MU-NLPC/Calc-aqua_rat huggingface dataset:
A waiter's salary consists of his salary and tips. During one week his tips were 5/2 of his salary. What fraction of his income came from tips ?  Choose the correct choice from the following choices.
A) 4/9 B) 5/4 C) 5/8 D) 5/7 E) 6/9

Solution: Income = salary (s) +tips = s + s*5/2 = s*7/2   Tips = s*7/2   fraction of his income came from tips = (s*5/2)/(s*7/2)= 5/7   ANSWER:5/7
Answer: D
A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work?	Select:
A) 20days
B) 15days
C) 30days
D) 45days
E) 50days

Solution: 10days work of A = 10/40 = 1/4   remaining work = 1-1/4 = 3/4   B can finish 3/4 work = 60*3/4= 
60*3/4 = 45
45days   Answer is 45days
Answer: D
When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder K when N is divided by 30? Choose the most appropriate option
A) (a) 4
B) (b) 7
C) (c) 11
D) (d) 13
E) (e) 17

Solution: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder K when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.(c) 11
Answer: C
For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 60 of this series?
Choices:	A) 5330	B) 5670	C) 5990	D) 6240	E) 6550

Solution: Each term of the series has the form (n+n+1+n+2) = 3n+3   Since the series goes from 1 to 60, the sum of the series is:   3(1+2+...+60) + 60(3) ( + +1+ +2)= 
( + +1+ +2) = 3
3n+3   Since the series goes from 1 to 60, the sum of the series is:   3(1+2+...+60) + 60(3)=   3(60)(61)/2 + 60(3) =   90*61 + 180= 
90*61 + 180 = 5_670
5670   The answer is 5670.
Answer: B
Which of the following is closer to (6!+4!)*(6!-4!)?  Select:
A) 587945  B) 647280  C) 587920  D) 658230  E) 954120

Solution: Notice that 6! = (6*5)(4!)   (6!+4!)*(6!-4!)=[6!(30+1)]*[6!(30-1)]   = 21/19   ≈ 647280   Answer: 647280
Answer: B
In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:4, If Rs 30,000 was their profit, how much amount did B receive.
Answers.
A) 1235  B) 62896  C) 6666  D) 8974  E) 5626

Solution: Explanation:   A:B = 3:4 = 3:4   => A:6666 = 3:2 = 3:2   => A:B:6666 = 3:4:2   6666 share = (2/9)*30000   = 6666   Option 6666
Answer: C
A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ems does the wheel move in 1 hour? Pick one:	A) 20000	B) 14000	C) 23000	D) 120000	E) None of these

Solution: Explanation :   Number of wheel moves in 1 hour = 10 * 60= 
10 * 60 = 600
600distance moved= 600 * 200 = 12000   Answer : 120000
Answer: D
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 13 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?	Pick one:
A) 25 B) 64 C) 36 D) 48 E) 61

Solution: Make a venn diagram to get a clear picture. Look at the diagram:   Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.   d + f = 20 (People who take Art and one other class)   b = 3e (people who take only Art is 3 times the people who take 64io and Calculus)   13 + 10 + 5 + b + d + e + f = 100 (Total people)   b + b/3 = 52   b = 39   Number of freshmen who take Art = 39 + 20 + 5= 
39 + 20 + 5 = 64
64   Answer 64
Answer: B
Find the value of x from logx 100 = 2  Answers:
A) 10  B) 12  C) 13  D) 14  E) 15

Solution: solution:   logb 1000 = 3   We can write it as,   b3 = 1000   b3 = 103   So from the above equation   b = 10   10NSWER IS 10
Answer: A
The bankerâ€™s discount of a certain sum of money is Rs. 90 and the true discount on the same sum for the same time is Rs. 60. The sum due is	Options.
A) 210
B) 180
C) 360
D) 450
E) None

