divelab/Sys2Bench huggingface dataset:
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price W per glass on the second day?
Options:
A) $015
B) $0.20
C) $0.30
D) $0.40
E) $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D.
Answer: D
Question: If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq. m. If the length is creased by 1 m and breadth is decreased by 1m, then the area is decreased by 5 sq. m. The perimeter of the floor is:
Options:
A)27
B)35
C)40
D)49
E)38
Rationale: Let length = x meters and breadth = y meters.
Then,
(x + 1) (y + 1) - xy = 21
x + y = 20 Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦1
And, xy - [(x + 1) (y - 1)] = 5
x - y = 6 Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦Ã¢â‚¬Â¦..2
Solving (i) and (ii), we get : x = 13 and y = 7
So, length = 13 m and breadth = 7 m.
Perimeter = [2 (13 + 7)] m = 40 m.
answer : C
Answer: C
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)108%
B)120%
C)160%
D)101%
E)100%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? =>
100%
Answer: E
Answer: E
Question: A 6 litre sol is 35% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
Options:
A)A.0.6
B)B.1
C)C.2.1
D)D.1.8
E)E.5.4
Rationale: 35% of 6 = 2.1
50% of 6 = 3
shortage is 0.9
so we need to have 0.9/50% to get 50% alcohol content.
= 1.8 D
Answer: D
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
Options:
A)500
B)334
C)555
D)664
E)5598
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer: Option A
Answer: A
Question: How many squares are there on a chess board ???
Options:
A)208
B)204
C)201
D)205
E)202
Rationale: B
204
Total 204 squares is there on chess board, including all sizes.
Answer: B
Question: Find the average of the series :115,125,135,145,155 ?
Options:
A)129
B)135
C)267
D)207
E)174
Rationale: Average = (115+125+135+145+155)/5
= 675/5
= 135
Answer: B
Answer: B
Question: James took a 3-hour bike ride. In the second hour he travlled 24 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
Options:
A)74.0
B)54.9
C)55.5
D)57.0
E)63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 24 , x = 20. Now, the distance travelled in the 3rd hour = 24+1/4âˆ—24= 30.
= 24+20+30=74
ANSWER:A
Answer: A
Question: A sum of money place at compound interest doubles itself in 10 years. In how many years will it amount to eight times itself?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 100 ---- 200 ---- 10
400 ---- 10
800 ---- 10
------
12 years
Answer: B
Answer: B
Question: In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 240 votes. What was the total number of votes?
Options:
A)600
B)900
C)1200
D)1500
E)1800
Rationale: Let V be the total number of votes.
0.2V = 240
V = 1200
The answer is C.
Answer: C
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)10 2/5
B)10 2/0
C)10 2/3
D)10 2/1
E)10 2/3
Rationale: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3 Answer: C
Answer: C
Question: If q is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of q?
Options:
A)51
B)54
C)72
D)50!+2
E)162
Rationale: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: E.
Answer: E
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $35. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)180xy
B)180/(xy)
C)20xy
D)315/(xy)
E)xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 35 / (xy/9) = 315/(xy).
The answer is D.
Answer: D
Question: If x and b are integers and (15^x + 15^(x+1))/4^b = 15^b what is the value of x?
Options:
A)2
B)3
C)4
D)5
E)Cannot be determined
Rationale: \frac{15^x( 1+ 15)}{4^b} = 15^b
(15^x . 4^2 ) / 4^b = 15^b. 4^0
15^x . 4^(2-b) = 15^b. 4^0
Equating the powers, x = b; 2-b = 0; So x = b = 2=A
Answer: A
Question: Out of 6 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
Options:
A)1/15
B)10/13
C)21/15
D)15/21
E)2/21
Rationale: The number of exhaustive events = 6C2 = 15.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/15.
ANSWER:A
Answer: A
Question: What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5%
Options:
A)Rs. 2
B)Rs. 1.25
C)Rs. 2.25
D)Rs. 0.5
E)None of these
Rationale: Explanation :
F = Rs. 8100
R = 5%
T = 3 months = 1/4 years
BD = FTR/100 = (8100 × (1/4) × 5)/100 = 2025/20 = 405/4 = Rs. 101.25
TD = FTR/(100+TR) = (8100 × (1/4) × 5)/(100 + (1/4 × 5) = (2025 × 5)/(100+(5/4))
= (2025 × 5 × 4)/(400+5) = (2025 × 5 × 4)/405 = (405 × 5 × 4)/81 = (45 × 5 × 4)/9
= 5 × 5 × 4 = Rs. 100
BD - TD = Rs. 101.25 - Rs. 100 = Rs. 1.25 Answer : Option B
Answer: B
Question: A worker is paid a regular rate of Rs.30 for completing a survey. The worker completes 100 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 20% higher than her regular rate. If she completed 50 surveys involving the use of her cellphone, how much did she get that week?
