divelab/Sys2Bench huggingface dataset:
Question: If x < y < 0, which of the following must be true?
Options:
A)x/y is a negative integer
B)xy is a negative integer
C)x+y is a negative integer
D)x-y is a positive integer
E)(-x)+ (-y) is positive integer
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since x<y eg. x=-2, y=-1 then -2-(-1)=-1
So, option E is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : E
Answer: E
Question: If W is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)W(W+1)(W-4)
B)N(N+2)(N-1)
C)N(N+3)(N-5)
D)N(N+4)(N-2)
E)N(N+5)(N-6)
Rationale: Now take W = 3k , W = 3k+1 W = 3k+2..put in all the choices. If by putting all the values of W we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: A
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
Options:
A)81:121
B)81:122
C)81:129
D)81:120
E)21:121
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Answer: A
Question: 4/x + 3x = 3(x+12)
Options:
A)-9
B)-1/3
C)-1/9
D)1/9
E)9
Rationale: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(4/X) + 3x = 3(x+12)
(4/x) + 3x = 3x + 36
4 + 3x^2 = 3x^2 + 36x
4 = 36x
1/9 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
D
Answer: D
Question: The price of a table is marked at $12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
Options:
A)8721
B)2304
C)7720
D)6221
E)7493
Rationale: A
8721
Actual price = 95% of 90% of 85% of $12000
= 95/100 * 90/100 * 85/100 * 12000 = $8721.
Answer: A
Question: Difference between two numbers is 4, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)5,9
B)7,9
C)9,8
D)11,12
E)13,3
Rationale: Explanation:
x – y = 4
4x – 6y = 6
x = 9 y = 5
A)
Answer: A
Question: Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
Options:
A)50
B)72
C)84
D)90
E)108
Rationale: A is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+2T) = 8T ==> T = 1/6 ==> 10 minutes
To travel double distance, 2(2+2T) = 8T ==> 1 ==> 60 minutes
Difference, 50 minutes
A
Answer: A
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)16 km/hr
B)17 km/hr
C)60 km/hr
D)15 km/hr
E)19 km/hr
Rationale: 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: C
Answer: C
Question: An investment of $3000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $3000 increased to $12000 by earning interest. In how many years after the initial investment was made the $3000 have increased to $24000 by earning interest at that rate?
Options:
A)16
B)22
C)20
D)18
E)30
Rationale: In 12 years the investment quadrupled (from $3,000 to $12,000).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $12,000 to $24,000).
Therefore, 12+6=18 years are needed $3,000 to increase to $24,000.
Answer: D.
Answer: D
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $15, what was the price before the first discount?
Options:
A)$45.10
B)$34.31
C)$28.44
D)$26.66
E)$65.23
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 15
(x - 25%x) - 25%(x - 25%x) = 15
Solve for x
x = $26.66
correct answer D
Answer: D
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
Options:
A)8 hrs
B)6 hrs
C)7 hrs
D)3 hrs
E)9 hrs
Rationale: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.
Answer: C
Answer: C
Question: If x > 3 and y < -3, then which of the following must be true ?
Options:
A)x/y > 1
B)x/y < -1
C)x/y < 0
D)x + y > 0
E)xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
D should be the answer.
Answer: D
Question: (3X+2)(2X-5)=AX^2+ KX+N;
THEN WHAT IS THE VALUE OF A-N+K?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: (3x+2)(2x-5)=6x^2-11x-10
So,A=6, K=-11, N=-10
Finally,
A-N+K=6-(-10)+(-11)
=6+10-11
=5
ANSWER:B
Answer: B
Question: when W is divided by 14, the reminder is 0. if W is three more than it value and when divided by 9 its remainder is 0. what is the value of W ?
Options:
A)42
B)14
C)28
D)30
E)70
Rationale: W is divided by 14 so that is multiple of 14 as 14,28,42...
W+3 is divided by 9 the remainder is 0 so it is divisible by 9. Consider from option let us take the number is 42 it is divisible by 14 but 42+3 is divisible by 9 so ans is A
Answer: A
Question: If 20 men can build a water fountain 56 metres long in 21 days, what length of a similar water fountain can be built by 35 men in 3 days?
Options:
A)10 m
B)14 m
C)17 m
D)19 m
E)20 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 21: 3 : : 56 : x
Therefore (20 x 21 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/420=14
Hence, the required length is 14 m.
