divelab/Sys2Bench huggingface dataset:
Question: In how many ways, a committee of 4 members can be selected from 5 men and 4 ladies, consisting of 3 men and 1 lady?
Options:
A)15
B)25
C)30
D)40
E)55
Rationale: (3 men out 5) and (1 lady out of 4) are to be chosen
Required number of ways = 5C3*4C1 = 40
Answer is D
Answer: D
Question: What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
Options:
A)s.2.04
B)s.2.08
C)s.3.67
D)s.2.83
E)s.2.42
Rationale: C.I. when interest is compounded yearly
= [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 9000 * 26/25 * 51/50 = Rs. 9547.2
C.I. when interest is compounded half-yearly
= [9000 * (1 + 2/100)2]
= (9000 * 51/50 * 51/50 * 51/50)
= Rs. 9550.87 Difference
= (9550.87 - 9547.2)
= Rs.3.67.
Answer: C
Answer: C
Question: The arithmetic mean of set X is zero. If Y = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of X consisting of all those elements in X which are more than two but less than three standard deviations away from the arithmetic mean of X, what could be equal to the standard deviation of X?
Options:
A)0.54
B)0.77
C)0.82
D)0.97
E)1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and Y = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S
Y consists of all those elements in X that are more than 2 but less than 3 XDs away from the arithmetic mean of X
If an element is 1 XD away from the mean, we can write it as either m + XD or m - XD
Similarly, if an element is 2 XDs away from the mean, we can write it as either m + 2*XD or m - 2*XD
So, if these elements lie within 2 and 3 XDs of mean, m=0
we can find which one of these values of XD satisfies each value within Y
Only XD = 0.77 does
Answer : B
Answer: B
Question: $20000 will become $60000 at 20% P.A. find the time?
Options:
A)2years
B)5years
C)7years
D)8years
E)10years
Rationale: SI = simple interest = A-P = 60000-20000 = $40000
R = 100SI/PT = 100*40000/20000*20 =10 years
Answer is E
Answer: E
Question: x is a positive integer of F less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Took me more than 2 mins to solve.
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer
Answer: D
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)5
B)8
C)9
D)4
E)2
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Answer: D
Question: If m+5/n is a prime integer, which of the following must be true?
1.n=5m
2. n is a prime integer
3. m+5/n is ODD.
Options:
A)None
B)1 only
C)2 only
D)1 and 2 only
E)2 and 3 only.
Rationale: I would pick up numbers and do .
i hope the question is (m+5)/n....
let m = 3 , n = 4
3+5/4 = 2 = Prime
1. n is not equal to 5m
2.n is not a prime number
3. (m+5)/n is not odd.
hence A
Answer: A
Question: The time on a clock is 20 minutes past 6. What is the angle between the hands of the clock?
Options:
A)60 degrees
B)120 degrees
C)90 degrees
D)50 degrees
E)70 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 190 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 190 - 120 = 70 degrees.
The answer is E.
Answer: E
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
Options:
A)286 m
B)899 m
C)200 m
D)166 m
E)187 m
Rationale: 2(l + 100) = 600 => l
= 200 m
Answer: C
Answer: C
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. If there are 30 5-rupee notes, 20-10-rupee notes, find the number of one-rupee notes.
Options:
A)180
B)150
C)130
D)200
E)170
Rationale: x+150+200=480, x=480-350=130, Ans: C
Answer: C
Question: After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article?
Options:
A)12000
B)15000
C)1200
D)1000
E)10000
Rationale: CP* (44/100) =4400
CP= 100 * 100 => CP
= 10000
Answer:E
Answer: E
Question: The cash difference between the selling prices of an book at a profit of 4% and 8% is $3. The ratio of the two selling prices is:
Options:
A)55:23
B)26:27
C)52:53
D)45:53
E)51:34
Rationale: Let C.P. of the book be $x.
Then, required ratio = 104% of x / 108% of x
= 104/108 = 26/27 = 26:27
B
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/19
B)2/19
C)2/21
D)2/97
E)2/18
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: C
Question: In one alloy there is 12% chromium while in another alloy it is 10%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)8.8%
B)9%
C)9.2%
D)8.6%
E)10.6%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.12*15+0.10*35=5.3 kg, so the percentage is 5.3/50*100=10.6%.
Answer: E.
Answer: E
Question: A car takes 6 hours to cover a distance of 630 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)48 Kmph
B)50 Kmph
C)52 Kmph
D)56 Kmph
E)70 Kmph
Rationale: Time = 6
Distence = 630
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 630/9 = 70 Kmph
E
Answer: E
Question: In an election, candidate Smith won 52% of the total vote in Counties A and W. He won 61% of the vote in County A. If the ratio of people who voted in County A to County W is 3:1, what percent of the vote did candidate Smith win in County W ?
Options:
A)A.25%
B)B.27%
C)C.34%
D)D.43%
E)E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County W
hence answer is A.
Answer: A
Question: In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
Options:
A)3.5%
B)2.4%
C)8.3%
D)5%
E)2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 114*95=10,830, which is 8.3% greater than the actual area.
Answer: C.
