divelab/Sys2Bench huggingface dataset:
Question: A girl has 12 jeans and 15 tops. In how many different ways can she select a jeans and a tops?
Options:
A)108
B)200
C)90
D)120
E)180
Rationale: The girl can select one jeans in 12 ways.
The girl can select one top in 15 ways.
The number of ways in which she can select one jeans and one top is 12*15=180
Answer:E
Answer: E
Question: If a person allocates 20 percent of his budget to house rent, 30 percent to food, and 25 percent to clothes, what fraction of his budget remains for other allocations?
Options:
A)3/5
B)4/5
C)1/2
D)1/3
E)1/4
Rationale: 100%-(20%+30%+25%)=25% remains for other allocations --> 25% = 25/100 = 1/4.
Answer: E.
Answer: E
Question: If a committee of 3 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)20
B)32
C)54
D)80
E)120
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
8*6*4 / 6 = 32. Answer B.
Answer: B
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 284 pounds. What is Jake’s present weight, in pounds?
Options:
A)176
B)180
C)184
D)188
E)192
Rationale: J + K = 284 and so K = 284 - J
J - 8 = 2K
J - 8 = 2(284-J)
3J = 576
J = 192
The answer is E.
Answer: E
Question: A and B complete a work in 80 days. A alone can do it in 40 days. If both together can do the work in how many days?
Options:
A)1.0875 days
B)0.1875 days
C)0.0675 days
D)0.0375 days
E)0.0775 days
Rationale: 1/80 + 1/40 = 0.0375 days
ANSWER:D
Answer: D
Question: A composer’s guild is planning its spring concert, and eight pieces have been submitted for consideration. The director of the guild knows that they will only have time to present five of them. If the pieces can be played in any order, how many combinations of pieces are possible?
Options:
A)56
B)21
C)10
D)50
E)19
Rationale: Combination question..
8C5 = 56..
IMO option A is correct..
Answer: A
Question: Line k is in the rectangular coordinate system. If the f-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?
Options:
A)-3f + 2y = 6
B)3f + 2y = -6
C)3f - 2y = 6
D)2f - 3y = 6
E)-2f - 3y = 6
Rationale: This question can be solved in much simpler way.
To find the f intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put f=0 in the equation of the line.
So
Sub f=0 in the answer choices check whether you are getting y=3.
A. -3f + 2y = 6 --- y = 3
B. 3f + 2y = -6 --- y = -3
C. 3f - 2y = 6 ----- y = -3
D. 2f - 3y = 6 --- y = -2
E. -2f - 3y = 6 --- y =-2
Eliminate answer B,C,D and E.
So the answer is A.
Answer: A
Question: John's annual salary after a raise of 15% is $45,000. What was his salary before the raise?
Options:
A)$49,007
B)$31,876
C)$54,765
D)$39,130
E)$42,123
Rationale: Let x be the salary before the increase. Hence x + 15% x = $45,000
Solve for x to find x = $39,130
correct answer D)$39,130
Answer: D
Question: The marks of 10 students of a class are 46,51,62,70,35,x,50,83,65,52. If the average marks is 55, find x.
Options:
A)36
B)34
C)42
D)46
E)52
Rationale: Average =( 46+51+62+70+35+x+50+83+65+52 )/10 = 55 Therefore x = 550- 514 =36 Answer : A
Answer: A
Question: The population of a town increases 20% and 25% respectively in two consecutive years. After the growth the present population of the town is 1500. Then what is the population of the town 2 years ago?
Options:
A)A)1000
B)B)1100
C)C)1200
D)D)1300
E)E)1400
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1500 * 100/120 * 100/125 = 1000
Answer: Option A
Answer: A
Question: If 21!/3^x is an integer, what is the greatest possible value of x?
Options:
A)3
B)4
C)5
D)D
E)7
Rationale: 21 - 7 *3
18 - 3*3*2
15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^9 is allowed. IMO D.
Answer: D
Question: Max bungee jumps from the top of a building straight to the ground at a constant speed. 5 seconds after he starts plummeting he passes the 10th floor. 10 seconds after he starts plummeting he passes the 5th floor. Each floor is 5 meters high. What is Mr. Wayne's speed in meters per second?