Solution: Sol.   Sum = B.D. * T.D. / B.D. - T.D. = Rs.[90 * 60 / 90 - 60] = Rs. [90 * 60 / 30] = Rs. 180   Answer 180
Answer: B
A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 4 km in stationary water	Choose the correct choice from the following answers.
A) 40 min B) 1hr C) 1hr 15 min D) 1hr 30 min E) 4 hr

Solution: rate down stream=(1/10*60)km/hr=6km/hr   rate up stream=2km/hr   speed still water =1/2(6+2)=4km/hr   required time =(4/4)= 
(4/4) = 1
1 hr   Answer(1hr)
Answer: B
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.	Choose the most appropriate option:
A) $1200 B) $1100 C) $1400 D) $1000 E) $1500

Solution: Given:   After a% decrease the price of the article is reduced by $180 --> pa=180;   After one more such change the price is further reduced by $153. $1200fter the first decrease the price became $(p−180), thus (p−180)a=153--> pa−180a=153a=15--->a=15 --> p∗0.15=180--> p=1,200   $1200nswer: $1200.
Answer: A
A question paper has 2 parts, A & B, each containing 7 questions. If a student has to choose 5 from part A & 4 from part B, in how many ways can he choose the questions?
Choose the correct choice from the following choices:
A) 1100
B) 1200
C) 1235
D) 1354
E) 735

Solution: There 7 questions in part A out of which 5 question can be chosen as = 7C5.   Similarly, 4 questions can be chosen from 7 questions of Part B as = 7C4.   Hence, total number of ways,   =7C5*7C4   =[7!/(2!5!)]*[7!/(3!*4!)]   = {21}*{7*6*5*4/(4*3*2*1)}   = 735.   73521 * 7*6*5*4/(4*3*2*1)= 
21 * 7*6*5*4/(4*3*2*1) = 735
735.   735
Answer: E
How many different positive integers are factors of 324 ?
Choose the correct choice from the following options:
A) 9
B) 16
C) 25
D) 36
E) 49

Solution: 18×18=6^2 × 3^2   So total factors = (5+1)(5+1) = 36   Answer: 36
Answer: D
The average monthly salary of the employees of a firm is Rs.60 out of the employees 12 officers get an average of Rs.400 per month and the rest an average of Rs. 56 per month , Find the number of emp Choose the correct choice:
A) 1032
B) 2766
C) 2882
D) 2788
E) 2772

Solution: 1032ctual average salary of 12 officers = 400   \inline \fn_jvn \therefore Total salary of 12 officers = 400 x 12 = 4800   1032verage of these 12 officers as a whole =60   Total salary of 12 officers as a whole = 60 x 12 = 720   The total salary of rest = 4800 - 720= 
4800 - 720 = 4_080
4080   Difference in average of the rest of officers= 60 - 56= 
60 - 56 = 4
4   Rest of the officers= \inline \fn_jvn \frac{4080}{4}=1020   Total number of employees = 1020 + 12= 
1020 + 12 = 1_032
1032   1032NSWER:1032
Answer: A
The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?  Choose the correct choice:
A) 21 B) 22 C) 23 D) 24 E) None of these

Solution: Let the initial number of members in the group be n.   Initial total weight of all the members in the group = n(48)   From the data,   48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23   Therefore there were 23 members in the group initially.   ANSWER:23
Answer: C
Club X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?  Choices
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: The number of members is 4j+3 = 5k+3.   Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.   31, 35, 39, 43 = 5(8) + 3   The club has 43 members.   43/6 = 6(7) + 1   The answer is 1.
Answer: A
An old priest fell on a bottom of the well of a church.
The well is 19 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ? Pick one
A) 15-days B) 14-days C) 11-days D) 19-days E) 10-days

Solution: 15-days   15-days   In 14-days, he will climb 14-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is	Choose the correct choice from the following answers:
A) 4:3
B) 3:4
C) 2:4
D) 4:2
E) 2:5

Solution: Req ratio = root(16):root of(9)=4:3   4:3NSWER 4:3
Answer: A
If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). The temperature required to boil liquid A and liquid B differed by 35 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?  Choose the correct choice from the following
A) a) 17
B) b) 13
C) c) 25
D) d) 45
E) e) 81