Options:
A)2200
B)1100
C)2500
D)2800
E)3300
Rationale: Amount earned using her cell phone = 50 * 36 = 1800
earned for remaining surveys = 50 * 30 = 1500
Total earning = 3300
Answer :E
Answer: E
Question: There are 24 students in a class one of them who is 18 years old left the class and a new comer filled his place. If the avg age of the class was there by lowered by one month . The age of new comer is
Options:
A)14years
B)15years
C)16 years
D)17 years
E)18 years
Rationale: Let new comer age was x.
Average age decreased by = 1 month = 1/12 years.
You can use this formula for these type of problems.
No. of students in class* aged decreased = difference of replacement
24 * 1/12 = 18 - x
2 = 18 - x
x = 16 years.
Age of new comer age was 16 years.
Answer: Option C
Answer: C
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes.
Options:
A)$0.94
B)$0.96
C)$0.98
D)$1.00
E)$1.20
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.08 * 80
90x - 80 = 6.4
90x = 86.64
x = 86.64/90 = 87/90 (approx) = 29/30 = 0.966
x is slightly under 0.9666 = 0.96
Answer: B
Answer: B
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
Options:
A)1 1/8 days
B)1 1/2 days
C)3 1/2 days
D)1 1/5 days
E)1 5/2 days
Rationale: 3/20 * 2 + (2 + x)/5 = 1
x = 1 1/2 days
Answer:B
Answer: B
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Options:
A)5 : 3
B)2 : 6
C)5 : 6
D)6 : 4
E)2 : 5
Rationale: Let 40% of A =(2/3)B
Then,40A/100=2B/3
2A/5=2B/3
A/B =(2/3 x 5/2) = 5/3
A : B = 5 : 3.
ANSWER A
Answer: A
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.2030?
Options:
A)Rs.2000
B)Rs.1750
C)Rs.2010
D)Rs.2005
E)None of these
Rationale: Explanation:
2030 = P [1 + (5*16/5)/100]
P= 1750
Answer: Option B
Answer: B
Question: If the cost of 12 books is equal to the selling price of 10 books, the profit per cent in the transaction is
Options:
A)16 2/3%
B)18%
C)20%
D)25%
E)30%
Rationale: Let C.P. of 12 books = Rs 12
Therefore, S.P. of 10 books = Rs 12
C.P. of 10 books = Rs 10
Therefore, Profit = 20%
ANSWER:C
Answer: C
Question: For which of the following values of s is (40+s)/s an integer?
Options:
A)3
B)4
C)9
D)11
E)40
Rationale: This problem has to be solved by checking the options
(40 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A: 43/3 - Not an Integer
Option B:44/4 - Not an Integer
Option C: 49/9 - Not an integer
Option D: 51/11 - Not an integer
Option E - 80/40- Integer
Correct Option: E
Answer: E
Question: A basket contains one dozen flowers. 7 of the flowers are Roses, three are sunflowers, and two are jasmine. If two flowers are randomly selected from the basket, one after the other, what is the probability that both will be rose flower?
Options:
A)1/11
B)11/4
C)7/22
D)5/4
E)8/9
Rationale: Probability of getting the first Rose flower - 7/12
Probability of getting the second Rose flower - 6/11
total probability = 7/12*6/11 = 7/22
correct option C
Answer: C
Question: Tom and Jerry enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Tom received $800 more than Jerry did, what was the profit made by their business in that year?
Options:
A)3000
B)4000
C)5000
D)6900
E)6677
Rationale: Say the profit was $x.
Tom share = x/6 (half of the third) + (x-x/3)*0.7
Jerry share = x/6 (half of the third) + (x-x/3)*0.3
Thus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.
answer is A
Answer: A
Question: 5555 × 9999 = ?
