divelab/Sys2Bench huggingface dataset:
Question: On his drive to work, Leo listens to one of three radio stations A, B or Q. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to Q. If Q is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Options:
A)0.027
B)0.09
C)0.417
D)0.657
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to Q and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: D
Question: How many positive integers less than 250 are there such that they are multiples of 15 or multiples of 14?
Options:
A)30
B)31
C)32
D)33
E)34
Rationale: 250/15 = 16 (plus remainder) so there are 16 multiples of 15
250/14 = 17 (plus remainder) so there are 17 multiples of 14
We need to subtract 1 because 15*14 is a multiple of both so it was counted twice.
The total is 16+17-1 = 32
The answer is C.
Answer: C
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?
Options:
A)10
B)20
C)30
D)40
E)35
Rationale: Present age of elder = x
younger= x-16
(x-6)(x-16-6)
x-6-3x-66
2x=60
x=30
ANSWER C
Answer: C
Question: A certain machine produces 1,100 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 6 days?
Options:
A)7,000
B)24,000
C)40,000
D)100,000
E)158,400
Rationale: Since 6 days consist of 24*6 hours the total is 144 hours.
Since every hour the machine produces 1100 units of product P the total product during 144 hours is 144*1100=158,400.
Correct Option : E
Answer: E
Question: (x^n-a^n) is completely divisible by (x-a), when?
Options:
A)n is any natural number
B)n is an even natural number
C)n is an odd natural number
D)n is prime
E)None of these
Rationale: For every natural number n,(x^n-a^n) is always divisible by (x-a).
Correct Option: A
Answer: A
Question: Sachin is younger than Rahul by 8 years. If the ratio of their ages is 7:9, find the age of Sachin
Options:
A)24.58
B)24.5
C)26
D)27
E)28
Rationale: If Rahul age is x, then Sachin age is x-8,
so (x-8)/x = 7/9
=> 9x-72 = 7x
=> 2x = 72
=> x = 36
So Sachin age is 36-8 = 28
Answer: E
Answer: E
Question: When a certain shoe store reduces the price of its best-selling style of shoe by 20 percent, the weekly sales of this style increase by 10 percent. Which of the following best describes the resulting change in the store's weekly revenue from sales of this style of shoe?
Options:
A)Revenue decreases by 10%
B)Revenue decreases by 12%
C)There is no change in revenue
D)Revenue increases by 12%
E)Revenue increases by 10%
Rationale: Old price = 10, old sales = 10 --> old revenue = 100;
New price = 8, new sales = 11 --> new revenue = 88.
Revenue decreased by 12%.
Answer: B.
Answer: B
Question: Three rugs have a combined area of 196 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
Options:
A)15 square meters
B)20 square meters
C)24 square meters
D)28 square meters
E)30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 194 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 15.
Answer: A.
Answer: A
Question: saran purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
Options:
A)12.45
B)10.5
C)16.3
D)45.12
E)23
Rationale: C
C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.
S.P. per kg = 819/50 = Rs. 16.38 = 16.30.
Answer: C
Question: What is the next number of the following sequence
2,3,6,18,108,?
Options:
A)1922
B)1944
C)1934
D)1936
E)1942
Rationale: 2*3=6
3*6=18
6*18=108
18*108=1944
therefore next no. is 1944
ANSWER:B
Answer: B
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 13
Options:
A)1
B)3
C)4
D)5
E)12
Rationale: case1
N=5,8,11,14,17,20
case 2
M=5,9,13,17,21
Therefore n=17
Remainder of 17/13 will be 4
C
Answer: C
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
Options:
A)17/22
B)17/25
C)17/21
D)17/29
E)17/98
Rationale: Explanation:
The number of exhaustive events = âµâ°Câ‚ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer: B
Answer: B
Question: In what time will $ 1000 become $ 1331 at 10% per annum compounded annually?
Options:
A)3 Years
B)4 Years
C)5 Years
D)2 Years
E)1 Year
Rationale: Principal = $ 1000; Amount = $ 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)3
n = 3 years.
Answer A.
Answer: A
Question: When 4 dice are thrown, what is the probability that the same number appears on each of them?
Options:
A)1/36
B)1/18
C)1/216
D)1/5
E)1/4
Rationale: Sample space (Denominator): When 4 dice are thrown simultaneously, then the total number of possible outcomes is 64 = 1296.
Event (Numerator): The chances that all the dice show same number (1,1,1,1),
(2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} is 6.
Probability = Event/ Sample space = 6/64 = 1/63 = 1/216.
ANSWER:C
Answer: C
Question: A speed of 14 metres per second is the same as :
Options:
A)50.4 km/hr
B)55 km/hr
C)60 km/hr
D)68.5 km/hr
E)None
Rationale: Sol.