Answer : B
Answer: B
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)None of these
Rationale: Explanation:
1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
ANSWER IS B
Answer: B
Question: A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/2
Rationale: Favorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits
Total Such Passwords = 5*5*5*5*5 = 5^5
Total Possible Password = 10*10*10*10*10 = 10^5
Probability = (5^5) / (10^5) = 1/2^5 = 1/32
Answer: option A
Answer: A
Question: A truck driver starts with the speed of 70 kmph with the truck driver decreasing speed every two hours by 10 kmph. The truck driver's speed does not drop below 50 kmph. In how many hours will it take the truck driver to travel 500 kms?
Options:
A)480 minutes
B)492 minutes
C)504 minutes
D)528 minutes
E)540 minutes
Rationale: Distance covered in first two hours = 70 Ã— 2 = 140 km
Distance covered in next two hours = 60 Ã— 2 = 120 km
Distance covered in next two hours = 50 Ã— 2 = 100 km
Distance covered in next two hours = 50 Ã— 2 = 100 km
Distance covered in first eight hours
140 + 120 + 100 + 100 = 460 km
Remaining distance = 500 â€“ 460 = 40 km.
Now, this distance will be covered at the speed of 50 km/hr.
âˆ´ Time taken = 40â„50 = 4â„5 hour.
Total time= 8 + 4â„5 = 8 4â„5 hour
Answer D
Answer: D
Question: In a game, a player can win by getting five consecutive tails in six throws of a coin. What is the probability of winning if the player gets a tail on the first throw?
Options:
A)1/32
B)1/16
C)3/16
D)1/8
E)3/8
Rationale: The only way to win is to get a tail on each of the next four throws.
P(four tails)=(1/2)^4=1/16
The answer is B.
Answer: B
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 17 members of this sequence?
Options:
A)878
B)900
C)743
D)928
E)1022
Rationale: I would split them up like this.
23 28 33 and so on (9 terms)....the 9th term = 23+8*5 = 63
27 32 37 and so on (8 terms)......the 8th term = 27+7*5 = 62
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+63)/2 * 9 = 387
(27+62)/2 * 8 = 356
= 743
C
Answer: C
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)2
B)3
C)5
D)6
E)8
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5.Answer: C
Answer: C
Question: If A : B : C = 3 : 4 : 7, then what is the ratio of (A / B) : (B / C) : (C / A)?
Options:
A)63 : 48 : 196
B)63 : 48 : 18
C)63 : 48 : 1928
D)63 : 48 : 1918
E)63 : 48 :121
Rationale: Hint: If a = kb for some constant k, then we can say that a is directly proportional to b.
A : B : C = 3 : 4 : 7
Assume, A = 3 k, B = 4 k, C = 7 k
Therefore,
A	=	(3k)	,	B	=	(4k)	,	C	=	(7k)
B	(4k)	C	(7k)	A	(3k)
A	=	(3)	,	B	=	(4)	,	C	=	(7)
B	(4)	C	(7)	A	(3)
L.C.M of 3, 4, 7 is 84
(3 x 84) / 4 = 63
(4 x 84) / 7 = 48
(7 x 84) / 3 = 196\
Correct option :A
Answer: A
Question: The length of a rectangle is increased by 45% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)1288
B)1299
C)1000
D)10000
E)11600
Rationale: 100 * 100 = 10000
145 * 80 = 11600
Answer: E
Answer: E
Question: Along a road lie an odd number of stones placed at intervals of 10m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is
Options:
A)35
B)15
C)29
D)31
E)29
Rationale: Explanation :
If he travels 10 m for the first stone he has to travel that dist back as well...so he travels 2 * 10 m dist for the first stone and so on.
=> 2400 = 2 * (10 + 20 + 30 .... 10n) using formula for AP
=> 2400 = 2 * n/2*(2*10 + (n-1)*10) .
=> 2400 = 10n2 + 10n .
On solving this, we get n = 15 as the positive root, so total numer of stones on both sides= 30.
and including the one which he was at = 31.
Answer : D
Answer: D
Question: How many words can be formed by using all letters of TIHAR
Options:
A)100
B)120
C)140
D)160
E)None of these
Rationale: Explanation:
First thing to understand in this question is that it is a permutation question.
Total number of words = 5
Required number =
5P5=5!=5∗4∗3∗2∗1=120
Option B
Answer: B
Question: How many odd prime numbers are there less than 100?
Options:
A)78
B)5
C)24
D)12
E)15
Rationale: Odd prime number less than 100:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
There is 24 the odd prime number
Answer is C
Answer: C
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 20 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
Options:
A)3,150
B)400
C)5,040
D)20,520
E)84,000
Rationale: MAGOOSHOFFICIAL SOLUTION:
For the large photos, we need 6C3, which we calculated in the article:
6C3 = 20
For the smaller photos, we need 20C19, which by symmetry must equal 20C1, and we have a formula for that. In fact, in the article above, we already calculated that 21C2 = 20.
