divelab/Sys2Bench huggingface dataset:
Question: On Thursday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
Options:
A)Monday
B)Wednesday
C)Thursday
D)Friday
E)Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Thursday, 3rd day is Sunday. Next day, which he won't have a new combination for, is Monday. (A)
Answer: A
Question: A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees?
Options:
A)A)182
B)B)208
C)C)220
D)D)224
E)E)302
Rationale: If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 181
x = 208
So the original number of employees is 208
Correct Answer - B
Answer: B
Question: The sale price sarees listed for Rs.500 after successive discount is 10% and 5% is?
Options:
A)427.5
B)879
C)342
D)762
E)269
Rationale: 500*(90/100)*(95/100)
= 427.5
Answer: A
Answer: A
Question: John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?
Options:
A)No loss or gain
B)Gain of $400
C)Loss of $400
D)Gain of $800
E)Loss of $800
Rationale: Cost of the profitable stock: x=96/1.2=80, so profit from it 96-80=16. Total profit 50*16=800
Cost of the non-profitable stock: y=96/0.8=120, so loss from it 96-120=-24. Total loss 50*(-24)=-1200
Total loss: 800+(-1200)=-400.
Answer: C.
Answer: C
Question: Suppose son name is 120,his brother name is 150 and his mother name is 180.find out his father's name???
Options:
A)190
B)210
C)230
D)240
E)250
Rationale: since difference between all name is =30
so father's name will be 180+30=210.
ANSWER:C
Answer: C
Question: If A lends Rs.2500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
A. Rs.107.50
Options:
A)112.5
B)122.5
C)132.5
D)114.5
E)212.5
Rationale: (2500*1.5*3)/100 => 112.50
ANSWER:A
Answer: A
Question: Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 3. Find the larger integer.
Options:
A)4
B)24
C)30
D)72
E)80
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.
If adding 6 to the smaller integer makes the ratio 1 to 3, then 3(x+6)=y.
Substituting y=4x into the second equation yields 3x+18=4x.
So, x=18 (smaller integer) and, y=4x=72 (larger integer) so D is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 4
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 1
If 6 is added to the smaller number, the ratio becomes 1 to 3
If we add 6 to the smaller number (1), we get 7.
So, the new ratio is 7 to 4.
No good. We want a resulting ratio of 1 to 3
ELIMINATE A
B) the larger number is 24
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 6
If 6 is added to the smaller number, the ratio becomes 1 to 3
If we add 6 to the smaller number (6), we get 12
So, the new ratio is 12 to 24 which is 1 to 2.
No good. We want a resulting ratio of 1 to 3
ELIMINATE B
C) the larger number is 30
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 7.5 (which is not an integer)
Since both numbers are integers, the larger number cannot be 30.
ELIMINATE C
D) the larger number is 72
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 18
If 6 is added to the smaller number, the ratio becomes 1 to 3
If we add 6 to the smaller number (18), we get 24
So, the new ratio is 24 to 72. This is the same as the ratio of 1 to 3
Therefore (D) is correct
E) the larger number is 80
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 20
If 6 is added to the smaller number, the ratio becomes 1 to 3
If we add 6 to the smaller number (20), we get 26
So, the new ratio is 26 to 80 which is 13 to 40.
No good. We want a resulting ratio of 1 to 3
ELIMINATE E
Therefore D is the only correct choice.
Answer: D
Question: The daily hotel rates for five hotels John was considering were $60, $125, $80, $70 and $x. If the median price was $5 lower than the average (arithmetic mean) price, which of the following could be $x?
Options:
A)$80
B)$85
C)$90
D)$95
E)$100
Rationale: Look at the options available
Value of x seems to $80 < = $x < = $100
A. $80
B. $85
C. $90
D. $95
E. $100
So position of $x is fourth
$60 , $70 , $80 , $x , $125
Median = $80
Median price was $5 lower than the average, so average = $85
$60 + $70 + $80 + x + $125 = $425
$x = $90 = Answer = C
Answer: C
Question: A 440-liter solution of Kola is made from 88% water, 8% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
Options:
A)4.52%.
B)7.5%.
C)9.2%.
D)10.5%.
E)11%.
Rationale: Denominator:
440+10+3.2+6.8=460
Numerator:
440(1-.88-.08)+3.2
440(0.04)+3.2
17.6+3.2
20.8
Ratio:
20.8/460=0.045
Answer: A
Answer: A
Question: For every positive integer n, form the number n / s(n), where s(n) is the sum of the digits of n in base 10. What is the minimum value of n/s(n) for 10 <= n <= 99.
Options:
A)1.2
B)3.45
C)1.9
D)2
E)4
Rationale: possibility to sum of digits 10
i.e
(1.9),(2,8),(3,7),(4,6),(5,5)
we get s/s()n are 1.9,2.8,3.7,4.6,5.5
so the minimum possibility of s/s(n)=19/10=1.9
ANSWER:C
Answer: C
Question: In one hour,a boat goes 11 km along the stream and 5 km against the stream.The speed of the boat in still water is :
Options:
A)3
B)5
C)8
D)9
E)10
Rationale: Solution
Speed in still water =1/2(11+5) kmph = 8 kmph.Answer C
Answer: C
Question: The cost price of a radio is Rs.1680 and it was sold for Rs.1450, find the loss %?
Options:
A)18
B)13
C)15
D)18
E)41
Rationale: 1680 ---- 230
100 ---- ? => 13%
Answer: B
Answer: B
Question: Out of 15 students in a class, 10 are wearing blue shirts, 2 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
Options:
A)10/21
B)20/31
C)30/41
D)40/51
E)50/61
Rationale: Total possible ways to choose 4 students out of 15 = 15C4 = 1365
The number of ways to choose 4 students with no green shirts = 13C4 = 715
P(no green shirts) = 715/1365 = 11/21
P(at least 1 green shirt) = 1 - 11/21 = 10/21
The answer is A.
