divelab/Sys2Bench huggingface dataset:
Question: A box contains 10 black,5 red and 4 green marbles. 3 marbles are drawn from the box at random. What is the probability that all the three marbles are of the same color?
Options:
A)143/969
B)134/969
C)120/969
D)19/969
E)120/134
Rationale: Explanation:
Total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles
3 marbles are drawn from 19 marbles at random. Therefore,
n(S) = 19C3= 969 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 10C3+ 5C3 + 4C3 = 120 +10 + 4 = 134
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 134/969
ANSWER:B
Answer: B
Question: The cost price of 12 articles is equal to the selling price of 10 articles. What is the profit percent?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: 10*SP = 12*CP
SP = 1.2*CP
The profit percent is 20%.
The answer is B.
Answer: B
Question: Calculate 469157 x 9999 = ?
Options:
A)4586970843
B)4686970743
C)4691100843
D)4586870843
E)NONE
Rationale: Answer
469157 x 9999 = 469157 x (10000-1)
= 4691570000 - 469157
= 4691100843.
Option: C
Answer: C
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 180 pastries ?
Options:
A)2 hours.
B)1 hours.
C)5 hours.
D)4 hours.
E)3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 180 pastries would take 180 ÷ 60 = 3 hours.
ANSWER E
Answer: E
Question: For any non-zero a and b that satisfy |ab| = ab and |C| = -c
|b - 4| + |ab - b| = ?
Options:
A)a) ab - 4
B)b) b - 2b + 4
C)c) ab + 4
D)d) 2b - ab - 4a
E)e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4
Answer: Option B
Answer: B
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 50 packages of gaskets. If 20 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
Options:
A)1105
B)1245
C)1275
D)1215
E)1150
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 20 % of the gaskets to X = 10 gaskets = 25*10 = 250
2.he sold 30 % of the gaskets to Y = 15 gaskets = 25*10+20*5= 350
3.he sold remaining 50% to z =25 gaskets = 25*10 =250 + 20*15=550
thus ,total money earned
250+350+550 = 1150
Answer is E
Answer: E
Question: Average of all prime numbers between 40 to 50
Options:
A)37
B)37.8
C)43.6
D)39.8
E)40
Rationale: Explanation:
Prime numbers between 40 and 50 are:
41, 43, 47
Average of prime numbers between 40 to 50 will be
(41+43+47 / 3)=131 / 3 =43.6
Option C
Answer: C
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 51 percent were employees. What percent were stockholders, who were not employees?
Options:
A)52
B)49
C)54
D)55
E)56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
51% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 51% = 49%.
Answer: B
Question: What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively?
Options:
A)456780
B)678910
C)997479
D)997918
E)997920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so D is the only possible answer.
Answer: D
Question: What is the square root of 3,249?
Options:
A)A)18
B)B)9
C)C)45
D)D)62
E)E)57
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
57*57=3,249
3249 divided by x = 57
x=57
(E)57
Answer: E
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
Options:
A)18
B)19
C)21
D)25
E)27
Rationale: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Answer: C
Question: For integers M and N, when M is divided by N, the remainder is odd. Which of the following must be true?
Options:
A)The sum M + N is odd
B)M and N share no common factors other than 1
C)MN is odd
D)M is odd
E)either integer M or integer N is odd
Rationale: either integer M or integer N is odd
E
Answer: E
Question: There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The simple logic is to divide total balls into three sets. Weigh any two sets against each other(these two must contain equal number of balls). From this we can identify which set contains the heavy ball. Divide this set into three and repeat until you find the heavier ball. Under this logic, the minimum number of weighings required turns out to be the smallest integer greater than or equal to log(n), where n is the total number of balls and the base of logarithm is 3. Or simply [log(n)/log(3)] with any base. Here, n = 6561. log 6561 / log 3 = 8
ANSWER:B
Answer: B
Question: A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. When A done the work?
Options:
A)10 days
B)12 days
C)13 days
D)9 days
E)14 days
Rationale: B+C ==>1/9+1/12 = 7/36
B ,C =in 3 days = 7/36*3 = 7/12
remaining work = 1-7/12 = 5/12
1/24 work is done by A in 1 day
5/12 work is done A 24*5/12 = 10 days
ANSWER A
Answer: A
Question: What is the area of a square with perimeter 12P ?