14 m/sec = [14 * 18/5] km/hr = 50.4 km/hr.
Answer A
Answer: A
Question: 22 percent of 300
Options:
A)50
B)55
C)62
D)77
E)66
Rationale: 1 % of 300 = 322 % of 300= 22*3 =66Answer :E
Answer: E
Question: If in a certain sequence of consecutive multiples of 50, the median is 725, and the greatest term is 1100, how many terms that are smaller than 725 are there in the sequence?
Options:
A)7
B)6
C)8
D)12
E)13
Rationale: Since the median is 725 we know there must be a even number of integers because 50 is not a multiple of 725.
So the list around 725 must go. 700 (725) 750 800 850 900 950 1000 1050 1100
Since we know there are 8 numbers greater than 725 then there must be 8 numbers less then 725.
answer:C
Answer: C
Question: If the city centers of New York and Paris are 3,627 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
Options:
A)6.5 × 10^6
B)1.8 × 10^7
C)2.3 × 10^8
D)4.5 × 10^9
E)6.8 × 10^10
Rationale: 3627 miles = 3627 x 5280 feet/mile x 12 inches/foot which is about 2.3 x 10^8 inches.
The answer is C.
Answer: C
Question: The amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5. If they worked a combined total of 80 hours, how many hours did the secretary who worked the longest spend on the project?
Options:
A)80
B)70
C)56
D)16
E)40
Rationale: 10x = 80
=> x = 8
Therefore the secretary who worked the longest spent 8 x 5 = 40 hours on the project
Option (E)
Answer: E
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
Options:
A)3 hrs
B)5 hrs
C)2 hrs 15 min
D)4hrs 24 min
E)4 hrs
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer: D
Answer: D
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and
15 students play all the sports. How many students play only cricket ?
Options:
A)36
B)38
C)39
D)47
E)37
Rationale: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)+N(C∩T)-2(N(B∩T∩C))
=75-30+24-(2*15)
=39
ANSWER:C
Answer: C
Question: A trader has 50 kg of rice, apart of which he sells at 10 per cent profit and the rest at 5 per cent loss. He gains 7 per cent on the whole. What is the quantity sold at 10 per cent gain and 5 per cent loss?
Options:
A)30kg, 10kg
B)40kg, 15kg
C)35kg, 40kg
D)40kg, 10kg
E)50kg, 10kg
Rationale: Ratio of quantities sold at 10%profit and 5%loss
=>12:3 = 4:1
Therefore,the quantity sold at 10%profit
=50/(4 +1) x 4
=40 kg
and the quantity sold at 5%loss
=50 - 40
=10 kg
ANSWER:D
Answer: D
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability R that the integer drawn is divisible by 8?
* A solution will be posted in two days.
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,R two out of three can be divided and the answer is D.
Answer: D
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Options:
A)1% gain
B)6% gain
C)8% gain
D)5% gain
E)9% gain
Rationale: Explanation:
Answer:A
Answer: A
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
Options:
A)187 m
B)787 m
C)877 m
D)600 m
E)788 m
Rationale: Distance covered by Amar = 18/4.8 (1.6km)
= 3/8(1600)
= 600 m
Answer:D
Answer: D
Question: If the number 72592*6 is completely divisible by 8, then the smallest whole number in place of * will be?
Options:
A)1
B)2
C)4
D)5
E)None of these
Rationale: The number 2x6 must be divisible by 8.
x=1 as 216 is divisible by 8.
Correct Option : A
Answer: A
Question: 3+2=12
4+1=16
5+9=65
6+8=78
7+3=??
Solve it?
Options:
A)12
B)16
C)68
D)42
E)91
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
3+2=3[2+(3-1)]=9+6-3=12
4+1=4[1+(4-1)]=16+4-4=16
5+9=5[9+(5-1)]=25+45-5=65
6+8=6[8+(6-1)]=36+48-6=78
7+3=7[3+(7-1)]=49+21-7=63
Answer :C
Answer: C
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
Options:
A)2420 ft
B)2524 ft
C)2600 ft
D)2740 ft
E)None
Rationale: Sol.
Distance = [1100 * 11/5] feet = 2420 feet.
Answer A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 1072 in 2 years and to Rs. 1144 in 4 years. The sum is:
Options:
A)Rs. 1000
B)Rs. 850
C)Rs. 500
D)Rs. 1200
E)Rs. 900
Rationale: S.I. for 2 years = Rs. (1144 - 1072) = Rs. 72.
S.I. for 1 year = Rs. 72/2 = Rs. 36.
Principal = Rs. (1072 - 72) = Rs. 1000.
Answer: Option A
Answer: A
Question: The area of a square field is 400 km2. How long will it take for a horse to run around at the speed of 20 km/h ?
