MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain toy store's revenue in November was 1/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?  Choose the correct choice from the following answers
A) 1/4	B) 1/2	C) 2/3	D) 2	E) 6

Solution: Let Dec rev =100   Then Nov rev is 1/5 (100) => 20   Therefore Jan rev = 3/4(Nov rev) = 3/4(20) => 15   Hence Dec rev = x*( Nov rev+Jan rev)/2   100 = x* (20+15)/2   x = 100/17.5 => 5.71=6   Ans) 6
Answer: E
If the probability of rain on any given day in City X is 40%, what is probability that it rains on exactly 3 days in a 4 day period?
Choices.
A) 16/25  B) 48/125  C) 96/625  D) 108/625  E) 132/625

Solution: One possible way is rain-rain-rain-no rain.   The probability of this is 2/5*2/5*2/5*3/5 = 24/625   The number of possible ways is 4C3 = 4, so we multiply this by 4.   P(rain on exactly 3 days) = 4*24/625 = 96/625   The answer is 96/625.
Answer: C
What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?	Choose one
A) 714 B) 814 C) 850 D) 866 E) None of these

Solution: Explanation:   In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.   Length of largest tile can be obtained from HCF of length and breadth.   So lets solve this,   Length of largest tile = HCF of (1517 cm and 902 cm)   = 41 cm   Required number of tiles =   Area of floor/Area of tile=(1517×902/41×41)=814   Option 814
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: Choose the correct choice from the following answers
A) 14 years
B) 10 years
C) 8 years
D) 17 years
E) None of these

Solution: Explanation:   Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   ⇒ 5x = 20   ⇒ x = 4.   ⇒ Age of the youngest child = x = 4 years.   14 yearsnswer: 14 years
Answer: A
What is the minimum value of |x-4| + |x+7| + |x-5| ?
Choose the most appropriate option:  A) -3  B) 3  C) 5  D) -12  E) 12

Solution: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.   |x-4| >= 0 --> Minimum occurs at x = 4   |x+7| >= 0 --> Minimum occurs at x = -7   |x-5| >= 0 --> Minimum occurs at x = 5   x = -7 --> Result = 11 + 0 + 12= 
11 + 0 + 12 = 23
23. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.   x= 4 --> Result = 0 + 11 + 1= 
0 + 11 + 1 = 12
12   x= 5 --> Result = 1 + 12 + 0= 
1 + 12 + 0 = 13
13   x= 7 --> Result = 3 + 14 + 2= 
3 + 14 + 2 = 19
19   So minimum value of the expression occurs at x= 4 and the resultant value = 12   Answer: 12
Answer: E
The probability that a number selected at random from the first 50 natural numbers is a composite number is  Choose the correct choice from the following:
A) 21/25
B) 17/25
C) 4/25
D) 8/25
E) 9/25

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   ANSWER:17/25
Answer: B
If you spend 1/4 of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month? Choose the correct choice from the following answers.
A) 2/20
B) 3/20
C) 4/20
D) 5/20
E) None

Solution: Solution:   1/4+3(20/100)=1/4+3/5=5+12/20=17/20   The sallary that will be spent = 17/20   Unspend will be = 1−17/20 =20−17/20 =3/20   Answer 3/20
Answer: B
Given the sum 195 of 13 consecutive integers, find the sum of 4th number and 7th number of the sequence
Select:
A) 65
B) 54
C) 26
D) 30
E) 27

Solution: The median is: 195/13= 
195/13 = 15
15.   The middle position is: 13/2= 
13/2 = 13/2 = around 6.5
6.5, rounded up: 7th position. So 15 is the value of the 7th position   Difference between 7th and 4th position= 3 positions less   15 - 3= 
15 - 3 = 12
12= is the value of the 4th position     15 + 12= 
  15 + 12 = 27
27= sum of 4th and 7th number.   Answer: 27
Answer: E
A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 2
matches are totally played, how many teams participated? Choose the correct choice from the following answers: A) 4 B) 5 C) 6 D) 2 E) 3