Options:
A) 16p^2
B) 4P
C) 9P^2
D) P/16
E) P^2/16
Rationale: Each side is 3p
A = (3p)^2 = 9p^2
Answer C
Answer: C
Question: Average of first five multiples of 3 is
Options:
A)9
B)11
C)13
D)15
E)17
Rationale: Explanation:
Average=3(1+2+3+4+5) / 5=45 / 5=9
Option A
Answer: A
Question: A bag contains 7 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
Options:
A)2/3
B)3/5
C)1/5
D)7/15
E)8/15
Rationale: Total number of balls = (7 + 5 + 6) = 18.
Therefore, n(S) = 18.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (7/18 + 5/18) = 2/3.
ANSWER:A
Answer: A
Question: The average of five numbers is 9. The average of first two numbers is 7 and the average of last two numbers is 12. What is the middle number?
Options:
A)7
B)8
C)5
D)10
E)6
Rationale: The total of five numbers = 5x9 = 45
The total of first 2 and last 2 numbers is = 2 X 7+2 X 12 = 38
So, the middle number is (45 - 38 ) = 7
A
Answer: A
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Options:
A)78 years
B)22 years
C)88 years
D)66 years
E)65 years
Rationale: Let's Son age is x, then Father age is x+24.
=> 2(x+2) = (x+24+2)
=> 2x+4 = x+26
=> x = 22 years
Answer: B
Answer: B
Question: What is the smallest 6 digit number exactly divisible by 111?
Options:
A)100010
B)100012
C)100011
D)100013
E)120012
Rationale: Smallest 6 digit number = 100000
100000/111 = 900, remainder = 100. Hence 11 more should be added to 100000
to get the smallest 6 digit number exactly divisible by 111
=> smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011
Answer is C
Answer: C
Question: The equation x/y - 2/5 = 0 is equivalent to each of the following EXCEPT
Options:
A)(x - y)/y = -3/5
B)(5x - 3y)/y = 21/5
C)(x + 3y)/y = 17/5
D)(x + y)/x = 7/2
E)x/y + 1 = 7/5
Rationale: x/y - 2/5 = 0
5x=2y
x= 2/5 * y or y = 5/2 *x
plug in x or y depending on the equation. all expressions are true except for
B. (5x - 3y)/y = 21/5
where y=-21
B. (5x - 3y)/y = 21/5
ANSWER:B
Answer: B
Question: A train travels from New York to Chicago, a distance of approximately 840 miles, at an average rate of 60 miles per hour and arrives in Chicago at 7:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
Options:
A)3:00
B)4:00
C)5:00
D)6:00
E)7:00
Rationale: 7:00 in evening in Chicago = 8:00 in evening in New York. So, the train was in Chicago 8:00 in the evening, New York time.
The trip took T=D/R=840/60=14 hours. Therefore, the train depart from New York at 8:00 - 14 hours = 6:00 in the morning, New York time.
Answer: D.
Answer: D
Question: A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?
Options:
A)87
B)92
C)12
D)10
E)11
Rationale: Explanation:
1 m2 ---- 1/2
? ----- 600 => 1200 m2
4x * 3x = 1200 => x = 10
Answer: Option D
Answer: D
Question: In how many ways the letters of the word RAIXBON be arranged?
Options:
A)4500
B)5479
C)6478
D)5040
E)7658
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
D)
Answer: D
Question: In Lulu company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
Options:
A)43.0
B)45.5
C)46.0
D)49.0
E)50.0
Rationale: In Lulu company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A
Answer: A
Question: The average age 6 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)14 years
B)17 years
C)18 years
D)12 years
E)11 years
Rationale: 6 * 2
= 12
Answer:D
Answer: D
Question: How many 3-digit positive integers are there, where each digit is positive, and no two adjacent digits are same?
Options:
A)576
B)3024
C)4096
D)4608
E)6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 8 possibilities
9*8*8 = 576.
A
Answer: A
Question: 15.06 * 0.001 = ?
Options:
A)15060000
B)0.001506
C)0.01506
D)0.1506
E)None of these
Rationale: Explanation:
Clearly after decimal 5 digits should be there.
Option C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)877m
B)180m
C)786m
D)165m
E)456m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: B
Question: In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 2) lies inside the circle and the point (5, -3) lies outside the circle. If the radius r of the circle r is an integer then r=
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (5,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (5,-3) ---> lesser than 7 units but the radius will also be greater than the distance of (-2,-3) from (-2,2) ----> greater than 5 units.