Options:
A)12 h
B)10 h
C)4 h
D)6 h
E)None of these
Rationale: Explanation Area of field = 400 km2. Then, each side of field = √400=20km Distance covered by the horse = Perimeter of square field = 20 × 4 = 80 km ∴ Time taken by horse = distances/peed=80/20=4h Answer C
Answer: C
Question: Look at this series: 2, 4, 8, 16, ... What number should come next?
Options:
A)128
B)64
C)32
D)24
E)56
Rationale: Explanation: This is a simple multiplication series; each number is multiple by 2 to the previous number. In other terms to say, the number is multiplied by 2 successively to get the next result.
1*2 = 2
2*2 = 4
4*2 = 8
8*2 = 16
16*2 = 32 and so on.
Answer: Option C
Answer: C
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds. What is the length of the platform in meters?
Options:
A)200 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 20 * 20 = 400 = Length of train
Length of platform = 600 - 400 = 200
Answer: A
Answer: A
Question: In an election between two candidates, one got 45% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was:
Options:
A)2200
B)3600
C)3270
D)3700
E)4000
Rationale: Number of valid votes = 80% of 4000 = 3200.
Valid votes polled by other candidate = 55% of 4000
=(55/100)X8000 =2200
ANSWER = A
Answer: A
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)Rs. 64.12
B)Rs. 64.19
C)Rs. 14.19
D)Rs. 64.10
E)Rs. 64.99
Rationale: Explanation:
S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000] = Rs. 464.10 Difference = (464.10 - 400) = Rs. 64.10
Answer: D
Answer: D
Question: The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is:
Options:
A)10
B)12
C)15
D)16
E)17
Rationale: Explanation:
Let the numbers be x and (22 - x). Then,
5x = 6(22 - x)
11x = 132 => x = 12
So, the numbers are 12 and 10.
ANSWER IS B
Answer: B
Question: If f(x) = x^2/(x^5 - 1), what is f(1/x) in terms of f(x)?
Options:
A)1/f(x)
B)-f(x)
C)2/f(x)
D)f(x)
E)3*f(x)
Rationale: If x = 2 then f(x) = 4/31 and f(1/x) = -4/31 which is equal to -f(x)
answer B
Answer: B
Question: In a company of total 1200 employees, 470 hold account in ICICI bank, 395 in HDFC Bank and 675 in SBI. 70 employees holds account in all the three Banks. The number of employees having account in ICICI Bank and HDFC Bank but not in SBI is equal to the number of employees having account in ICICI Bank and SBI but not in HDFC Bank, and this number is equal to 6.25% of the total number of employees. Answer the following questions based on this information.
What is the percentage of employees who have account in SBI only ?
Options:
A)25%
B)30%
C)40%
D)45%
E)55%
Rationale: Explanation :
Reqd % = 480/1200 x 100 = 40%
Answer : Option C
Answer: C
Question: A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 2000. He sold both the items together for Rs. 6000. What percentage of profit did he make?
Options:
A)80%
B)50%
C)40%
D)48%
E)10%
Rationale: The total CP = Rs. 2000 + Rs. 2000
= Rs. 4000 and SP = Rs. 6000
Profit(%) = (6000 - 4000)/4000 * 100
= 50%
Answer: B
Answer: B
Question: 110AB
In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 55, what is the greatest possible value of B x A?
Options:
A)0
B)5
C)10
D)15
E)25
Rationale: 55 is a multiple of 11 and hence the divisibility for 11 is also valid here. (sum of digits in odd place-sum of digits in even should be either 0 or 11).
i.e. (1+0+B)-(1+A)=0 OR 11
implies B-A=0
The only possible values being 00. or 55.
Answer choice E.
Answer: E
Question: Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 1 women will be selected ?
Options:
A)1/6
B)1/4
C)2/7
D)2/3
E)1/2
Rationale: Group 1: 3 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 1 women from group 2 - 3C2*2C1 = 6 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*1*2 = 6 ways
Total Favorable cases = 6+6 = 12
Total Possible ways of selecting students 2 from each group = 4C2*3C2 = 6*3 = 18
Probability = 12/18 = 2/3
Answer : Option D
Answer: D
Question: Find the odd man out. 1050, 510, 242, 104, 46, 16, 3
Options:
A)46
B)104
C)510
D)1050
E)None of these
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 104. Answer : Option B
Answer: B
Question: A train passes a platform in 44 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)240
B)250
C)360
D)230
E)220
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×44 = 660
=> L = 660-300 = 360 meter
Answer is C.
