= 192   12R2 = 192   R2 = 16   R = 4.   Answer:4
Answer: C
Sandy had $217 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? Choose the correct choice.
A) $270	B) $290	C) $310	D) $330	E) $350

Solution: Let the money Sandy took for shopping be x.   0.7x = 217   x = 310   The answer is $310.
Answer: C
Peeta asks Katniss, 'It is 12 pm as per my watch right now.Do you know what will be the time 23, 999, 996 hours later?'
Katniss knows the answer. Do you ?	Options:
A) 9am	B) 6pm	C) 4am	D) 7am	E) 8pm

Solution: A   9pm   The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: A
If the tens digit of positive integers t, y are 6, how many values of the tens digit of 2(t+y) can be there?	Choose the correct choice from the following answers
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: If the tens digit of positive integers t, y are 6, how many values of the tens digit of 2(t+y) can be there?   A. 2   B. 3   C. 4   D. 5   E. 6   -> If t=y=60, 2(t+y)=240 is derived. If t=y=69, 2(t+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is 4.
Answer: C
A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price A. The store sold the first 150 copies in the first week at 80% more than A, and then over the next month, sold a 100 more at 20% more than A. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than A. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?	Choose the correct option: A) 30% loss B) 10% loss C) 10% profit D) 20% profit E) 60% profit

Solution: [[A(150)(1.8)+A(100)(1.2)+A(150)(0.6)]/400A] - 1   [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1   [(5.4 + 2.4 + 1.8)/8] - [8/8]   +1.6/8   +20%   answer is 20% profit
Answer: D
If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is: Choose the correct choice from the following.
A) 1 B) 100 C) 121 D) 141 E) 1000

Solution: mn=121 121 can be obtained by multiplying   121*1= 
  121*1 = 121
121,n=1   (m-1)n+1=121   if we choose m=1 and n=121   then the answer will be 1   so there r two possible answers 1 and 121   ANSWER:121
Answer: C
Calculate the area of a triangle, if the sides of are 52 cm, 48 cm and 20 cm, what is its area? Options:
A) 480 cm2
B) 580 cm2
C) 380 cm2
D) 180 cm2
E) 280 cm2

Solution: The triangle with sides 52 cm, 48 cm and 20 cm is right angled, where the hypotenuse is 52 cm.   480 cm2rea of the triangle = 1/2 * 48 * 20= 
1/2 * 48 * 20 = 480
480 cm2   480 cm2nswer: 480 cm2
Answer: A
If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? Options.
A) 10%
B) 15%
C) 20%
D) 25%
E) None

Solution: 100   125   -----   125 ----- 25   100 ------ ? => 20%   ANSWER:20%
Answer: C
In front of you lies a figure made up with 20 x 10 square blocks. Will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares?  Pick:	A) 11647	B) 11550	C) 12654	D) 26537	E) 32651

Solution: B   11550   There is just one way to find it out and that is the generic computing method.   The number of squares and rectangles formed = (Summation of column numbers)   = (1 + 2 + 3 +......+ 19 + 20) * (1 + 2 + 3 +......+ 9 + 10)   = 210 * 55= 
210 * 55 = 11_550
11550
Answer: B
Pipe A can fill the tank in 30 minutes and pipe B in 20min and pipe C can empty the tank in 90 minutes. How long it will take to fill the tank if three of the pipes are operating together? Choose the correct choice from the following:
A) 10.55
B) 12.0
C) 13.1
D) 13.85
E) 15.2

Solution: Pipe A fills 1/30th of the tank in a minute and pipe B, 1/20th. Pipe C empties in 90min   (1/30)+(1/20)-(1/90)=(1/x)   13/180=1/x => x=180/13 => x=13.85 minutes   Answer: 13.85
Answer: D
The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.	Choose the most appropriate option.
A) 24 B) 23 C) 119 D) 120 E) None of these

Solution: Explanation:   Number of words which can be formed = 5! - 1 = 120 - 1= 
120 - 1 = 119
119.   ANSWER IS 119
Answer: C
A restaurant meal cost $24.6 and there was no tax. If the tip was more than 20 percent but less than 18 percent of the cost of the meal, then the total amount paid must have been between	Choose the most appropriate option:
A) $40 and $42
B) $29 and $29
C) $38 and $40
D) $37 and $39
E) $36 and $37

Solution: The total amount for the meal was between 24.6*1.2=29.5 and 24.6*1.18=~29. Only option which covers all possible values of the meal is B.   Answer: $29 and $29.
Answer: B
Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.825.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?	Choose the correct choice.
A) Rs.5358  B) Rs.5458  C) Rs.3370  D) Rs.4358  E) Rs.3358

Solution: Let the sum lent by Manoj to Ramu be Rs.P.   Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85   27P = 62100 = 82485   P = (82585 + 62100)/27 = Rs.5358   Rs.5358NSWER:Rs.5358
Answer: A
Gary is 15 years younger than Simon, and Kim is twice as old as Gary. If S is Simon’s age and K is Kim's age, what is the relationship between K and S?	Choose the correct choice from the following
A) K = 2S + 10  B) K = 2S + 10  C) K = 2S - 30  D) K = 2S − 10  E) K = 2S − 5

Solution: G=S-15 and K=2G --> K=2S-30   Answer K = 2S - 30
Answer: C
In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is? Choose the correct choice from the following choices
A) 76  B) 78  C) 86  D) 88  E) 90

Solution: Divisor = (6 * 3) + 2= 
(6 * 3) + 2 = 20
20   5 * Quotient= 20   Quotient = 4.   Dividend = (Divisor * Quotient) + Remainder   Dividend = (20 * 4) + 6= 
(20 * 4) + 6 = 86
86.   86)
Answer: C
If the integer d is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when d is rounded to the nearest ten. which of the following is a possible value of d? Choices.
A) 64 B) 67 C) 99 D) 133 E) 147

Solution: We have to check options 1 by 1.   64 rounded to nearest hundred = 100   64 rounded to nearest ten = 60   now difference = 40   the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.   therefore 40/60)*100 = 66 2/3 ==>this is the answer.   99 rounded to nearest ten = 100   133 rounded to nearest ten = 130   133 rounded to nearest hundred d= 100=64
Answer: A
If Juan takes 14 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Choose the correct choice
A) 14x/y	B) 14y/x	C) x/(14y)	D) 14/(xy)	E) xy/14

Solution: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.   Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.   We can find Juan’s rate as follows: Rate = Distance/Time = y yards/14 seconds   Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:   Time = Distance/Rate   Time = x yards/(y yards/14 seconds)   Time = (x yards) x (14 seconds/y yards)   Time = 14x/y seconds   14x/ynswer 14x/y.
Answer: A
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?	Choices
A) 120 cm2
B) 820 cm2
C) 128 cm2
D) 110 cm2
E) 220 cm2

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120 cm2rea of the triangle = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2   120 cm2nswer: 120 cm2
Answer: A