divelab/Sys2Bench huggingface dataset:
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 1:2 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
Options:
A)1:1
B)2:1
C)3:1
D)5:1
E)6:1
Rationale: Vessel A = 300 gallons --> milk = 100, water = 200;
Vessel B = 500 gallons --> milk = 300, water = 200;
Vessel A + B = 800 gallons --> milk = 400, water 400
The ratio =400/400 --> 1:1
Answer: A
Answer: A
Question: A can finish a work in 24 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Options:
A)6
B)5
C)5.5
D)7
E)8
Rationale: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
24
Therefore 1 work is done by A in ( 24 x 1 ) = 8 days.
E
Answer: E
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 70 and n is not prime, what is the greatest possible value of f(n)?
Options:
A)68
B)65
C)62
D)60
E)55
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 68 = 2*2*17. This is not a product of distinct prime numbers. Hence incorrect
Option B: 65 = 5*13. This is a product of distinct prime numbers.
Rest all the options are smaller that 65.
Correct Option: B
Answer: B
Question: In an election between two candidates first candidate got 20% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
Options:
A)3500 votes
B)4000 votes
C)4500 votes
D)9800 votes
E)9900 votes
Rationale: Total = 100 %,
First person got 20%
second person got remaining 80 % of votes.
than 80 % = 2800
80% = 80Ã—35 = 2800
100% =100Ã—35 =3500 votes
A
Answer: A
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.27000. A's share is?
Options:
A)9000
B)2778
C)6000
D)2889
E)6612
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 27000 = 9000
Answer:A
Answer: A
Question: Mary invested a certain sum of money in a bank that paid simple interest. The amount grew to $260 at the end of 2 years. She waited for another 3 years and got a final amount of $350. What was the principal amount that she invested at the beginning?
Options:
A)$220
B)$230
C)$240
D)$200
E)$250
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $260
At the end of 5 years, Amount = $350
This means she earned an interest of $90 in 3 years. Or $30 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $60 in 2 years.
Hence Principal Amount = $260 - $60 = $200 Option D
Answer: D
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
7 ~ 2 ~ 7 ~ 4 = ____
Options:
A)2418
B)2910
C)2940
D)3749
E)4470
Rationale: A
2418
2418
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418
Thus 2418 is the missing number.
Answer: A
Question: A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
Options:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
Rationale: A Zayn's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y
1997- x1---- y1-- x1+y1
x1= a*x .....(P)
y1= 1.07*y...(Q)
x1+y1/x+y = 1.01
solve using P and Q and find x/y
Answer: A
Question: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,200. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
Options:
A)850
B)1,600
C)1,700
D)2,550
E)3,400
Rationale: Assume the cost of the least sized (26 Inch) TV = x
Cost of 28 inches TV = x + 200
Cost of 30 inches TV = x + 400
Cost of 32 inches TV = x + 600
Total cost = 4x + 1200 = 3200
Therefore x = 2000/4 = 500
Price of 28inch + 30 inch = 700 + 900 = 1600
Option B
Answer: B
Question: If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^2+b is an even number. 2. ab is even number 3. (a + b) is always an odd number.
Options:
A)II only
B)III only
C)I,II only
D)I only
E)I,III only
Rationale: 1^2+2 = 1+2 =3
So Option I false.
odd*even = even. Option II is true
odd + even = odd. Option III is true
Answer : D
Answer: D
Question: In a class, there are 27 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
Options:
A)6
B)12
C)18
D)24
E)26
Rationale: Explanation:
Let the number of boys be x. Then, (3/4)x = 27 or x = 27 x(4/3) = 36.
If total number of students is y, then (2/3) y = 36 or y = 36 x (3/2) = 54.
Therefore Number of girls in the class = (54 - 36) = 18.
Answer: C
Answer: C
Question: The difference between simple and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is?
Options:
A)Rs.7
B)Rs.3
C)Rs.8
D)Rs.1
E)Rs.4
Rationale: S.I. = (1200 * 10 * 1)/100
= Rs. 120
C.I. = [1200 * (1 + 5/100)2 - 1200]
= Rs. 123 Difference = (123 - 120)
= Rs. 3.
Answer:B
Answer: B
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
Options:
A)5 days
B)3 days
C)2 days
D)9 days
E)10 days
Rationale: Answer: Option A
2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: A
Question: The S.I. on a certain sum of money for 6 years at 14% per annum is half the C.I. on Rs. 7000 for 2 years at 7% per annum. The sum placed on S.I. is?