Options:
A)5
B)6
C)10
D)15
E)12
Rationale: 10 Floors * 5 Meter/Floor = 50 Meters
Time= 10 sec
Rate * 10 = 50
Rate= 50/10
=5
Answer is A
Answer: A
Question: In how many different number of ways 7 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)200
B)210
C)230
D)250
E)15120
Rationale: 9p5 = 9 X 8 X 7 Ã— 6 Ã— 5 = 15120
E)
Answer: E
Question: 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?
Options:
A)65 liters
B)88 liters
C)10 liters water
D)45 liters
E)8 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 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. Answer: C
Answer: C
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B?
Options:
A)17 years
B)19 years
C)29 years
D)8 years
E)12 years
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
5x = 20 => x = 4
Hence, B's age = 2x = 8 years.
Answer: D
Answer: D
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 5 percent, but profits were 10 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Options:
A)80%
B)105%
C)120%
D)124.2%
E)95%
Rationale: the profit 0f 2009 interms of 2008 = 0.95*10/10*100=95%
E
Answer: E
Question: A person can swim in still water at 10 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 12 km?
Options:
A)2
B)7
C)5
D)9
E)6
Rationale: M = 10
S = 4
US =10 - 4 = 6
D = 12
T = 12/6 = 2
Answer: A
Answer: A
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Options:
A)6620
B)9278
C)2782
D)5772
E)5286
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: A
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
Options:
A)1/4
B)1/6
C)7/12
D)5/36
E)11/36
Rationale: n(S)36
n(E)=5
P(E)=5/36
ANSWER D 5/36
Answer: D
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 38 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)2
B)4
C)8
D)12
E)32
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 38 + 40 + 10 - (12) - 2x
x = 8
So, answer will be C
Answer: C
Question: The set X = {10,11,12,13,14}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
Options:
A)7/20
B)3/20
C)7/10
D)3/10
E)3/5
Rationale: The total number of x and y pairs is 5*4=20.
There are six pairs such that x / y is an integer.
The probability that x / y is an integer is 6/20=3/10.
The answer is D.
Answer: D
Question: The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?
Options:
A)7 and 12
B)8 and 12
C)9 and 12
D)10 and 12
E)None of these
Rationale: Let x and y be the two numbers such that x is larger than y. The statement "the larger number is four less than twice the smaller number" may be formulated by
x = 2y - 4
We use the sum of the two numbers to write a second equation.
x + y = 20
Substitute x by 2y - 4 in x + y = 20 to obtain
2y - 4 + y = 20
Solve for y to find
y = 8 and x = 2y - 4 = 12
Answer B
Answer: B
Question: Average between two sets of numbers is closer to the set with morenumbers?
Options:
A)70
B)80
C)85
D)90
E)95
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: B
Question: A can finish a work in 12days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
Options:
A)10days
B)12days
C)6days
D)7days
E)5days
Rationale: B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/24 work is done by A in 1day
5/12 work is done by A in 12*5/12 = 5days
Answer is E
Answer: E
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
Options:
A)29777
B)37500
C)27889
D)2776
E)29971
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)
(9x + 1100000 - 11x)/100 = 39000/4 = 9750
x = 62500
Sum invested at 9% = Rs. 62500
Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.
Answer: B
Answer: B
Question: If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
Options:
A)16 2/3%
B)16 2/8%
C)16 2/1%
D)16 1/3%
E)16 2/7%
Rationale: Let the price of the article be Rs. 100.
20% of 100 = 20.
New price = 100 + 20 = Rs. 120
Required percentage = (120 - 100)/120 * 100
= 20/120 * 100 = 50/3 = 16 2/3%.
Answer:A
Answer: A
Question: The average of 25 results is 8. The average of first 12 of them is 14 and that of last 12 is 17. Find the 13 result?
Options:
A)52
B)68
C)78
D)92
E)65
Rationale: 13th result = sum of 25results - sum of 24 results
18*25-14*12+17*12 = 78
Answer is D
Answer: D
Question: How many integers between 300 and 1400 are there such that their unit digit is odd?
Options:
A)350
B)450
C)550
D)650
E)750
Rationale: There are 1100 numbers from 301 to 1400 (inclusive).
Half of the numbers are odd, so there are 550 odd numbers.
The answer is C.
Answer: C
Question: Caleb spends $64.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
Options:
A)29
B)10
C)20
D)40
E)45
Rationale: Solution -
Lets say, Single hamburgersxand Double hamburgersy
Given that,
x+y=50 and 1x+1.5y=64.50. By solving the equations y=29. ANS A.