Solution: 2 ways to solve this problem..   summation(x)=n(n-1)/2   n(n-1)/2=2;   n^2-n-4=0   Ans : 2   ANSWER:2
Answer: D
The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 432 sq meters, then what is the width (in meters) of the rectangular plot?	Choices: A) 10 B) 11 C) 12 D) 13 E) 14

Solution: Area = L*W = 3W^2 = 432   W^2 = 144   W = 12   The answer is 12.
Answer: C
The total number of digits used in numbering the pages of a book having 360 pages is Choose the correct choice from the following.
A) 972	B) 990	C) 1098	D) 1305	E) 1405

Solution: Total number of digits   = (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)   = (1 x 9 + 2 x 90 + 3 x 261) = (9 + 180 + 783)= 
(9 + 180 + 783) = 972
972.   972NSWER:972
Answer: A
Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 12 times as heavy as water?
Select:  A) 1:2  B) 3:7  C) 4:1  D) 5:2  E) 6:5

Solution: G = 19W   C = 9W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   19W+9Wx = x+1 * 12W   19+9x = 12(x+1)   x = 7/3   Ratio of gold with copper = 1:7/3 = 3:7   Answer is 3:7
Answer: B
The sum of two numbers is 20 and the sum of their squares is 140. Find the product of the two numbers.	Choose the correct choice from the following answers
A) 130	B) 140	C) 120	D) 145	E) 150

Solution: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=20 a^2+b^2=140So, 20^2=140+2ab2ab=400-1402ab=260ab=130130ns 130
Answer: A
A river 4m deep and 22 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?  Choose the correct answer:  A) 4500  B) 2678  C) 2933  D) 2761  E) 2882

Solution: (2000 * 4 *22 )/60   = 2933 M3   Answer:2933
Answer: C
An amount of Rs.1560 was divided among A, B and C in the ratio 1/2:1/3:1/4. Find the share of C?	Pick one:
A) Rs.367 B) Rs.386 C) Rs.369 D) Rs.360 E) Rs.362

Solution: Let the shares of A, B and C be a, b and c respectively.   a:b:c = 1/2:1/3:1/4   a:b:c = 6/12:4/12:3:12 = 6:4:3   Share of C = 3/13 * 1560 = Rs.360.   Answer:Rs.360
Answer: D
In how many ways can five members be selected from a group of twelve members?
Choose the correct choice.
A) 12C5
B) 12C8
C) 12C4
D) 11C3
E) 10C1

Solution: five members can be selected from twelve members in   12C5   = 12C5 ways.   12C5nswer: 12C5
Answer: A
Sum of products of three numbers taken two at a time is 131. Sum of squares of the three numbers is 138. What is the sum of the three numbers?  Choose the correct choice from the following choices:
A) 20	B) 88	C) 26	D) 18	E) 17

Solution: Explanation:   All the data given in the question points to the equation mentioned below:   Considering the three numbers to be a,b and c:   (a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca   Accordingly, substitute for a, b and c and solve:   => a2+b2+c2= 138, ab+bc+ac = 131. Thus, 2(ab+bc+ac)= 2*131= 
2*131 = 262
262   (a+b+c)2= 138+262= 
138+262 = 400
400.   Therefore, a+b+c= 20   20NSWER: 20
Answer: A
A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is Choose the correct option.
A) 1/3 B) 2/3 C) 2/5 D) 1/4 E) 1/2

Solution: 1 st jar (alchohol) = 40%   2nd jar = 19%   after mix = 26%   mean = 7:14=1:2=>2/1+2=2/3   ANSWER 2/3
Answer: B
It takes Greg 6 minutes to run a mile, and it takes Pete 8 minutes. If Greg and Pete both begin running at exactly 8:30 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
Answers
A) 8:36 am	B) 8:38 am	C) 8:48 am	D) 8:54 am	E) 9:00 am

Solution: Since Greg will run s miles after s × 6 minutes and Pete will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 6 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 6 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 6 and 8 is 24, so in the context of the question, this would be 24 minutes. Therefore, the first time they will finish running a mile at the same time is 8:30 + 24 minutes, or 8:54 a.m. The answer is (8:54 am).
Answer: D
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: Choices
A) 9000 B) 9400 C) 9600 D) 9800 E) 9900