Answer: C
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 4 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Options:
A)25
B)35
C)76
D)80
E)90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 4 = 72
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 72 + 4 = 76
C
Answer: C
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive E difference between n and m?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result E will be 8 - 5 = 3
And answer B
Answer: B
Question: In a fuel station the service costs $2.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
Options:
A)122.6$
B)128.9$
C)243.7$
D)298.85$
E)312.12$
Rationale: Mini van cost= 65*0.6+2.05
truck capacity =65(1+120/100)=143 lts.
cost of truck=143+0.6+2.05
Total cost =3* 41.05(car)+2*87.85(truck)=298.85
ANSWER:D
Answer: D
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 9 units?
Options:
A)126 sq.units
B)170 sq.units
C)190 sq.units
D)940 sq.units
E)149 sq.units
Rationale: Explanation:
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 * 9 = 126 sq.units
Answer: Option A
Answer: A
Question: A sweet seller sells 3/5th part of sweets at a profit of 10% and remaining at a loss of 5%. If the total profit is Rs 1500, then what is the total cost price of sweets?
Options:
A)Rs 36,500
B)Rs 37,000
C)Rs 37,500
D)Rs 38,500
E)None of these
Rationale: Assume A be the cost price.
Therefore,
[{(3/5) x A x (10/100)} – {(2/5) x A x 5/100}] = 1500
Or A = Rs 37,500
ANSWER:C
Answer: C
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 95 on the S scale?
Options:
A)42
B)45
C)48
D)51
E)54
Rationale: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(95)/5 - 12 = 57-12 = 45
The answer is B.
Answer: B
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of four rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.
The relative speed of Sandy and Molly is 4 - 1 = 3 rounds per hour.
The time required to complete one round at this speed is 1/3 hours = 20 minutes.
The answer is B.
Answer: B
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)6
B)9
C)8
D)12
E)2
Rationale: Explanation:
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer:D
Answer: D
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 6 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Options:
A)22 km
B)20 km
C)65 km
D)18 km
E)36 km
Rationale: Distance = Relative Speed * Time
= (6 + 3) * 4 = 36 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: E
Answer: E
Question: A clock loses a minute every three hours for 5 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
Options:
A)11:54:40 AM
B)11:56:24 AM
C)12:16:40 PM
D)11:54:24 AM
E)11:46:24 PM
Rationale: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 40 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 11 days = 86.40 - 40 = 46.4 minutes.
11AM + 46.4 minutes = 11:46 and 4/10th of a minute or 24 seconds.
Answer: E
Answer: E
Question: A retailer sold 2 houses at each $15000. On 1st house he got 20% profit and on 2nd house he loss 5% then find his net profit or loss?
Options:
A)10%
B)9%
C)14%
D)15%
E)12%
Rationale: A = 20%
B = -5%
profit% = 20-5 + (-100/100) = 14%
Answer is C
Answer: C
Question: There are six leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
Options:
A)4 leopard and one sheep
B)5 leopard and one sheep
C)6 leopard and one sheep
D)7 leopard and one sheep
E)None
Rationale: Solution:
5 leopard and one sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer B
Answer: B
Question: The red triangle is equilateral with a side of 23 centimetres. Its perimeter is
Options:
A)68 cm
B)69 cm
C)70 cm
D)71 cm
E)None
Rationale: Solution:
All three sides of an equilateral triangle are equal. Thus, its perimeter will be 23 × 3 = 69 cm
Answer B
Answer: B
Question: The simple form of the ratio 9/8:3/4 is?
Options:
A)5:8
B)5:5
C)5:9
D)3:2
E)5:1
Rationale: 9/8 : 3/4 = 3:2
Answer: D
Answer: D
Question: How many even integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?
Options:
A)37
B)38
C)39
D)40
E)46
Rationale: total 51 even integers
out of which 7 will be divided by 7 and 6 will be divided by 9
(for 7..find intervals of 14 as we are taking even numbers
112,126...196
(for 9..find intervals of 18 as we are taking even numbers
108,126...198)
126 is common
so 51-7-6+1 = 39 will not be divided by 7 or 9
ANSWER:C
Answer: C
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
Options:
A)98 days
B)60 days
C)56 days
D)76 days
E)45 days
Rationale: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
Answer: B
Answer: B
Question: If e=1 and (e-b)/c = 1 which of the following is NOT a possible value of b?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: Equation is:
(e-b)/c = 1 where e = 1
so plug in 1 for e and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: D
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 34% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
Options:
A)35.67%
B)66.90%
C)68.57%
D)69.57%
E)none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 34% of 1100 ) + ( 32% of 900)
= 374 + 288 = 662
Failed = 2000 - 662 = 1338
Failed % = [(1338/2000) x 100]%
= 66.9%.
ANSWER:B
Answer: B
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)2
B)6
C)5
D)3
E)8
Rationale: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer: D
Answer: D
Question: Of the 8 members of flight crew, 7 are trained to serve economic class customer, 5 are trained to serve business class customer, and 4 can serve both. If one member is chosen at random, what is the probability that the member chosen will be someone who can serve either type of customer?