Answer: A
Question: 5b2 is a three-digit number with b as a missing digit. If the number is divisible by 6, the missing digit is:
Options:
A)2
B)3
C)6
D)7
E)8
Rationale: Let the number be 5b2. Clearly, it is divisible by 2.
Now, 5+b+2= (7+b) must be divisible by 3. So, b= 2.
ANSWER:A
Answer: A
Question: The average salary of 16 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?
Options:
A) $18,714
B) $18,500
C) $18,000
D) $15,850
E) $12,300
Rationale: total salary... 16*20k=320k
5 emp @ 25k =125k
4 emp @ 16k =64k
remaing 7 emp sal = 320k-125k-64k =131k
average=131k/7 = 18714
Ans :A
Answer: A
Question: If 314,314 bottles of water need to be placed in boxes and each box can contain at most 9 bottles of water. How many bottles of water will be in the last unfilled box?
Options:
A)4
B)5
C)6
D)7
E)10
Rationale: The number of bottles of water that can be placed in boxes of 9 bottles is the first number that is divisible by 9 that occurs before 314,314.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 314,314 = 16 and 9 is divisible by 9.
Hence, we need to remove 7 to this number for it to be divisible by 9
Correct Option: D
Answer: D
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
Options:
A)166
B)105
C)178
D)177
E)169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: B
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 460?
Options:
A)18%
B)21%
C)25.9%
D)19%
E)None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 460, Discount = 621 - 460 = 161
Discount % = 161/621 * 100 = 25.9%
ANSWER:C
Answer: C
Question: The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.
Options:
A)40 yrs
B)42 yrs
C)45 yrs
D)46 yrs
E)47 yrs
Rationale: The average age of 30 boys of a class is equal to 14 yrs:
i.e Sum of all boys:30*14
include class teacher:31 candidates in a class
& avg age is:15 yr
i.e. sum of all:31*15(include class teacher)=465
so,the age of the class teacher:465-420=45yr
answer will be 45 yrs
ANSWER:C
Answer: C
Question: In how many years, Rs. 150 will produce the same interest at 6% as Rs. 400 produce in 2 years at 4½% ?
Options:
A)4 years
B)6 years
C)8 years
D)9 years
E)12 years
Rationale: Explanation :
Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.400 at 4½ % for 2 years
150×6×n/100=400×9/2×2/100
150×6×n=400×9/2×2
150×6×n=400×9
n=4 years
Answer : Option A
Answer: A
Question: If P = k^3 – k, where k and P are positive integers, and k is given by the expression k=(10x)n+54k=(10x)n+54, where x and n are positive integers, then what is the remainder when P is divided by 4 ?
Options:
A)0
B)1
C)2
D)3
E)cannot be determined
Rationale: p=k^3-k
=k(k^2-1)
=(k-1)k(k+1)
as can be seen, p is a product of three consecutive integers. now k can be both even and odd.
now look into the given expression of k
k=(10x)n+54k=(10x)n+54
5454 will always be odd. and (10x)n(10x)n will always be even
thus k= even + odd =odd
Also, k =1 is not possible ( because p is a positive integer)
so lets try k=3
p=(3-1)(3)(3+1)
=2*3*4
ANSWER:A
Answer: A
Question: If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?
Options:
A)40
B)60
C)100
D)140
E)160
Rationale: Explanation:
Let’s say t = total current inventory of chairs. The first sentence states that 50 + t = (3/2)t. First solve for the current inventory:
50 + t = (3/2)t
50 = (3/2)t − t
50 = (1/2)t
100 = t
The manager wants to increase this by 40%.
40% of 100 is 40, so the new inventory will be 140.
Answer: (D).
Answer: D
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent Q of the distribution is less than m +d ?
Options:
A)16%
B)32%
C)48%
D)84%
E)92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, Q=(68+16)% or (100-16)% of the population is less than m+d.
Answer: D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?
Options:
A)76
B)100
C)27
D)80
E)25
Rationale: 1/2 * d (8+ 6) = 700
d = 100
Answer: B
Answer: B
Question: Given 3^n, for any real integer of n, which of the following is a possible resultant?
Options:
A)242
B)244
C)243
D)254
E)245
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.
Cycle of 4, the answer with last digit 3.
Answer: C
Answer: C
Question: Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 8, when a # b = 100?
Options:
A)5
B)8
C)10
D)13
E)17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 8 = 10/2 + 8 = 13.
The correct answer is D
Answer: D
Question: How many odd three-digit integers greater than 700 are there such that all their digits are different?