Thus the radius is >5 but <7and as it is an integer, the only possible value of radius = 6 units.
A is the correct answer.
Answer: A
Question: Mark and Cody invest in a business and each put in $12000. After 3 months, Cody withdraws half of his capital. How should they share the profits after 12 months?
Options:
A)10:7
B)3:2
C)8:5
D)4:3
E)11:8
Rationale: Mark invests $12000 for 12 months, but Cody invests $12000 for the first 3 months and then withdraws $6000. So, the investment of Cody for remaining 9 months is $6000 only.
Mark:Cody
12000*12 : (12000*3) + (6000*9)
144000 : 90000
Mark:Cody = 8:5
Answer: C
Answer: C
Question: Sum of two numbers is 63. Their difference is 1/8 of their sum. their L.C.M is
Options:
A)231
B)153
C)351
D)345
E)355
Rationale: Explanation:
Let the numbers be x and y
According to the problem
X + y = 63
x - y = 1/8 ( x+y)
x-y = 1/8 * 63, x-y = 9
2x = 72, x= 36 and y = 27
L.C.M of 36 and 27 is 351
Answer: Option C
Answer: C
Question: If x,p,q, and r are positive integers and (p)×(q)×(r)=x^2, which of the following could be the values of p,q, and r?
Options:
A)3, 16, 25
B)9, 25, 24
C)2,16, 32
D)2, 9, 16
E)8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*16*32 = 2*4*4*8*4 =4*4*8*8
ans C
Answer: C
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 10 more revolutions than gear P?
Options:
A)10
B)12
C)15
D)20
E)25
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 10 = 30/3 more revolutions is 60/3 = 20 seconds.
The answer is D.
Answer: D
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
Options:
A)30
B)40
C)20
D)50
E)25
Rationale: Let the present age of the husband = h
Present age of the wife = w
Present age of the child = c
3 years ago, average age of husband, wife and their child = 27
=> Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81
=> (h-3) + (w-3) + (c-3) = 81
=> h + w + c = 81 + 9 = 90 --- equation(1)
5 years ago, average age of wife and child = 20
=> Sum of age of wife and child before 5 years = 2 × 20 = 40
=> (w-5) + (c-5) = 40
=> w + c = 40 + 10 = 50 --- equation(2)
Substituting equation(2) in equation(1)
=> h + 50 = 90
=> h = 90 - 50 = 40
i.e., Present age of the husband = 40
Answer is B.
Answer: B
Question: Factor: x4y3 â€“ 16y3
Options:
A)A) 3y3(x2 + 4)(x + 2)(x -2)
B)B) y3(x2 + 4)(x + 2)(x -2)
C)C) 3y3(x2 + 4)(x + 2)(x -3)
D)D) 3y3(x2 + 4)(x + 3)(x -2)
E)E) 3y3(x2 + 4)(x + 2)(x -4)
Rationale: x4y3â€“ 16y3.
= y3(x4 â€“ 16).
= y3[(x2)2 - 42].
= y3(x2 + 4)(x2 - 4).
= y3(x2 + 4)(x2 - 22).
= y3(x2 + 4)(x + 2)(x -2).
Answer: (B) y3(x2 + 4)(x + 2)(x -2)
Answer: B
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
A)18 days
B)11 days
C)77 days
D)188 days
E)66 days
Rationale: 8/12 + 6/x = 1
X = 18 days
Answer: A
Answer: A
Question: A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net invests of the first year?
Options:
A)Rs. 3359
B)Rs. 2500
C)Rs. 4000
D)Rs. 3212.5
E)None
Rationale: Solution: The total cost for the year = 250000+2% of 2500000+2000 = Rs. 257000.
For getting return of 15% he must earn = 257000*15/100 = Rs. 38550 per year.
Then, monthly rent = 38550/12 = Rs. 3212.5.
Answer: Option D
Answer: D
Question: The average of 13 numbers is 14.8. If the average of the first seven numbers is 14.6 and that of the last seven numbers is 14.4,then the middle number is?