Solution: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick A which is the only number near half of 35. The other answer choices are too far apart so no need to calculate.
Answer: A
Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?  Choose the most appropriate option.
A) 3 hours
B) 6 hours
C) 4 hours
D) 8 hours
E) 10 hours

Solution: Number of pages typed by Ronald in one hour = 32/6 = 16/3   Number of pages typed by Elan in one hour = 40/5= 
40/5 = 8
8   Number of pages typed by both in one hour= ((16/3) + 8) = 40/3   Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.   ANSWER:8 hours
Answer: D
A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? Choices:  A) 90  B) 2,700  C) 4,500  D) 2,550  E) 324,000

Solution: Together the two machines make 30+55= 
30+55 = 85
85 copies per minute. So, in half an hour they will make 85*30=2,550 copies.   Answer: 2,550.
Answer: D
Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?	Choose the most appropriate option
A) 1  B) 2  C) 3  D) 5  E) 6

Solution: 3) 3
Answer: C
How much 60% of 50 is greater than 40% of 30?  Choose the correct choice from the following choices:
A) 18	B) 99	C) 66	D) 55	E) 71

Solution: (60/100) * 50 – (40/100) * 30   30 - 12= 
30 - 12 = 18
18   18nswer: 18
Answer: A
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible?	Choose the correct choice from the following.
A) 3 B) Z=4 C) Z=5 D) Z=6 E) Z=8

Solution: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}   Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.   {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}   Hence 8.Z=8
Answer: E
A 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Choose the correct choice from the following answers
A) 20
B) 12
C) 13
D) 14
E) 16

Solution: Amount of salt = 8.0   Assume x gallons of water are added.   8.0 / 80 + x = 8/100   800 = 8x + 640   8x = 160   x = 20   Correct Option: 20
Answer: A
Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Choose the correct choice from the following answers:
A) 5418 B) 5498 C) 5460 D) 5179 E) 5418

Solution: 5000 * 104/100 * 105/100= 
5000 * 104/100 * 105/100 = 5_460
> 5460   Answer:5460
Answer: C
The sum of four consecutive even numbers is 84. What would be the largest number? Choose the correct choice from the following options.
A) 33
B) 88
C) 24
D) 123
E) 12

Solution: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 = 84 => x = 11   Smallest number is: 2(x +1) = 24.   Answer: 24
Answer: C
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Choose the most appropriate option:
A) 5:9  B) 5:5  C) 5:3  D) 5:2  E) 5:1

Solution: Let 40% of A = 2/3 B. Then,   40A/100 = 2B/3 => 2A/5 = 2B/3   A/B = (2/3 * 5/2) = 5/3   A:B = 5:3.   Answer:5:3
Answer: C
Out of seven numbers, average of first six number is 40 and average of last six number is 35. the first number is 55. What is the difference between first and last number?
Choose the correct choice from the following choices: A) 30 B) 37 C) 41 D) 59 E) None

Solution: Let the seven numbers be represented by   {a,b,c,d,e,f,g}   let sum(b-f) be the sum of numbers b through f.   For the average of the first six we have   (a + sum(b-f))/6 = 40   (a + sum(b-f)) = 240   We are given that the first number, a, is 55, so we have   sum(b-f) = 240 - a   sum(b-f) = 240 - 55   sum(b-f) = 185   Now for the average of the last six numbers we have   (sum(b-f) + g)/6 = 35   (sum(b-f) + g) = 210   185 + g = 210   g = 210 - 185= 
210 - 185 = 25
25   The first number is 55 and the last number is 25 so, their difference is 30.   30nswer 30
Answer: A
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 4 to 5. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Choose the correct choice
A) 168 B) 210 C) 280 D) 420 E) 240