Options:
A)40
B)56
C)72
D)80
E)104
Rationale: 2 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 144
Now take numbers in the range 700 - 900.
Total numbers where all digits are different = 144 (as before)
[highlight]Number of odd numbers = 2 * 8 * 5 = 80[/highlight] (now there are 5 possibilities for the unit's digit)
D
Answer: D
Question: The vertex of a rectangle are (1, 0), (9, 0), (1, 2) and (9, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
Options:
A)5
B)4
C)1/2
D)1/5
E)1/8
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 1). The slope of a line passing through (0,0) and (5, 1) is 1/5.
The answer is D.
Answer: D
Question: The months of the calendar have been coded in the following ways:
January = 1071
February = 682
March = 1353
April = 154
May = 1335
June = 1046
July = 1047
August = 168
Using the same coding method, can you find out how to code September
Options:
A)19|9|9
B)19|9|8
C)19|9|7
D)19|9|6
E)19|9|5
Rationale: Solution:
19|9|9
Explanation:
This is simple. All the months have been coded with a distinctive way.
Let's see about January:
January = 1071 = 10|7|1
10 is the position of J, the first letter of January in alphabetical order.
7 is the number of letters used in forming the word January.
1 is the position of January in the calendar.
For February:
February = 682 = 6|8|2
6 is the position of F, the first letter of February in the alphabetical order.
8 are the number of letters used in forming the word.
2 is the position of February in the calendar.
Similarly, September = 19|9|9
19 is the position of S, the first letter of September in the alphabetical order.
9 are the number of letters used in forming the word.
9 is the position of September in the calendar.
Answer A
Answer: A
Question: The price of a certain painting increased by 10% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
Options:
A)102%
B)105%
C)95%
D)93.5%
E)90%
Rationale: Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 10 = 110
Price at the end of year 2 = 110 - 110*0.15 = 110*0.85 = 93.5
Hence required answer = (93.5/100)*100% = 93.5%
Answer is D.
Answer: D
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Options:
A)1877 ways
B)1440 ways
C)1678 ways
D)1976 ways
E)1286 ways
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: B
Question: total 52 matches are conducted in Knockout match type. How many players will be participated in that tournament?
Options:
A)60
B)51
C)53
D)56
E)50
Rationale: 51 players
ANSWER:B
Answer: B
Question: The sum of three numbers is 343. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
Options:
A)20
B)30
C)38
D)105
E)None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 343
or 49x = 343 or x = 7
⇒ Second number = 15x = 15 × 7 = 105
Answer D
Answer: D
Question: Pipes A and B can fill a tank in 8 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
Options:
A)1 13/17 hours
B)2 8/11 hours
C)3 9/17 hours
D)4 4/5 hours
E)None
Rationale: Solution
Net part filled in 1 hour	= (1/8 + 1/6 -1/12)
= 5/24.
Therefore, the tank will be full in 24/5 hrs.	â€¹=â€º 4 4/5 hrs.
Answer D
Answer: D
Question: WHEN A PERSON SELLS TWO ITEMS $1300 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
Options:
A)no loss no gain
B)2% gain
C)5% gain
D)4% loss
E)1% loss
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : D
Answer: D
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 30 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
A)64%
B)66%
C)72%
D)76%
E)80%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*130/100 = 78
In june Total income = 78+ 40 = 118
% of Mrs Lee's income = 72/112 =66.10
(B)
Answer: B
Question: If you roll 2 dice, what is the probability of rolling a 5?
Options:
A)1/9
B)1/12
C)1/3
D)5/12
E)2/13
Rationale: The answer is 1/9, as there are 4/36 ways to add the sum of 5 with 2 dice. Answer: A
Answer: A
Question: There are 12 red balls, 10 blue balls, 12 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
Options:
A)10
B)23
C)43
D)40
E)16
Rationale: The worst case scenario would be if we pick 11 red balls, 9 blue balls, 11 (?) balls and 8 black balls. In this case we'll have 11+9+11+8=39 balls and still won't have all the balls of one color. The next 40rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: D
Answer: D
Question: Two poles of height 6 meters and 11 meters stand on a plane ground. If the distance between their feet is 12 meters then find the difference in the distance between their tops:
Options:
A)12m
B)5m
C)13m
D)11m
E)12m
Rationale: distance between their tops = sqrt( 12^2+(11-6)^2) = sqrt 169=13m
ANSWER:C
Answer: C