divelab/Sys2Bench huggingface dataset:
Question: Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?
Options:
A)23
B)24
C)25
D)26
E)27
Rationale: Explanation :
If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible
number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible
number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible
number of books = 15,19,23,27
Hence ,the common number is only 23 so it will be answer.
Answer : A
Answer: A
Question: Out of 15 students in a class, 7 are from Maharashtra, 5 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Options:
A)12/13
B)11/13
C)10/15
D)1/15
E)4/14
Rationale: Total possible ways of selecting 4students out of 15 = 15C4 = (15*14*13*12)/(4*3*2*1) =1365
The number of ways of selecting a 4 students in which no student belongs to Karnataka = 10C4
Number of ways of selecting atleast one student from Karnataka = 15C4-10C4 = 1155
Probability = 1155/1365 = 11/13
Answer is B
Answer: B
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
Options:
A)A)650
B)B)656
C)C)696
D)D)724
E)E)756
Rationale: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 men ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 woman ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 men and 2 women ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=
756
=21+210+525= 756
E)
Answer: E
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)7 months
B)3 months
C)5 months
D)8 months
E)10 months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER A
Answer: A
Question: The product of the squares of two positive integers is 400. How many pairs of positive integers satisfy this condition?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First break down 200 into 20*20 and further into the prime factors 2*2*5*2*2*5. Now we are looking for all the possible pairs (2 numbers) of squares whose product results in 400.
1st: 2^2*10^2 (i.e. the first two 2's and two times 2*5 = 10)
2nd: 4^2*5^2 (i.e. two times 2*2 = 4 = 4^2 and 5^2).
3rd: 1^2*20^2 (i.e. two times 2*2*5 and 1^2 = 1)
Answer D.
Answer: D
Question: (1/32)+(1/33)+……+(1/62)+(1/63) is including in which of the following ranges?
Options:
A)2
B)1
C)1/2~1
D)1/2
E)3
Rationale: Number of terms in the given series = 32.
The lowest term is 1/63 , the largest being 1/32.
Thus, the sum of the given series will be more than
1/63 + 1/63.....1/63 (32 times)
---> 32*(1/63) = 32/63
less than 1/32 + 1/32...... 1/32 (32 times)
---> 32*(1/32) = 32/32 = 1 (approx)
C is thus the correct answer.
Answer: C
Question: The average of 11 numbers is 50. If the average of first 6 numbers is 49 and that of last 6 is 52.Find the 6th number.
Options:
A)54
B)55
C)56
D)57
E)58
Rationale: avg = 50 so total sum of 11 numbers = 550
let 6th number is x, so according to the given condition
sum of first 5 numbers = 49*6 - x = 294 - x
sum of last 5 numbers = 52*6 - x = 312 - x
so 6th number x = 550 - (294 - x) - (312 - x) = 2x - 56
so x = 2x - 56 implies x = 56
ANSWER:C
Answer: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)786sq.units
C)167sq.units
D)178sq.units
E)176sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer:A
Answer: A
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 60 per cent larger than the original. By what percentage has the area of the logo increased?
Options:
A)50
B)80
C)100
D)143.36
E)250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 6.24 , so radius is 3.12
New area = 9.7344π
Increase in area is 5.7344π
% increase in area = 5.7344/4*100
So, % increase is 143.36%
Answer will be (D)
Answer: D
Question: At a dinner party 6 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
Options:
A)5
B)10
C)24
D)32
E)120
Rationale: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
6!/6=120
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
E
Answer: E
Question: If x, y, and z are all factors of 45, which of the following must be true?
Options:
A)The product xyz > 45
B)Either x = y, y = z, or x = z
C)x – y – z = even
D)The product xyz is odd
E)yz/x is an integer
Rationale: All the factors of 45 are odd numbers.
The product of odd numbers is odd.
The answer is D.
Answer: D
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 60 percent on clothing, 20 percent on food, and 20 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A)10
B)20
C)30
D)25
E)15
Rationale: Assume she has $200 to spend.