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600.   Answer: Option 9600
Answer: C
If the man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.  Choose the correct choice from the following options:
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: Let the distance be x   Difference Between time = 12 min, which is 12/60 in hour which is 1/5   Now x/5-x/6 = 1/5   6x-5x/30 = 1/5   x/30 = 1/5   x = 30/5= 
30/5 = 6
6 So the required distance= 6   ANSWER:6
Answer: C
85% of a number is added to 24, the result is the same number. Find the number? Answers.
A) 257	B) 267	C) 187	D) one hundred sixty (160)	E) 122

Solution: (85/100) * X + 24 = X   3X = 480   X = 160   Answer:one hundred sixty (160)
Answer: D
A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr?	Answers.
A) 12 km/hr	B) 14 km/hr	C) 10 km/hr	D) 8 km/hr	E) 9 km/hr

Solution: Explanation:   The person needs to cover 6 km in 45 minutes   Given that he covers one-half of the distance in two-thirds of the total time   => He covers half of 6 km in two-thirds of 45 minutes   => He covers 3 km in 30 minutes   Hence, now heneed to cover the remaining 3 km in the remaining 15 minutes   Distance = 3 km   Time = 15 minutes = 1/4 hour   Required Speed=Distance/Time = 3/(1/4)= 
3/(1/4) = 12
12 km/hr   12 km/hrnswer: Option 12 km/hr
Answer: A
The units digit of (3)^(44) + (10)^(46) is: Select:
A) 2 B) 4 C) 1 D) 8 E) 0

Solution: any power of anything ending in zero always has a units digit of 0. So the first term has a units digit of 0.   The period is 4. This means, 3 to the power of any multiple of 4 will have a units digit of 1.   3^44 has a units digit of 1   .   Of course  0 + 1= 
 0 + 1 = 1
1   1
Answer: C
What is the greatest prime factor of 1+2+3+。。。+22?  Select the correct option
A) 17 B) 29 C) 23 D) 37 E) 11

Solution: find the sum from direct formula = n(n+1)/2 = 22(22+1)/2 = 11*23...   23 is a PRIME number, so ans is 23..   23 is the answer
Answer: C
Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $ 600 at the end of another 2 years. What was the rate of interest in which he invested his sum?  Choose the correct choice from the following:
A) 100% B) 12.5% C) 67% D) 25% E) 33%

Solution: Lets assume the Principal Amount (initial amount invested) to be P   rate of interest to beRand time as T. We need to find R   Now After a time of 3years the principal P amounts to $400 and after a time of 5years ( question says after another 5years so 3+2) P becomes $600.   Formulating the above data   100%mount (100%1) at end of 3years   100%1= P(1 + 3R/100) = 400   100%mount (100%2) at end of 8years   100%2 = P(1 + 5R/100) = 600   Dividing 100%2 by 100%1 we get   (1 + 5R/100)/(1 + 3R/100) = 6/8   after cross multiplication we are left with R =100   Option: 100%
Answer: A
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Choose the correct answer
A) 9 minutes
B) 7
C) 6
D) 5
E) 4

Solution: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.   9 minutesnswer:9 minutes
Answer: A
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Choose the correct choice from the following choices.
A) 5 B) 18 C) 12 D) 24 E) 10

Solution: Explanation:   Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters.   Correct Option : 10
Answer: E
Last year for every 100 million vehicles that travelled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, hom many of those vehicles were involved in accidents (1 billion=1,000,000,000)? Choices.
A) 288	B) 320	C) 2880	D) 3200	E) 28800

Solution: Explanation:   If r is halved then it is possible to substitute 1/2r for r in the formula and simplify:   1/(2(1/2r))^3=1/(8(1/8r^3))=1/r^3   Compared to the original where:   V=1/(2r)^3=1/(8r^3), the new value of V is 1/r^3 or   8(1/(8r^3))=8V   When r is halved then V is multiplied by 8.   Answer: Option 320
Answer: B
A train 100 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
Choose the correct choice.
A) 6 sec.
B) 7 sec.
C) 9 sec.
D) 11 sec.
E) None