Now, by the FCP, we just multiply these: total number of possible albums = 20*20 = 400.
Answer = B
Answer: B
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)202
B)278
C)377
D)750
E)378
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2
= 750
Answer: D
Answer: D
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 90 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 2 at its maximum rate ?
Options:
A)2hrs, 48mins
B)5hrs, 15mins
C)7hrs, 12mins
D)13hrs, 4mins
E)14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/90 --> x=1/630 --> (time) = (reciprocal of rate) = 630 minutes x/2 = 5 hours and 15 minutes.
Answer: B.
Answer: B
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 60% ?
Options:
A) 0
B) 1.66
C) 2.55
D) 1.22
E) 4.88
Rationale: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/60 (this probability is less than 60%)
Solving for x we get, x(x-1)< 3/2. This implies that the maximum value of x can be 1.22.
Answer D!
Answer: D
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)5 days
B)18 days
C)1 ½ days
D)25 days
E)69 days
Rationale: Explanation:
3/20 * 2 + (2 + x)/5 = 1
x = 1 ½ days
Answer C
Answer: C
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 2 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)60 gallons
B)100 gallons
C)120 gallons
D)80 gallons
E)130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 2 gallons\
Volume of whole = 2 * 40 =80 gallons.
ANSWER:D
Answer: D
Question: Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?
Options:
A)2:1
B)3:4
C)3:8
D)3:1
E)3:2
Rationale: The ratio of the investments made by A and B =
100000: 50000=> 2:1.Answer: A
Answer: A
Question: Two stations A and B are 20 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9
B)10
C)11
D)12
E)8
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 20
45x = 45
x = 1.
So, they meet at 8 a.m.
Answer: Option E
Answer: E
Question: In a question on division with zero remainder, a candidate took 15 as divisor instead of 5. The quotient obtained by him was 35. The correct quotient is?
Options:
A)A)105
B)B)24
C)C)28
D)D)29
E)E)30
Rationale: Number = (35 * 15) = 525
Correct quotient = 525/5 = 105
A)
Answer: A
Question: If John covers a certain distance in 1 hr. 24 min. by covering two third of the distance at 4 kmph and the rest at 5 kmph, then find the total distance
Options:
A)4 km
B)6 km
C)6.8 km
D)7.2 km
E)None of these
Rationale: Explanation:
Let the total distance be y km. Then,
(2/3)y/4 +(1/3)y/5 =7/5
y/6 + y/15 = 7/5
7y =42
y = 6 km
ANSWER B
Answer: B
Question: Which of the following options is equal to 3.75 x 10(power 5)?
Options:
A)175000
B)372000
C)375000
D)365000
E)374000
Rationale: = 3.75 x 10(power 5)
= 3.75 x 100000
= 375000.
Answer is C.
Answer: C
Question: A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 4 or 15?
Options:
A)17/30
B)2/5
C)3/10
D)4/15
E)11/30
Rationale: Number of Multiples of 4 from 1 through 30 = 30/4 = 7
Number of Multiples of 15 from 1 through 30 = 30/15 = 2
Number of Multiples of 4 and 15 both from 1 through 30 = Number of Multiples of 15*4(=60) = 0
Total favourable cases = 7 + 2 - 0 = 9
Probability = 9 / 30 = 3/10
Answer: option C
Answer: C
Question: Before a salary hike, the weekly salary of a worker for 40 hours in a week was as much as he is paid now for 35 hours of work in a week. What is the percent increase in his salary for an hour?
Options:
A)11 1/3
B)12 1/4
C)13 1/5
D)14 2/7
E)15
Rationale: 280 is multiple of both 40 and 35
so I would rather take this value as the salary.
40 hrs 280$
1 hr=7$
Similarly
35 hrs 280$
1 hr=8$
Now 8-7=1$ increase in salary per hour now to calculate %
1/7*100=14 2/7
ANSWER:D
Answer: D
Question: Length of a rectangular plot is 32 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)56 m
B)66 m
C)76 m
D)86 m
E)96 m
Rationale: Let breadth = x metres.
Then, length = (x + 32) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 32) + x] = 200
2x + 32 = 100
2x = 68
x = 34.