Options:
A)11.6
B)12.6
C)10.6
D)9.6
E)8.6
Rationale: Middle number = 14.6*7 + 14.4*7- 14.8*13 = 102.2+100.8-192.4=10.6
Answer is C
Answer: C
Question: Of the 440 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
Options:
A)240 to 280
B)230 to 260
C)240 to 260
D)200 to 260
E)180 to 260
Rationale: W=260
P=300
ALL=440
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+60=440
BOTH=180
now pay attention to the fact, that both at most can be 260, since W=260
E
Answer: E
Question: 3/7 of a congregation are men while 11/21are women. What is the increase in percentage from ratio of men to ratio of women in the congregation?
Options:
A)A) 69%
B)B) 54%
C)C) 18.81%
D)D) 16%
E)E) 81.82%
Rationale: Ratio of men: 3/7
Ratio of women: 11/21
percentage increase is (difference/initial quantity)*100
(3/7)/(11/21 )* 100= 81.82%
Correct options is E
Answer: E
Question: If x is 20 percent more than y and y is 70 percent less than z, then x is what percent of z?
Options:
A)500%
B)250%
C)500/3%
D)36%
E)60%
Rationale: Z = 100 ; Y = 30 so X = 36
X as % of Z = 36/100 * 100 => 36%
Answer will be (D)
Answer: D
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
Options:
A)Rs.3601
B)Rs.3618
C)Rs.3600
D)Rs.3619
E)Rs.3610
Rationale: Manager's monthly salary
= Rs. (1600 * 21 - 1500 * 20)
= Answer:C
Answer: C
Question: 1/6 = 4/5 . which method did you use to determine whether this proportion is true or false?
Options:
A)true
B)neutral
C)false
D)not sure
E)none
Rationale: 1/6= 3/18. cross multiplication: 1 * 18 = 18, 3 * 6= 18,
we see that 18 are not equal to 18. so there is proportion. corrcet answer: (A)
Answer: A
Question: During a certain season, a team won 70 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
Options:
A)180
B)170
C)156
D)150
E)100
Rationale: We are first given that a team won 70 percent of its first 100 games. This means the team won 0.7 x 100 = 70 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
70 + 0.5T – 50 = 0.7T
20 = 0.2T
200 = 2T
100 = T
Answer is E.
Answer: E
Question: You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Appleland).
What is highest number of apples you can get to Bananaville?
Options:
A)767
B)833
C)916
D)1123
E)907
Rationale: Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go.
Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville.
Answer: B
Question: In how many different ways can 5 girls and 6 boys form a circle such that the boys and the girls alternate?
Options:
A)28800
B)14000
C)12000
D)14400
E)None of these
Rationale: Explanation :
In a circle, 6 boys can be arranged in 5! ways
Given that the boys and the girls alternate.
Hence there are 5 places for girls which can be arranged in 5! ways
Total number of ways = 5! x 5! = 24 x 120 = 14400. Answer : Option D
Answer: D
Question: When a Bike is sold for Rs. 63,000, the owner loses 10%. At what price must that Bike be sold in order to gain 10%?
Options:
A)74000
B)75000
C)76000
D)77000
E)78000
Rationale: 90 : 63000 = 110 : x
x = (63000 x 110)/90 = 77,000.
Hence, S.P. = Rs. 77,000.
Answer: Option D
Answer: D
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1278
B)1200
C)2887
D)1688
E)2768
Rationale: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Options:
A)23/35
B)23/38
C)23/15
D)22/35
E)21/35
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (6C1 * 9C1)/15C2 + 6C2/15C2
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Answer: A
Question: In a bag, there are six 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
Options:
A)42
B)60
C)61
D)84
E)960
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
C
Answer: C
Question: Sandy is younger than Molly by 14 years. If their ages are in the respective ratio of 7:9, how old is Molly?
Options:
A)36
B)45
C)54
D)63
E)72
Rationale: S = M - 14
S / M = 7/9
9S = 7M
9(M-14) = 7M
M = 63
The answer is D.
Answer: D
Question: A cyclist rides a bicycle 7 km at an average speed of 10 km/hr and again travels 10 km at an average speed of 7 km/hr. What is the average speed for the entire trip?
Options:
A)7.59
B)7.79
C)7.99
D)8.19
E)8.39
Rationale: distance = 17 km
time = 7/10 + 10/7 = (49 + 100) / 70 = 149 / 70 hours
average speed = (17 * 70) / 149 = 7.99 km/h
The answer is C.
Answer: C