Options:
A)a) 1/9
B)b) 0
C)c) 1/6
D)d) 1/4
E)e) 1/3
Rationale: You know how to solve for Total number of people who can serve at least one type of customer:
Total = n(A) + n(B) - n(A and B)
Total people who can serve at least one type of customer = 7 + 5 - 4 = 8
So All 8 people know how to serve at least one type of customer. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to serve any type of customer
Answer (B)
Answer: B
Question: In a certain city, 70 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
Options:
A)30,000 to 75,000 inclusive
B)30,000 to 90,000 inclusive
C)60,000 to 75,000 inclusive
D)60,000 to 90,000 inclusive
E)90,000 to 120,000 inclusive
Rationale: The maximum percentage with both is 50% which is 75,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 20% which is 30,000 households.
This means that 30% of households have only recorders but not cable television.
The other 20% of households with recorders have cable television.
The answer is A.
Answer: A
Question: A present value of a machine is $700. Its value depletion rate is 10% per annum then find the machine value after 2 years?
Options:
A)$900
B)$810
C)$915
D)$715
E)$567
Rationale: P= $700
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=700*9/10 * 9/10
=$567
Answer is E
Answer: E
Question: After 2 games, team B had an average of 61.5 points per game. If it got only 47 points in game 3, how many more points does it need to score to get its total above 500?
Options:
A)805
B)740
C)670
D)530
E)330
Rationale: (2*61.5) + 47 +x >500
123+47+x > 500
170+x >500
=> x>330
Option E
Answer: E
Question: 12 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)55 days
B)77 days
C)20 days
D)88 days
E)15 days
Rationale: 12 * 25 = 20 * x => x
= 15 days
Answer: E
Answer: E
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Options:
A)12
B)66
C)87
D)88
E)66
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: A
Answer: A
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
Options:
A)18
B)20
C)23
D)24
E)26
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
Option 'D'
Answer: D
Question: In an office, 50 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Options:
A) 8
B) 64
C) 50
D) 144
E) 160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(50/100)*Workers = x+16 = > x = 8
Answer A
Answer: A
Question: At a florist shop on a certain day, all corsages sold for either $40 or $45. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 20 percent. What was the store's actual revenue from corsages that day?
Options:
A)$200
B)$400
C)$600
D)$800
E)$1000
Rationale: I am doing it elaborately, hope it will help you.
Let, No. of corsages @ $40 = x, no. of corsages @ $45 = y and revenue= r
so, 40 x+45 y=r.........(1)
Now,
Given the situation, 40(x+8) + 45(y-8)= r-.2r
=> 40 x+320+45 y-360 = .8r
=> 40x+45y = .8r+40............(2)
so, r = .8r+40
=> r = 200
The answer is A.
Answer: A
Question: Ten percent of Country Y's yearly exports come from fruit exports. One-fifth of all fruit exports from Country Y are orange exports. If country Y generates $400 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
A)$21.25m
B)$25.5m
C)$106.25m
D)$127.5m
E)$20000m
Rationale: 10/100*1/5*(total) = 400
1/50*(total) = 400
(total) = 400*50 = 20000
Answer: E
Answer: E
Question: In how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
Options:
A)From 2 to 6 inclusive.
B)From 98 to 102 inclusive.
C)From 122 to 126 inclusive.
D)From 128 to 132 inclusive.
E)From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
Q=1+28+70+28+1 = 128 Answer is D.
Answer: D
Question: If a is an integer larger than 1, and x=60a, then x must be a multiple of which of the following?
Options:
A)8
B)9
C)12
D)18
E)120
Rationale: X must be divisible by 60 .
a , an integer less than 1 means a could be 0,-1,-2,....... and x = 60a
so if a= 0, x = 0*60=0 is divisible by 12 ( recall 0 is divisible by any integer)
if a= -1, then -60 is divisible by 12 but not 8,9,18 and 120 , if a-2 , then -120 is divisible by 60 and so on
Answer is C
Answer: C
Question: Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
Options:
A)21005
B)10500
C)25200
D)5376
E)None of these
Rationale: Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D
Answer: D
Question: The unit digit in the product (784x618x917x463) is
Options:
A)2
B)3
C)4
D)5
E)None of them
Rationale: Unit digit in the given product = Unit digit in (4x8x7x3)=2
Answer is A
Answer: A
Question: A toy factory stores its toys in either a big box or a small box. The big box can store 35 toys while the small box can store 14 toys. If the factory is to store 86 newly manufactured toys, what is the least number of toys that will be left unboxed?
Options:
A)2
B)1
C)3
D)5
E)4
Rationale: Total toys to be stored 86
The big box can store 35
small box can store 14
storing 85 toys in big box 85/35 =2 r 16
store remainder in small box 16/14=1 r 2
least number of toys that will be left unboxed=2
Answer: A
Answer: A
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
Options:
A)y = 2x
B)y = x + 9
C)y = x^2 - 3
D)y = x^3 + x
E)y = x^4
Rationale: x^4 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: E
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
Options:
A)25
B)378
C)20
D)27
E)121
Rationale: M = 15
S = 10
DS = 15 + 10 = 25
Answer: A
Answer: A