Hence, length = x + 32 = 66 m
B
Answer: B
Question: Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
Options:
A)17hr
B)14hr
C)12hr
D)19hr
E)20hr
Rationale: Explanation:
relative speed =5.5−5=0.5 kmph (because they walk in the same direction)
distance =8.5 km
time=distance/speed=8.5/0.5=17 hr
ANSWER IS A
Answer: A
Question: In how many years will a sum of money doubles itself at 30% per annum on simple interest?
Options:
A)7%
B)3%
C)5%
D)8%
E)2%
Rationale: P = (P*30*R)/100
R = 3%
Answer:B
Answer: B
Question: A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m.?
Options:
A)8
B)7
C)6
D)5
E)3
Rationale: Sol.
Relative speed = (2 + 3) = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9.30 a.m.
Answer B
Answer: B
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)388
B)267
C)215
D)288
E)261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.
Answer: C
Answer: C
Question: If the price has fallen by 15% what percent of its consumption be: increased so that the expenditure may be the same as before?
Options:
A)A)11%
B)B)10%
C)1/9 %
D)3/13 %
E)%
Rationale: 100 – 15 = 85
85------15
100------? => 3/13%
ANSWER:D
Answer: D
Question: If 7:13::301:x then the value of ‘x’ is:
Options:
A)493
B)537
C)559
D)587
E)567
Rationale: Given the question;
7:13::301:x
7/13 = 301/x
7x = 301*13
x = 301*13/7
x = 559
ANSWER:C
Answer: C
Question: Find large number from below question The difference of two no. is 1365. On dividing the larger no. by the smaller, we get 6 as quotient and the 15 as remainder?
Options:
A)1234
B)1456
C)1256
D)1456
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: If the S.P of Rs. 45 results in a 50% discount on the list price, What S.P would result in a 40% discount on the list price?
Options:
A)s. 54
B)s. 56
C)s. 58
D)s. 60
E)s. 62
Rationale: Let the list price be Rs. X,
50/100*x = 45, x = 45*100/50 = 90
Required S.P = 60% of Rs. 90
= 60*90/100
=54
ANSWER:A
Answer: A
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 12000, then find the annual income of A?
Options:
A)Rs. 420000
B)Rs. 403200
C)Rs. 201600
D)Rs. 504000
E)None of these
Rationale: B's monthly income = 12000 * 112/100 = Rs. 13440
B's monthly income = 2 parts ----> Rs. 13440
A's monthly income = 5 parts = 5/2 * 13440 = Rs. 33600
A's annual income = Rs. 33600 * 12 = Rs. 403200
ANSWER:B
Answer: B
Question: A is 50% of B. A is also 150% of C. What is the relation between B and C?
Options:
A)B is 30% of C
B)C and B are equal
C)C is 75% of B
D)B is 150% of C
E)B is 300% of C
Rationale: if...
A=.5B
A=1.5C
then...
.5B=1.5C
Divide all by .5
B=3C
so...
B is 300% of C
The answer is E
Answer: E
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/38
C)31/34
D)31/31
E)31/36
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: A
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive
Options:
A)Rs. 600
B)Rs. 700
C)Rs. 800
D)Rs. 900
E)None
Rationale: Solution: Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 * (6/31) = 150*6 = Rs. 900.
Answer: Option D
Answer: D
Question: In how many different number of ways 8 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)151252
B)151225
C)151211
D)151200
E)151250
Rationale: 10p6 = 10 x 9 x 8 x 7 x 6 x 5 = 151200
C)
Answer: C
Question: The faces of Cuboid are to be painted by 6 different colors. In how many ways can be this be done?
Options:
A)A.720
B)B.256
C)C.1
D)D.12
E)E.36
Rationale: If I have to paint 6 sides with 6 different colour...
First face can have 6c1 options,
2nd would have 5c1, and subsequent ones would have 4c1, 3c1, 2c1 and 1 options respectively.
Total options = 6c1 X 5c1 x 4c1 x 3c1 x 2c1 x 1 = 720 distinct ways
Correct answer - A
Answer: A
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 36 seconds. What is the length of the goods train?
Options:
A)470 m
B)240 m
C)260 m
D)270 m
E)None of these
Rationale: Explanation:
Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.
Time = 36 sec.
Let the length of the train be x metres.
Then,[ (x+250)/36 ]= 20
=> x + 250 = 720
=> x = 470. Answer: A
Answer: A
Question: If the sum of a set of 5 different positive prime numbers is 94, which of the following prime numbers must be in the set?
Options:
A)2,7,43
B)3,11,31
C)5,71,31
D)7,43,53
E)11,43,31
Rationale: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
Option A
Answer: A