Solution: Solution   Speed of the train relative to man	=( 68 - 8 )= 
( 68 - 8 ) = 60
60 Kmph= 60 x 5 / 18   =50/3 m/sec.   Time taken by it to cover 100 m at (50 /3)m/sec   = (100 x 3/50)sec   = 6 sec.   6 sec.nswer 6 sec.
Answer: A
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Answers
A) 1800 B) 900 C) 2500 D) 2700 E) None of these

Solution: Explanation :   Let required number of bottles be x   More machines, more bottles(direct proportion)   More minutes, more bottles(direct proportion)   ⇒ 6 × 1 × x = 10 × 4 × 270   ⇒ x = (10 × 4 × 270)/6 = (10 × 4 × 90)/2 = 10 × 4 × 45 = 1800. 1800nswer : Option 1800
Answer: A
When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor? Choose the correct option:	A) 11	B) 17	C) 13	D) 23	E) 37

Solution: let that divisor be x   since remainder is 15 or 27 it means divisor is greater than 27.   now  242-15= 
 242-15 = 227
227=kx (k is an integer and 234 is divisble by x)   similarly  698-27= 
 698-27 = 671
671= lx (l is an integer and 689 is divisible by x)   adding both 698 and 242   = (227+671)+15+27   =x(k+l) + 42   when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5= 
42-5 = 37
37   hence 37
Answer: E
If 4 less than x is 4 greater than y, then a number z that is 2 greater than x reduced by y is equal to Choose the correct choice from the following answers.
A) 4
B) 9
C) 14
D) y + 9
E) 10

Solution: 10 it is....nice one....   10
Answer: E
John had a stock of 800 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?  Answers
A) 26.5%  B) 36.5%  C) 71.7%  D) 56.5%  E) 70.0%

Solution: Let N be the total number of books sold. Hence   N = 75 + 50 + 64 + 78 + 135 = 272   Let M be the books NOT sold   M = 960 - N = 960 - 402 = 688   Percentage   Books not sold / total number of books = 688/960= 0.72 = 71.7%   correct answer 71.7%
Answer: C
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?  Answers.
A) 240  B) 270  C) 295  D) 360  E) 300

Solution: Explanation:   Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   ANSWER IS 270
Answer: B
Valerie buys 3 new dresses on average every year for the last 5 years. In order to increase her average to 4 dresses per year, how many dresses should Valerie buy next year? Answers.
A) 1	B) 5	C) 6	D) 9	E) 12

Solution: Solution   Average of 6 years = 4 .   âˆ´ Required number of dresses= (6x4)-(5x3)   = 24- 15= 
24- 15 = 9
9.   Answer 9
Answer: D
A contractor undertook to make 15 km of roadway in 40 weeks. In 10 weeks, 3 km was complete by 180 men working 8 hours a day. The men then agreed to work 1 hour a day overtime, And some boys were engaged to assist them, the work was finished in the stipulated time(40 weeks). How many boys were employed, if the work of 3 boys is equal to that of 2 men? Choose the most appropriate option.
A) 48	B) 50	C) 22	D) 27	E) 221

Solution: Explanation:   Let the capacity of man = 3 units, and boy = 2 units per hour.   Now total work = 3×180×8×7×10 = 3 km. - - - - - - - (1)   Let k boys were recruited. Now total work = (3×180+2×k) ×9×7×30 = 12km. - - - - - - (2)   50y dividing 2nd equation by 1st,   ⇒ (540+2k)×9×7×303×180×8×7×10=4(540+2k)×9×7×303×180×8×7×10=4   ⇒ k = 50   Answer: 50
Answer: B
If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D?  Choose the most appropriate option:	A) 55	B) 61	C) 69	D) 90	E) 97

Solution: c + d = 11   5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=90=15   90=15   c+d=9=C+15=9=C=9-15=-6   C=-6   5C + 890=5(-6)+8(15)=-30+120= 
-30+120 = 90
90   Hence, 90 is the right answer.
Answer: D
If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
Select:  A) 11 1/9  B) 10 1/9  C) 12  D) 15  E) 18