Solution: A:B:C:D=2x:3x:4x:5x, for some positive number x. Total time 2x+3x+4x+5x=14x.   If 2x 2 +3 +4 +5= 
2 +3 +4 +5 = 14
14x.   If 2x= 60 then 14x = 420;   If 3x = 60 then 14x = 280;   If 4x = 60 then 14x = 210;   If 5x = 60 then 14x = 168;   Only answer choices which is not obtained is 240.   Answer: 240.
Answer: E
The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations W could be chosen from this menu? Choose the correct choice: A) 10 B) 20 C) 40 D) 80 E) 100

Solution: W=4401 * 5402   = 4 * (5*4*3!)/(3!2!)   = 4 * 10= 
4 * 10 = 40
40   Answer - 40
Answer: C
When we multiply a certain two digit number by the
sum of its digits 405 is achieved. If we multiply the
number written in reverse order of the same digits
by the sum of the digits,we get 486.Find the number?  Pick one
A) 40
B) 45
C) 50
D) 55
E) 60

Solution: Let the number be x y.   When we multiply the number by the sum of its digit   405 is achieved.   (10x+y)(x+y)=405....................1   If we multiply the number written in reverse order by its   sum of digits we get 486.   (10y+x)(x+y)=486......................2   dividing 1 and 2   (10x+y)(x+y)/(10y+x)(x+y) = 405/486.   10x+y / 10y+x = 5/6.   60x+6y = 50y+5x   55x=44y   5x = 4y.   From the above condition we conclude that the above   condition is satisfied by the second option i e b. 45.   ANSWER : 45 45
Answer: B
For an agricultural experiment, 500 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?  Choose the correct choice from the following answers.
A) 35.7%
B) 25%
C) 32%
D) 30.8%
E) 60%

Solution: From the first plot 0.30*500= 
0.30*500 = 150
150;   From the second plot  0.50*200= 
 0.50*200 = 100
100;   Total percent= (150+100)/(500+200) = 0.357.   35.7%nswer: 35.7%.
Answer: A
There are 2 sections A and B in a class, consisting of 40 and 30 students respectively. If the average weight of section A is 50kg and that of section B is 60kg, Find the average of the whole class? Choose the correct choice.
A) 50.78kg B) 49.32kg C) 61.67kg D) 69.15kg E) 54.28kg

Solution: Total weight of 40+30 students = 40*50 + 30*60 = 2000+1800= 
2000+1800 = 3_800
3800/70= 54.28 kg   Answer is 54.28kg
Answer: E
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/7.
If a jar cannot contain more than 500 balls, how many yellow balls are in the Jar?  Choose the correct choice from the following options: A) 125. B) 124. C) 133. D) 140. E) 149.

Solution: We need to get some number which is less than 500 and exactly divisible by 8,5 and 7   Lets take LCM of three balls 8,5 and 7 = 280.   The probability of drawing a blue ball is 1/8...For every 8 balls we get 1 BLUE ball then out of 280 balls we get 35 BLUE balls.   The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 280 balls we get 56 REB balls.   The probability of drawing a green ball is 1/7. For every 7 balls we get 1 GREEN ball then out of 280 balls we get 40 GREEN BALLS.   Then out of 280 - ( 35 + 56 + 40 )= 
280 - ( 35 + 56 + 40 ) = 149
149 YELLOW balls.   IMO option 149. is correct.
Answer: E
If x - 5 > 2 and x + 3 < 7, the value of x must be between which of the following pairs of numbers?	Select.
A) -3 and 10 B) -3 and 4 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 < 7   x < 4   We know that x is greater than 3 and less than 4.   The answer is 3 and 4.
Answer: D
The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 88 kg and 93 kg join the group. Find the initial number of members in the group?	Choose the most appropriate option.
A) 23
B) 24
C) 25
D) 26
E) 27

Solution: Let the initial number of members in the group be n.   Initial total weight of all the members in the group = n(48)   From the data,   48n + 88 + 93 = 51(n + 2) => 51n - 48n = 79 => n = 26   Therefore there were 26 members in the group initially.   ANSWER:26
Answer: D
If 20 toys cost Rs, 234, what do 35 toys cost?	Choose the most appropriate option.
A) 409.5 B) 564.5 C) 546.5 D) 654.5 E) None of them