Answer: C
Question: What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/4
Options:
A)2/5
B)3/5
C)7/12
D)1/7
E)None of these
Rationale: Explanation:
2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/4 = 1.25
So biggest is 5/4 and smallest is 2/3
Their difference is 5/4 - 2/3 = 7/12
Option C
Answer: C
Question: If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus?
Options:
A)equal to 12
B)equal to 34
C)greater than 1
D)equal to 1
E)None
Rationale: Explanation:
If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is 90°90°, rhombus is also a square and therefore areas will be equal)
Hence greater than 11 is the more suitable choice from the given list
Answer: Option C
Answer: C
Question: What decimal fraction is 50 ml of a litre ?
Options:
A).5
B).05
C).05
D)0.05
E)None of these
Rationale: Answer
Required fraction = 50/1000
= 5/100
= .05
Correct Option: B
Answer: B
Question: how many internal diagonals does a hexagon (six sided polygon) have?
Options:
A)5
B)6
C)8
D)9
E)10
Rationale: Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 6
No. of diagonals = 6(6 - 3)/2
= 9
Ans D
Answer: D
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Options:
A)65 min
B)99 min
C)56 min
D)1Z min
E)12 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.
Answer: D
Answer: D
Question: The odds against ram solving the problem are 7 to 3 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
Options:
A)1/4
B)5/21
C)16/21
D)23/28
E)17/24
Rationale: Odds against Ram are 7:3 so probability that he will solve the problem is 3/10.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 3/10 + 7/12 - (3/10)*(7/12) = 17/24
E
Answer: E
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 3:1 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)18:13
B)16:13
C)19:13
D)14:11
E)13:11
Rationale: Vessel A = 300 gallons --> milk = 100, water = 200;
Vessel B = 500 gallons --> milk = 375, water = 125;
Vessel A + B = 800 gallons --> milk = 475, water 325.
The ratio = 475/325 --> 19/13
Answer: C
Answer: C
Question: The average of 11 results is 46, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)21
B)56
C)100
D)25
E)23
Rationale: 1 to 11 = 11 * 46 = 506
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 506 = 100
Answer:C
Answer: C
Question: Village P’s population is 1200 greater than Village Q's population. If Village Q’s population were reduced by 800 people, then Village P’s population would be 6 times as large as Village Q's population. What is Village Q's current population?
Options:
A)1050
B)1100
C)1150
D)1200
E)1250
Rationale: P = Q+1200.
P=6(Q-800).
6(Q-800)=Q+1200.
5Q=6000.
Q=1200.
The answer is D.
Answer: D
Question: 80 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
Options:
A)0.45
B)0.55
C)0.65
D)0.32
E)0.35
Rationale: Say there are 100 people in that group, then there would be 0.8*0.40*100=32 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=32/100.
Answer: D
Answer: D
Question: A baseball card decreased in value 40% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
Options:
A)28%
B)30%
C)32%
D)46%
E)72%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.6 = 60
After second year price = 60 *0.9 = 54
final decrease = [(100 - 54)/100] * 100 = 46%
correct answer - D
Answer: D
Question: What is the greatest value of x such that 4^x is a factor of 21! ?
Options:
A)5
B)6
C)3
D)2
E)4
Rationale: Pretty simple, really.
If m = 6, then 4m = 24, which is 12x2, both of which are included in 21!
Since 6 is the largest number here, its the answer.
Answer is B
Answer: B
Question: Taylor is making a bracelet. He Starts with 3 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
Options:
A)89
B)90
C)95
D)97
E)87
Rationale: Repeating sequence = 3 + 6 + 2 = 11.
As the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)
Out of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)
none of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10
Hence, answer is E
Answer: E
Question: A man can row with a speed of 13 kmph in still water. If the stream flows at 53 kmph, then the speed in downstream is?
Options:
A)28
B)16
C)20
D)87
E)24
Rationale: M = 13
S = 3
DS = 13 + 3
=16
Answer: B
Answer: B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)2 kmph
C)7 kmph
D)8 kmph
E)9 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: How many words can be formed by using all letters of the word ‘DESK’ ?
Options:
A)16
B)20
C)24
D)28
E)32
Rationale: The word contains 4 different letters.
The number of permutations is 4! = 24
The answer is C.
Answer: C
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
Options:
A)4:9
B)4:3
C)4:6
D)4:2
E)4:1
Rationale: 4 πr2 : 3 πr2 => 4:3
Answer:B
Answer: B
Question: Find the average of all numbers between 5 and 37 which are divisible by 4
Options:
A)25
B)20
C)45
D)30
E)35
Rationale: Explanation:
Average=(4+8+12+16+20+24+28+32+36) / 4)=180 / 4=45
Option C
Answer: C
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?
Options:
A)625
B)286
C)266
D)191
E)811
Rationale: Explanation:
Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x = 625.
Answer: A
Answer: A