Options:
A)55500005
B)55511115
C)55522225
D)55533335
E)55544445
Rationale: E
55544445
5555 × 9999 = 5555 ( 10000-1)
= 5555 × 10000 - 5555 × 1
= 55550000 - 5555
= 55544445
Answer: E
Question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)15 sec
B)16 sec
C)18 sec
D)20 sec
E)25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
ANSWER: D
Answer: D
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
A)12 days
B)15 days
C)16 days
D)18 days
E)none
Rationale: A's 2 day's work = (1/20 * 2) = 1/10
(A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 6/60 = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days.
Whole work will be done in (3 x 5) = 15 days.
Answer = B
Answer: B
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is
Options:
A)2 : 9
B)2 : 3
C)2 : 2
D)2 : 1
E)2 : 7
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.4) <=> k = 0.4/0.6 = 2/3.
Required ratio = 2/3 : 1 = 2 : 3.
Answer: B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Options:
A)24/455
B)3/91
C)12/455
D)15/91
E)None of these
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
ANSWER:C
Answer: C
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)6
B)8
C)9
D)5
E)2
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)30 km/hr
B)45 km/hr
C)60 km/hr
D)75 km/hr
E)85 km/hr
Rationale: Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
ANSWER IS C
Answer: C
Question: If a - b = 6 and a2 + b2 = 48, find the value of ab.
Options:
A)8
B)10
C)12
D)6
E)19
Rationale: 2ab = (a2 + b2) - (a - b)2
= 48 - 36 = 12
ab = 6.
Answer: D
Answer: D
Question: The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?
Options:
A)2000
B)3000
C)4000
D)5000
E)6000
Rationale: Explanation:
Let monthly income of A = a
monthly income of B = b
monthly income of C = c
a + b = 2 × 5050 .... (Equation 1)
b + c = 2 × 6250 .... (Equation 2)
a + c = 2 × 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
i.e., Monthly income of A = 4000
Answer: Option C
Answer: C
Question: Express the ratio 3 2/3 : 7 1/3 in its simplest form.
Options:
A)1:21
B)1:1
C)2:1
D)1:2
E)2:11
Rationale: Solution
We first convert the mixed numbers 3 2/3 and 7 1/3 into fractions
3 2/3 = 3*3 / 3 + 2 / 3 = 11 / 3
7 1/3 = 7*3 / 3 + 1 / 3 = 22 / 3
The ratio 3 2/3 : 7 1/3 can be expressed as
11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22
Simplify
= 11 / 22 = 1 / 2
The ratio is 1 / 2 or 1:2
ANSWER IS D
Answer: D
Question: If k is a positive integer, which of the following must be divisible by 27?
Options:
A) (k – 4)(k)(k + 3)(k + 7)
B) (k – 4)(k – 2)(k + 3)(k + 5)
C) (k – 2)(k + 3)(k + 5)(k + 6)
D) (k + 1)(k + 3)(k + 5)(k + 7)
E) (k – 3)(k + 1)(k + 4)(k + 6)
Rationale: 24=8*3.
Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.
Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.
So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.
Answer: E.
Answer: E
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 2.10 km and 1.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)99
B)277
C)84
D)96
E)22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 2.10 + 1.4 = 3.5 km = 3500 m.
Required time = 3500 * 3/125 = 84 sec.
Answer:C
Answer: C
Question: What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
Options:
A)0
B)2
C)3
D)5
E)7
Rationale: Explanation:
Unit digit in (6374)1793 = Unit digit in (4)1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
ANSWER IS A
Answer: A
Question: Last year a worker saved 10% of her annual salary. This year, she made 10% more money than last year and she saved 12% of her salary. The amount she saved this year was what percent of the amount she saved last year?
Options:
A)126%
B)128%
C)130%
D)132%
E)134%
Rationale: Let x be the worker's salary last year.
Last year, she saved 0.1x.
This year, she saved 0.12(1.1x)=0.132x
0.132x/0.1x=132%
The answer is D.
Answer: D
Question: Today is Thursday. The day after 59 days will be?
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)
= Sunday
Answer : Option D
Answer: D
Question: Father is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)20 years
B)21 years
C)22 years
D)28 years
E)25 years
Rationale: age consider as x
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
ANSWER C
Answer: C
Question: 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 24. What is half of that number?
Options:
A)670
B)750
C)945
D)375
E)315
Rationale: Let no. be x
4/15*5/7*x - 4/9*2/5*x =8
by further solving
20x/105- 8x/45=8
4x/315=24
x=1890
we have to find x/2
=1890/2=945
ANSWER:C
Answer: C
Question: If pq > 0, which of the following must be negative?