Solution: 0.2/11 1/9 + 0.8/B = 20   1/11 1/9 + 4/B = 100   0.8/11 1/9 + 0.2/B = 30   4/11 1/9+ 1/B = 150   15/B = 250   B = 3/50 work per day   11 1/9 = 3/100 work per day   Combined rate = 3/40 + 3/100 = 9/100   Time taken when working together = 100/9 = 11(1/9) days   11 1/9nswer (11 1/9)
Answer: A
Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option?	Answers
A) 1/2 B) 1/6 C) 1/12 D) 6/10 E) 3/10

Solution: as coin has only two faces then probability must be 1/2   1/2NSWER:1/2
Answer: A
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday ?
Pick
A) 34	B) 66	C) 25	D) 18	E) 12

Solution: Explanation:   M + Tu + W + Th = 4 x 48 = 192   Tu + W + Th + F = 4 x 46 = 184   M = 42   Tu + W + Th = 192 - 42= 
192 - 42 = 150
150   F= 184 â€“ 150 = 34   34nswer: 34
Answer: A
A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs.9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent?
Select the correct option:
A) 2377.55  B) 2477.55  C) 2577.55  D) 2677.55  E) 2777.55

Solution: as question says,   30s+35p=20a+27L =9000 say eqn 1   6s=7p , 15p=12a , 10a=9L   or   6s=7p , 7p=(12*7)/15 a =(28/5)a , (28/5)a= (28/50)*9L   OR   6s=7p=(28/5)a=(252/50)L = K   now   s=(k/6), p= (k/7) , a=(.1785k) , L=(.1984k)   put these value in eqn one you will got value of k is 475.511   now 6s=k   hence s=k/6=79.25   there are 30 students hence 79.25*30=2377.55   2377.55NSWER:2377.55
Answer: A
If 40% of a certain number is 160, then what is 30% of that number?	Choose the correct option:  A) 270  B) 380  C) 120  D) 360  E) 180

Solution: Explanation:   40% = 40*4= 
40*4 = 160
160   30%= 30*4= 
30*4 = 120
120   Answer: Option 120
Answer: C
The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?	Select:
A) 1/12	B) 1/9	C) 2/3	D) 1 1/9	E) 2 1/9

Solution: Total bought = 4/9+2/3   left part 8/18--->4/9   so used part 4/9+2/3-4/9=2/3   ANSWER:2/3
Answer: C
A train travels from city A to city B. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?  Select the correct option:  A) 30  B) 45  C) 54  D) 72  E) 90

Solution: Using the RTD chart, with A being the first quarter, B the rest of the trip and All the combinedtrip.   _______R_____T______D   A.........90........3..........270   B.........54.......15.........810   All........60.......18........1080   Let me explain how we fill in the chart:   1) Starting with what we know, we add 90 and 60   2) Picking an easy number for the total distance (6*9=54), so I chose 540. Multiply by 2 to get the whole trip, and we get 1080. Add 1080 for all-distance.   3) 1/4 of the whole distance happened at a Rate of 90. So, 1080/4=270, add 270 under A-D.   4) 2080 - 270 = 810, for the rest of the trip. Add 810 under B-D.   5) Claculate the individual Times for A and All, using T=D/R. Add the results, 3 and 18, under A-T and All-T.   6) 18-3=15, this is the remaining Time for B. Add 15 under B-T.   7) Finally, 15R=810 -->R=810/15 --> R= 54ANS 54
Answer: C
Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 1/2 brand X and 1/2 brand Y. what fraction of the cost of the blend is Brand X?  Choose the correct option:	A) a. 1/3	B) b. 2/5	C) 3. 2/3	D) 4. 1/5	E) 5. 3/4

Solution: Assume Cost of X= Ca = 200 , Cost of Y = Cb=100   The blend contains 0.5 X and 0.55 Y ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 
0.5*200+0.5*100 = 150
150   Thus fraction of X in the blend= 0.5*200/150 = 2/3.   Answer : 3. 2/3
Answer: C
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:  Choices:  A) 32  B) 38  C) 44  D) 52  E) 63

Solution: Therefore, since the remainder when q is divided by r is 7, then r>7;   Similarly, since the remainder when s is divided by t is 3, then t>3.   Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:   32=8*4   44=11*4   52=13*4   63=9*7   However, 38=1*38 or 19*2, thus rt cannot equal to 38.   Answer: 38.
Answer: B