Options:
A)603.75
B)555.75
C)569.55
D)256.25
E)563.23
Rationale: C.I. = [7000 * (1 + 7/100)2 - 7000]= (7000 * 11/10 * 11/10 - 7000) = Rs. 1014.3.Sum = (507.15 * 100)/(6 * 14)= Rs.603.75Answer:A
Answer: A
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)Rs.1678
B)Rs.1640
C)Rs.2341
D)Rs.3041
E)None of these
Rationale: Explanation:
(x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 â€“ 1025 = 1640
ANSWER IS B
Answer: B
Question: What is the difference between the largest number and the least number written with the digits 5, 3, 1, 4?
Options:
A)6084
B)3788
C)4086
D)2721
E)1812
Rationale: Explanation:
1345
5431
------------
4086
Answer:C
Answer: C
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)38028
B)38000
C)32977
D)38128
E)38982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100)
= 38000
Answer:B
Answer: B
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter Q of liquid A was contained by the can initially?
Options:
A)10
B)20
C)21
D)25
E)27
Rationale: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total
If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4
Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4
Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.
Hence C is the correct answer.
A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.
Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) Q= 7*3 = 21.C
Answer: C
Question: In a school of 850 boys, 40% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
A)A)125
B)B)627
C)C)187
D)D)721
E)E)159
Rationale: 40 + 28 + 10 = 78%
100 – 78 = 22%
850 * 22/100 = 187
Answer:C
Answer: C
Question: If the area of circle is 440 sq cm then its circumference?
Options:
A)74.2
B)88
C)99
D)266
E)12
Rationale: 22/7 r2 = 440 => r = 11.8
2 * 22/7 * 11.8 = 74.2 Answer: A
Answer: A
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)Rs.1261
B)Rs.9261
C)Rs.9621
D)Rs.9162
E)Rs.9100
Rationale: Explanation:
A = 8000(21/20)3 = 9261
ANSWER IS B
Answer: B
Question: If 'A' runs faster than ‘E’ but not as fast as 'D' and 'D' runs faster than 'C' but not as fast as' ‘B’, then the person who runs the fastest is
Options:
A)A
B)B
C)C
D)D
E)E
Rationale: B is the fastest
ANSWER:B
Answer: B
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
Options:
A)890 km
B)390 km
C)890 km
D)990 km
E)380 km
Rationale: The total distance covered by the car in the first 10 hours
= 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48
= sum of 10 terms in AP whose first term is 30 and last term is 48
= 10/2 [30 + 48] = 390 km.
Answer:B
Answer: B
Question: The arithmetic mean of the 3 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s +1?
Options:
A)2 + s + a
B)22 + a
C)2s
D)2a + 2
E)5 + a
Rationale: (3s+3)/5=s+1=a
(9s+54)/9=s+6=5+a
E
Answer: E
Question: Solve the quickfire maths brain teaser âˆš36% = ?
Options:
A)30%
B)40%
C)60%
D)19%
E)29%
Rationale: âˆš36%
=> âˆš36/âˆš100
=> 6/10
=> 60/100
=> 60%
C
Answer: C
Question: Find 4consecutive even integers so that the sum of the 1st two added to twice the sum of the last 2 is equal to 742.
Options:
A)340
B)540
C)742
D)780
E)870
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 742 is written as
x + (x + 2) + 4 x + 20 = 742
Solve for x and find all four numbers
x = 120 , x + 2 = 122 , x + 4 = 124 , x + 6 = 126
As an exrcise, check that the sum of the first two added to twice the sum of the last two is equal to 742
C
Answer: C
Question: The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 2x 3x
8x cube + 27x cube = 945
35x cube = 945
x cube = 27 => x = 3
Answer: A
Answer: A
Question: A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
Options:
A)15
B)30
C)28
D)24
E)32
Rationale: number of workers = 10* (25-10)/10 = 15
Answer is A
Answer: A
Question: A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
Options:
A)6/25
B)5/16
C)4/9
D)3/7
E)2/5
Rationale: Let x be the fraction of her take-home pay that the worker saved.
Let P be the monthly pay.
12xP = 8(1-x)P
12xP = 8P - 8xP
20xP = 8P
x = 2/5
The answer is E.