Solution: Let the required cost be Rs. x. Then,   More toys, More cost	(Direct Proportion)   . = x=(35 X 234)/20=409.50   409.5nswer is 409.5
Answer: A
Nicole cycles at a constant rate of 15 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?	Choose the correct choice from the following choices.
A) x/3
B) x/2
C) x
D) 3x/2
E) 2x

Solution: In x minutes, Jessica travels (x/60)*30 = x/2 miles   The time it takes Nicole to travel x/2 miles is (x/2) / 15 = x/30 hours = 2x minutes   Jessica needs to wait 2x - x = x minutes.   The answer is x.
Answer: C
A bakery currently has 7 pies and 4 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
Choose the correct choice.
A) 3/11
B) 5/11
C) 14/33
D) 29/77
E) 36/77

Solution: The total number of ways to choose 5 from 11 is 11C5 = 462.   The number of ways that include 3 pies is 7C3*4C2 = 35*6= 
35*6 = 210
210   P(exactly 3 pies)= 210/462 = 5/11   The answer is 5/11.
Answer: B
In the rectangular coordinate system, if the line x = 6y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?	Choose the correct choice from the following choices
A) 1/2 B) 1/3 C) 1/4 D) 1/5 E) 1/6

Solution: x = 6y+5, and thus y = x/6 - 5/6   The slope is 1/6.   The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2   p/2 = 1/6 and thus p = 1/3   The answer is 1/3.
Answer: B
I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 70 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?  Choose the correct choice from the following answers:	A) 8715	B) 0152	C) 3581	D) 4900	E) 9126

Solution: D   5625   n^1   70 * 70= 
70 * 70 = 4_900
4900(sum of first 70 odd numbers).   50 * 50= 
50 * 50 = 2_500
2500 (sum of first 50 odd numbers).
Answer: D
Mary, Peter, and Lucy were picking chestnuts. Mary picked three times as much as much chestnuts than Peter. Lucy picked 5 kg more than Peter. Together the three of them picked 30 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Pick.
A) 10, 15, and 5 B) 15, 10, and 5 C) 15, 5, and 10 D) 10, 5, and 15 E) 5, 10, and 15

Solution: M = 3P   L = P+5   M + P + L = 30   3P + P + (P+5) = 30   P = 5, M = 15, L = 10   Therefore, Mary, Peter, and Lucy picked 15, 5, and 10 kg, respectively.   The answer is 15, 5, and 10.
Answer: C
If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added?
Choose the correct choice from the following options
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Given there are 20 apples.If 1 extra apple is added, then it becomes 21 which can be divided equally that is 7 apples to each baby.   Option 1 is correct.
Answer: A
The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)  Choose the correct choice from the following answers
A) 1	B) 4	C) 7	D) 11	E) 10

Solution: We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients...   3 ingredient blends:   A4C   A4D   ACD   4CD   Total blends = 4   4
Answer: B
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?  Choose the correct choice from the following choices.
A) 31 5/8 years	B) 31 5/7 years	C) 31 9/7 years	D) 38 5/7 years	E) 31 5/4 years

Solution: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)   = (134 + 70 + 18)/7   = 31 5/7 years.   Answer:31 5/7 years
Answer: B
H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is? Pick:
A) 22 * 35 * 72
B) 22 * 35 * 78
C) 22 * 35 * 72
D) 22 * 35 * 71
E) 22 * 35 * 73

Solution: 3240 = 23 * 34 * 5; 3600 = 24 * 32 * 52   H.C.F = 36 = 22 * 32   Since H.C.F is the product of lowest powers of common factors, so the third number must have (22 * 32 ) as its factor.   Since L.C.M is the product of highest powers of common prime factors, so the third number must have 35 and 72 as its factors.   Third number = 22 * 35 * 72   22 * 35 * 72nswer:22 * 35 * 72
Answer: A