TAX
Clothing = 60% = $120= $12.00
Food = 20% = $ 40 = $0.00
Items = 20% = $ 40 = $ 8.00
Total tax = $20.00
% of total amount = 20/200 * 100 = 10%
Answer A
Answer: A
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)80
C)100
D)415
E)150
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Anawer is A
Answer: A
Question: A,B,C invested the capitals in a business. If A invested Rs. 10,000 more than B and C invested Rs.20,000 more than A, then how should a profit of Rs.14,000 be divided among A,B and C? Given : Capital of B is Rs.10,000
Options:
A)2000,1000,3000
B)1000,3000,4000
C)3000,2000,5000
D)4000,2000,8000
E)4000,3000,8000
Rationale: A==20,000
B==10,000
C==40,000
so, ration are 2:1:4
profit 14000
so,, 14000/7==2000
so,, A==4000, B==2000,, C==8000
ANSWER:D
Answer: D
Question: he time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)35 kmph
B)28 kmph
C)14 kmph
D)88 kmph
E)12 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph. Answer: C
Answer: C
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,300. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
Options:
A)1. $15,600
B)2. $15,750
C)3. $16,820
D)4. $18,300
E)5. $19,200
Rationale: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 6,300, thus the highest price in June was 16,500+6,300=22,800.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 22,800, thus the range for May-June is 22,800-4,500=18,300.
Answer: D.
Answer: D
Question: Find the missing figures :
?% of 40 = 2.125
Options:
A)5.31
B)6.51
C)8.71
D)7.71
E)4.51
Rationale: (i)	Let x% of 40 = 2.125. Then , (x/100)*40 = 2.125
X = (2.125 * 100/40) = 5.31
Answer is A.
Answer: A
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Options:
A)6
B)7
C)8
D)9
E)4
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6 Answer: A
Answer: A
Question: The average weight of 60 men sitting in a plane had some value. A new person added to them whose weight was 100 kg only. Due to his arrival, the average weight of all the men decreased by 20 kg. Find the average weight of first 25 men?
Options:
A)1203
B)1302
C)1300
D)1320
E)1301
Rationale: 60x + 100 = 61(x â€“ 20)
x = 1320
D
Answer: D
Question: A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
Options:
A)Rs. 7000
B)Rs. 9000
C)Rs. 14000
D)Rs. 17000
E)Rs. 27000
Rationale: Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 12 * 2)/100 = 840
=> 30x/100 - 24x/100 =840
=> 6x/100 = 840
=> x = 14000.
ANSWER:C
Answer: C
Question: If x < y < z and y-x > 9, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
Options:
A)6
B)7
C)8
D)13
E)10
Rationale: We have:
1) x<y<z
2) y-x>9
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>9, the least value for y-x must be 11, the least value for x must be 2, and, thus, the least possible value for y must be 13 (y-2=11, y=13)
2<13<z, since z is odd, the least possible value for z is 15
z-x=15-2=13
Answer D
Answer: D
Question: A company decreased the price of its main product by 75%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
Options:
A)1.33
B)2.33
C)3.33
D)4.33
E)1.45
Rationale: For the total revenue to remain the same when the price is 3/4, the number of products sold must 3/4 times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/75% = 1.33
Answer : A
Answer: A
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)4/9
B)5/9
C)7/9
D)8/9
E)1/3
Rationale: Explanation:
Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9
ANSWER IS B
Answer: B
Question: Rs.6490 is divided so that 4 times the first share, six times the 2nd share and twice the third share amount to the same. What is the value of the first share?
Options:
A)s 6490
B)s1880
C)s1660
D)s1550
E)s1770
Rationale: A+B+C = 6490
4A = 6B = 2C = x
A:B:C = 1/4:1/6:1/2 = 3:2:6
3/11 * 6490 =Rs1770
Answer:E
Answer: E
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
Options:
A)8 days
B)10 days
C)12 days
D)14 days
E)None
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A)
Answer: A
Question: There are 10 books on a shelf: 4 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
Options:
A)31/90
B)3/10
C)1/3
D)4/7
E)28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 4 English books) and one book is Spanish (out of 3 Spanish books) i.e. 4C1*3C1
Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1
Case-3: One book is English (out of 4 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 4C1*2C1
Total favourable Outcomes = 4C1*3C1+3C1*2C1+4C1*2C1 = 12+6+8 = 26
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 26/45 = 4/7
D
Answer: D
Question: Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!.