Options:
A)p/q
B)-p/q
C)-p/-q
D)-p * -q
E)pq
Rationale: Given pq> 0 So both will be the positive integers. If both are positive, then A,C,D,E also positive.
Answer :B
Answer: B
Question: The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along theboundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Options:
A)143530 m
B)145600 m
C)153600 m
D)134500 m
E)155600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: C
Question: A can give B 150 meters start and C 300 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12
B)111.67
C)111.64
D)111.11
E)176.47
Rationale: A runs 1000 m while B runs 850 m and C runs 700 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 700)/850 = 823.53 m.
B can give C = 1000 - 823.53= 176.47 m.
Answer:E
Answer: E
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)(2^96 + 1)
B)(2^16 + 1)
C)(2^95 + 1)
D)(2^95 - 1)
E)(2^75 + 1)
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
A)
Answer: A
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years?
Options:
A)14000
B)14400
C)14500
D)14600
E)14700
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 × 120/100 = 14400
B
Answer: B
Question: A=√[2√63 + 2/(8+3√7)] =
Options:
A)8 + 3√7
B)4 + 3√7
C)8
D)4
E)√7
Rationale: In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)
sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]
A=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4
Answer is 4.D
Answer: D
Question: A train 100 m long crosses a platform 180 m long in 14 sec; find the speed of the train?
Options:
A)72 kmph
B)58 kmph
C)54 kmph
D)94 kmph
E)59 kmph
Rationale: D = 100 + 180 = 280
T = 14
S = 280/14 * 18/5 =72 kmph
Answer:A
Answer: A
Question: As x increases from 169 to 155, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
Options:
A) I only
B) III only
C) I and II
D) I and III
E) II and III
Rationale: I. 2x - 5 --> x decreases from 169 to 155 --> 2x decreases --> 2x - 5 decreases.
II. 1 - 1/x --> x decreases from 169 to 155 --> 1/x increases --> 1 -1/x decreases.
III. 1/(x^2 - x) --> x decreases from 169 to 155 --> x^2-x decreases --> 1/(x^2 - x) increases.
Answer: B.
Answer: B
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
Options:
A)1500
B)1528
C)1298
D)1528
E)1282
Rationale: P = 15(100/10)2
=> P = 1500
Answer: A
Answer: A
Question: Suppose you flip a fair coin five times. What is the probability that, in five flips, you get at least one head?
Options:
A)27/32
B)25/32
C)17/32
D)15/32
E)31/32
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^5
probability of flipping at least 1 head = 1 - (1/2)^5 = 31/32
Answer : E
Answer: E
Question: What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?
Options:
A)10
B)11
C)12 number
D)13
E)14
Rationale: We describe 2 solutions. Let S = {1, 2, . . . , 9}. Observe that the sum of the elements of S
is divisible by 3. So the problem is the same as asking for the number of ways that 2 elements
of S can be chosen so that their sum is divisible by 3 (the other 7 elements of S correspond to a
7-element set as in the problem). Choosing 2 elements of S with sum divisible by 3 corresponds
to either choosing 2 numbers divisible by 3 (which can be done in 3 ways) or choosing 1 number
that is one more than a multiple of 3 and 1 number that is one less than a multiple of 3 (which can
be done in 3 · 3 = 9 ways). Hence, the answer is 3 + 9 = 12.
correct answer C
Answer: C
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
Options:
A)11%
B)25%
C)29%
D)55%
E)45%
Rationale: 900 --- 100
100 --- ? => 11.11%
Answer: A
Answer: A
Question: A bag holds 2 blue marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be blue?
Options:
A)1/12
B)1/10
C)3/10
D)2/5
E)1/2
Rationale: Given: 2B and 3 G marbles
Required: Probability that 2 marbles removed without replacement are both blue
Initially we have to pick one red from a total of 2 blue and 3 green marbles
After one blue has been picked, we need to pick 1 blue from a total of 1 blue and 3 green marbles.
P(Both blue) = (2/5)*(1/4) = 1/10
Option B
Answer: B
Question: If n is an integer greater than 6, which of the following must be divisible by 2?
Options:
A)1. n (n+1) (n-4)
B)2. n (n+2) (n-1)
C)3. n (n+3) (n-5)
D)4. n (n+4) (n-2)
E)5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
B
Answer: B