Answer: E
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
Options:
A)3388
B)2788
C)1500
D)2792
E)7791
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500'
Answer:C
Answer: C
Question: A and B invests Rs.5000 and Rs.6000 in a business. After 6 months, A withdraws two-fifth of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)3:5
B)7:8
C)5:6
D)3:4
E)7:9
Rationale: A : B
(5000*6)+(3000*6) : (6000*8)+(4000*4)
48000 : 64000
3 : 4
Answer: D
Answer: D
Question: A certain car uses 12 gallons of gasoline in traveling 300 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
A)2
B)4
C)5
D)8
E)10
Rationale: 300/10 = 30. The difference is 30 - 25 = 5.
Answer C
Answer: C
Question: How many 13-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234567654321.
Options:
A)100
B)610
C)729
D)900
E)9000000
Rationale: Take the task of building palindromes and break it intostages.
Stage 1: Select the 13th digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in9ways
Stage 2: Select the 12th 11th 10th, 9th, 8th, 7th,
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
IMPORTANT: At this point, the remaining digits are alreadylocked in.
Stage 3: Select the 6th, 5th, 4th, 3rd, 2nd, 1st digit
So, we can complete this stage in1way.
By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 13-digit palindrome) in(9)(10)(10)(10)(10)(10)(10)(1)(1)(1)(1)(1)(1)ways (= 9000000 ways)
Answer: E
Answer: E
Question: There are 15 students in a class. For a competition Teacher wants only 10 students to need to join it.What is the possible combinations are there?
Options:
A)230
B)275
C)300
D)235
E)273
Rationale: The question is out of 15 students, 10 students to be need.
15C10=15!/10!*5!=15*14*13*12*11*10!/10!*5*4*3*2*1=273
Option E is answer
Answer: E
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/9
B)5/2
C)5/1
D)5/6
E)5/3
Rationale: Explanation:
P(at least one graduate) = 1 - P(no graduates) =
1 - â¶Câ‚ƒ/Â¹â°Câ‚ƒ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6
Answer:D
Answer: D
Question: Which of the following is not a leap year?
Options:
A)1200
B)800
C)700
D)2000
E)1400
Rationale: Explanation:
Remember the leap year rule (Given in the formulas)
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.
800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc).
Hence 800,1200 and 2000 are leap years
700 is not a 4th century, but it is a century. Hence it is not a leap year
Answer: Option C
Answer: C
Question: How many seconds does Sandy take to cover a distance of 500 meters, if Sandy runs at a speed of 15 km/hr?
Options:
A)100
B)120
C)140
D)160
E)180
Rationale: 15 km/hr = 15000 m / 3600 s = (150 / 36) m/s = (25 / 6) m/s
time = 500 / (25/6) = 120 seconds
The answer is B.
Answer: B
Question: There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
Options:
A)22
B)38
C)32
D)60
E)28
Rationale: Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
Answer: D
Answer: D
Question: 1, ? , 9,7,7,9,1310,9,1,4,9,16,16,.... what comes in ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 1,4,9,7,7,9,13,10,9,1,4,9,16,16,....
ANSWER:B
Answer: B
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)Rs.720
B)Rs.920
C)Rs.537
D)Rs.540
E)Rs.637
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer:D
Answer: D
Question: A woman borrowed some amount, after 3 years he paid Rs.10,400/- with 10% interest, then how much Amount she borrowed?
Options:
A)Rs.7000/-
B)Rs.8000/-
C)Rs.8800/-
D)Rs.8900/-
E)Rs.9000/-
Rationale: principal P = ?
Rate of interest R = 10%
Time T = 3 years
Accumulated Amount A = Rs.10400/-
A = P + I
A = P + PTR/100
A = P(1+ TR/100)
Rs.10400/- = P [1 + 3*10/100]
Rs.10400/- = P [1/1 + 3/10]
Rs.10400/- = P [10+3/10] = P[13/10]
Rs.10400/- = P * 13/10
==> P = Rs.104000/13
==> P = Rs.8000/-
B
Answer: B
Question: Gasoline varies in cost from $0.97 to $1.17 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
Options:
A)$15.07
B)$15.23
C)$15.50
D)$15.70
E)$15.72
Rationale: Solution:
We know that the per gallon cost of gasoline varies from $0.97 - $1.17.
Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.
Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.
So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).
Case 1: for 30 gallons the cost is 30*0.97 to 30*1.17 which is $29.10 to $35.10
Case 2: for 20 gallons the cost is 20*0.97 to 20*1.17 which is $19.40 to $23.40
Thus, the maximum cost of the 480 mile trip is $35.10 and minimum is $19.40
so the difference is $35.10 - $19.40 = $15.70
Answer: D
Answer: D
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Options:
A)456
B)744
C)912
D)1200
E)1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
ANSWER:B
Answer: B
Question: . In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
Options:
A)3323
B)1000
C)2877
D)2992
E)7111
Rationale: 20 * 10 * 5 = 1000
Answer: B
Answer: B
Question: Find the distance covered by a man walking for 10min at a speed of 6km/hr?
Options:
A)1km
B)2km
C)3km
D)1.5km
E)4km
Rationale: Distance = 6*10/60 = 1km
Answer is A
Answer: A
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 320 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Options:
A)600
B)640
C)500
D)520
E)720
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 320) = 2 + 2(extra)
=> 2x - 640 = x => x = 640.
ANSWER:B
Answer: B
Question: Ramesh spends 40% of his monthly salary on food, 40% of the remaining on conveyance and clothes and saves 50% of the remaining amount. If his monthly salary is Rs.17,000, how much money does he save every month ?
Options:
A)3060
B)2787
C)2697
D)2671
E)1922
Rationale: Explanation:
Ramesh's monthly income = Rs.17,000
He spends 40% on food.
The total money spent on food = 40/100 * 17000 = Rs. 6800
Now, his monthly remaining income = Rs.17000 – Rs.6800 = Rs. 10200
Out of Rs. 10200, he spends 40% on conveyance and clothes.
The total money spent on conveyance and clothes = 40/100 * 10200 = Rs. 4080
Now, his monthly remaining income = Rs.10200 – Rs.4080 = Rs. 6120
Out of Rs. 6120, he saves 50%.
Amount saved = 50/100 * 6120 = Rs. 3060
ANSWER:A
Answer: A
Question: A set S = {x, -8, -5, -2, 2, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
Options:
A)1
B)0
C)2
D)-1
E)Cannot be determined
Rationale: Median of the set = (-2+2)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +17-15 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer C
Answer: C
Question: Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 7n+1 or 7n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 7n+1 or 7n-1 is a prime number.
Options:
A)1,2,3
B)2,3
C)only 2
D)only 1
E)1,2
Rationale: Every prime number greater than 3 can be written in the form of 7n+1 or 7n-1 where n is an integer. So 1 can be possible.
3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 7n+1 or 7n-1.
E
Answer: E
Question: Find the value of y from (12)^1 x 6^4 ÷ 432 = y?
Options:
A)2134
B)2234
C)2540
D)2560
E)36
Rationale: 36
E
Answer: E
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 70 km/hr. When will he overtake the thief?
Options:
A)6:34 p.m
B)9:34 p.m
C)6:00 p.m
D)2:30 p.m
E)1:34 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 70(x - 1/2) => x = 7/2 hrs.
So, the thief is overtaken at 5:34 p.m.'
Answer: C
Answer: C
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 36, Find x and y ?
Options:
A)x=4,y=8
B)x=9,y=64
C)x=4,y=7
D)x=4,y=9
E)x=5,y=8
Rationale: 9+64=73
when reversed 37
73-37=36
x=9,y=64
ANSWER:B
Answer: B
Question: If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B)
Options:
A)1/2
B)2/3
C)3/2
D)4/5
E)4/7
Rationale: P(A|B) = P(A ∪ B)/P(B)
P(A|B) = (6/15)/(4/15) = 3/2.
C
Answer: C
Question: If 16% of 40% of a number is 8, then the number is
Options:
A)200
B)225
C)125
D)320
E)None of these
Rationale: Explanation:
Let 16/100×40/100×a=8
a = 8×100×100/16×40=125
Correct Option: C
Answer: C
Question: P and Q started a business investing Rs 60000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options:
A)7:5
B)17:3
C)4:1
D)17:7
E)5:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 60000:15000
= 60:15
= 4:1
Option C
Answer: C
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is?
Options:
A)24
B)26
C)28
D)30
E)None
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Option A
Answer: A
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)778
B)280
C)288
D)111
E)121
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: B