Options:
A)468
B)469
C)470
D)467
E)471
Rationale: Let me give you one quick way to solve such questions.
3! = 6 => the answer must be of the form 106n106n
Only A and C have even powers. Hence B C E are out
Out of A and C only A's power is divisible by 3, hence C is out.
Hence A is the answer
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 1 sec to pass a telegraph post, then the length of the train is?
Options:
A)10
B)20
C)30
D)15
E)45
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 1 = 20 m.
Answer: Option B
Answer: B
Question: A shepherd had n goats in the year 2000. In 2001 the no. of goats increased by 40%. In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew up 30%. In 2004, he sold 10% goats and then he had only 34,398 goats. The percentage increase of the no. of goats in this duration was :
Options:
A)16.66%
B)14.66 percent
C)11.33%
D)20%
E)None
Rationale: Solution: There is no need of the number of goats given i.e. 34,398.
Initially, let there be 100 goats. Then
100 == 40% ↑==> 140 ==30%↓(declined to 70%)==> 98 ==30%↑ ==> 127.4 ==10%↓(sold)==> 114.66
Hence, % increase = 14.66% [As 100 becomes 114.66].
Answer: Option B
Answer: B
Question: If y exceeds x by 25%, then x is less than y by?
Options:
A)80%
B)9%
C)20%
D)24%
E)10%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer: C
Answer: C
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
Options:
A)2/21
B)3/31
C)4/17
D)3/19
E)probability=8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: E
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)10000
B)297
C)9279
D)2767
E)2676
Rationale: 100 * 100 = 10000
125 * 80 = 10000
Answer:A
Answer: A
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Options:
A)360
B)334
C)456
D)132
E)564
Rationale: Explanation:
The given digits are six.
The number of four digit numbers that can be formed using six digits is â¶Pâ‚„ = 6 * 5 * 4 * 3 = 360.
Answer: A
Answer: A
Question: The simple interest on a certain sum of money for 2 l/2 years at 12% per
annum is Rs. 40 less tban the simple interest on the same sum for 3 ½ years at 10% per annum. Find the sum.
Options:
A)Rs. 700.
B)Rs. 200.
C)Rs. 600.
D)Rs. 800.
E)Rs. 400.
Rationale: Let the sum be Rs. x
Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40
(7x/20)-(3x/10)=40
x = (40 * 20) = 800.
Hence, the sum is Rs. 800.
Answer is D.
Answer: D
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > YD
B)XB < YD
C)AX > XB
D)AX > CY
E)AX > AB
Rationale: A--X------B
C----Y----D
XB > YD.
Answer: A.
Answer: A
Question: Three houses of the same type were advertised to be let in a locality. Two men made separate applications for a house. What is the probability that each of them applied for the same house.
Options:
A)1/3
B)2/3
C)1/6
D)1/9
E)1/27
Rationale: Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3
Let us consider case where all 2 men choose House no 1
So for First men it will be 1/3,second men 1/3
So probability of selecting house no 1 is 1/3*1/3= 1/9
And since there are 3 such house so probability that each men select the same house is 3*1/9 or 1/3
Ans is A
Answer: A
Question: If 10% of 30% of 50% of a number is 90, then what is the number?
Options:
A)4000
B)6000
C)4400
D)4500
E)None of these
Rationale: Let the number be a
Given, 10/100 * 30/100 * 50/100 * a = 90
=> 1/10 * 3/10 * 1/2 * a = 90
=> a = 10 * 20 * 10 * 2 = 6000.
ANSWER:B
Answer: B
Question: The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit?
Options:
A)$3000
B)$1000
C)$2000
D)$5000
E)$6000
Rationale: C
$2000
Let C.P. be $x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000.
Answer: C
Question: A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes half an hour and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
Options:
A)1/4
B)1/3
C)2/5
D)5/4
E)3/8
Rationale: The rate of the basic system is 1 room/half hour = 2 rooms per hour
The rate of the advanced system is 1 room/1.5 hours = 2/3 of a room per hour
The combined rate is 8/3 rooms per hour.
The time to ventilate one room is 3/8 of an hour.
The answer is E.
Answer: E
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Options:
A)8
B)6
C)5
D)4
E)2
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6. For re. 1.
Toffees sold = 6 * 5/6 = 5
Answer: C
Answer: C
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 15,000 after 3 years at the same rate?
Options:
A)2372
B)2572
C)4542
D)4965
E)3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 15000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 15000 x 1 +	10 3	- 1
100
= Rs. 15000 x	331
1000
= 4965.
D
Answer: D
Question: Henry earns $120 a week from his job. His income increased and now makes $180 a week. What is the percent increase?
Options:
A)70%
B)60%
C)50%
D)40%
E)30%
Rationale: Increase = (60/120)*100 = (1/2)*100 = 50%.
C
Answer: C
Question: There are 5 blue pillow covers, 3 white pillow covers, and 9 green pillow covers in the wardrobe. What is the least number of pillow covers that you have to take out to make sure that you will have a matching pair?
Options:
A)4
B)3
C)12
D)6
E)9
Rationale: Since there are 3 colors, if you take 3 pillow covers, you could still have 1 pillow cover per color and not have a match.
Therefore, upon taking the 4th pillow cover, you will definitely have a match since the 4th pillow cover will form at least a pair with the 1st 3
So 3+1 = 4
Answer is A
Answer: A
Question: A 5-year investment note offers a 10% return on purchase, and a compounding 5% for each year after the first. If there is a $500 penalty for early redemption, and the note is redeemed for $6430 after the second year, what was the original purchase price?
Options:
A)$ 6,000
B)$ 6,048
C)$ 6,100
D)$ 6,150
E)$ 6,200
Rationale: Since the note was redeemed after 2 years, so a penalty of $500 has to be submitted. So the amount that is redeemed after 6430 is after the deduction of $500.
Hence the amount after being compounded is 6930.
Let the initial amount be P.
After the return, the amount becomes 1.1P.
Now use this 1.1P as the principle in the compound interest formula to get the amount 6930.
A=1.1P(1+5/100)A=1.1P(1+5/100)
where A=6930.
Therefore, use
6930=1.1P(1+5/100)6930=1.1P(1+5/100) to get P as $6000.
ANSWER:A
Answer: A
Question: x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: x, y, a, and b are positive integers of S. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E.
Answer: E
Question: The value of 51/4 * (125)0.25 is:
Options:
A)5
B)5(5)
C)5√5
D)√5
E)None
Rationale: Sol.
51/4 * (125)0.25 = 50.25 * (53)0.25 * 5(3*0.25) = 50.25 * 50.75
= 5(0.25 + 0.75) = 51=5.
Answer A
Answer: A
Question: Before leaving for his business trip, Chad asks his assistant to choose and pack three shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the shirts packed but the blue shirt will not?
Options:
A)3/7
B)4/7
C)5/14
D)11/28
E)15/56
Rationale: The total number of ways to choose 3 shirts from 8 is 8C3 = 56
The number of ways to choose a pink shirt plus 2 shirts from 6 is 6C2 = 15
P(a pink shirt but not a blue shirt) = 15/56
The answer is E.
Answer: E
Question: For which of the following does f(x)−f(y)=f(x−y) for all values of x and y?
Options:
A)f(a)=a^2
B)f(a)=a/2
C)f(a)=a+5
D)f(a)=2a−1
E)f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(x) = x^2 and f(y) = y^2
so L.H.S = x^2 - y^2
and R.H.S = (x-y)^2 ==> x^2 + y^2 -2xy.
so L.H.S not equal to R.H.S
with option 2. f(x) = x/2 and f(y) = y/2
L.H.S = x/2 - y/2 ==> 1/2(x-y)
R.H.S = (x-y)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: B
Question: In a group of 100 adults, 40 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
Options:
A)48
B)52
C)54
D)40
E)62
Rationale: 12 left-haded women compose 100-40=60% (or 3/5) of all women, so there are total of 5*12=60 women --> 100-60=40 men.
Answer: D.
Answer: D
Question: A man, a woman and a boy can together complete a piece of work in 4 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?
Options:
A)36days
B)32days
C)34days
D)42days
E)49days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/4
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 woman’s 1 day’s work = 1/4 – 2/9 = 1/36
Therefore, the woman alone can finish the work in 36 days.
Answer: Option A
Answer: A