Answer: A
Question: Cole drove from home to work at an average speed of 80 kmh. He then returned home at an average speed of 120 kmh. If the round trip took a total of 3 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)85
E)108
Rationale: First round distance travelled (say) = d
Speed = 80 k/h
Time taken, T2 = d/80 hr
Second round distance traveled = d (same distance)
Speed = 120 k/h
Time taken, T2 = d/120 hr
Total time taken = 3 hrs
Therefore , 3 = d/80 + d/120
LCM of 80 and 120 = 240
3= d/80 + d/120
=> 3 = 3d/240 + 2d/240
=> d = 240 * 2/ 5 Km
Therefore, T1= d/80
=> T1 = (240 *3) / (5 x 80)
=> T1 = (9 x 60) / 5 -- in minutes
=> T1 = 108 minutes.
E
Answer: E
Question: On a sum of money, the S.I. for 2 years is $600, while the C.I. is $612, the rate of interest being the same in both the cases. The rate of interest is?
Options:
A)3%
B)4%
C)5%
D)6%
E)7%
Rationale: Difference in C.I. and S.I for 2 years = $612 - $600 = $12
S.I for one year = $300
S.I. on $300 for 1 year = $12
Rate = (100 * 12)/(300) = 4%
The answer is B.
Answer: B
Question: The sum of number of boys and girls in a school is 300. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
Options:
A)50
B)40
C)60
D)100
E)75
Rationale: We have x+x% of 300 = 300
x + x/100 * 300 = 300
4 * x = 300
x = 75
Answer is E
Answer: E
Question: John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.8 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
Options:
A)13 seconds
B)17 seconds
C)26 seconds
D)34 seconds
E)42.5 seconds
Rationale: Let t be the time that John spent for his final push.
Thus, per the question,
4.2t = 3.8t+15+2 ---> 0.4t = 17 ---> t = 42.5 seconds.
E is the correct answer.
Answer: E
Question: In a box of 8 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)6/11
B)8/15
C)9/20
D)11/25
E)15/28
Rationale: P(neither pen is defective) = 6/8*5/7 = 15/28
The answer is E.
Answer: E
Question: âˆš1.5625 = ?
Options:
A)1.05
B)1.25
C)1.45
D)1.55
E)1.65
Rationale: Explanation:
1|1.5625( 1.25
|1
|-------
22| 56
| 44
|-------
245| 1225
| 1225
|-------
| X
|-------
1.5625 = 1.25.
ANSWER IS B
Answer: B
Question: The sum of three consecutive integers is 312. What is the sum of the next three consecutive integers?
Options:
A)315
B)321
C)330
D)415
E)424
Rationale: a+(a+1)+(a+2)=3a+3=312
(a+3)+(a+4)+(a+5)=(3a+3)+9=312+9=321
Answer: B.
Answer: B
Question: If 20x = 49y, which of the following must be true?
I. x > y
II. x^2 > y^2
III. x/7 is an integer
Options:
A)I only
B)II only
C)III only
D)I and III
E)None
Rationale: For x = 1,y = 20/49 and x>y. However, for x=-49,y = -20 and y>x. I is clearly not the right answer.
For y=0, x=0. Thus, even II doesn't hold good.
x/7 = 7y/20. For y=0, x/7 is an integer, however for y=1, it is not.
None of the options are (must be)true
ANSWER:E
Answer: E
Question: Three hundred gallons of fuel are purchased at $0.90 per gallon. The fuel is consumed at a rate of $0.50 worth of fuel per hour. At this rate, how many hours are required to consume the 300 gallons of fuel?
Options:
A)510
B)520
C)530
D)540
E)550
Rationale: The fuel is consumed at this rate: $0.50/$0.90 = 5/9 gallons per hour.
The time it takes to consume 300 gallons is: 300 / (5/9) = 540 hours.
The answer is D.
Answer: D
Question: An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?
Options:
A)1
B)5
C)11
D)15
E)17
Rationale: Can (85/100 * n) be 1? No because in that case, n will not be an integer.
Can (85/100 * n) be 5? No because in that case, n will not be an integer.
Notice that 85 = 5*17.
So 85/100 = 17/20
(17/20 * n) = 17
n = 20 (an integer)
We will not get n as integer in any of the other options.
ANSWER:E
Answer: E
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(9 (x – y) (y – z) (z – x))
is equal to :
Options:
A)0
B)1/12
C)1
D)1/4
E)1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(9(x – y) (y – z) (z – x)) = 1/3.
ANSWER:E
Answer: E
Question: The least common multiple of positive integer d and 3-digit integer n is 690. If n is not divisible by 3 and d is not divisible by 2, what is the value of n?
Options:
A)115
B)230
C)460
D)575
E)690
Rationale: The LCM of n and d is 690 = 2*3*5*23.
d is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to d.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Answer: B
Question: Two stations A and B are 110 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)18 a.m
B)10 a.m
C)167 a.m
D)18 a.m
E)11 a.m
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) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: B
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets?
Options:
A)420
B)550
C)490
D)450
E)520
Rationale: 10 * 157 = 1570
3 * 100 + 5 * 150 = 1050
1570 – 1050 = 520
Answer:E
Answer: E
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)3 kmph
C)8 kmph
D)7 kmph
E)5 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)79.7
B)79.8
C)76.2
D)79.2
E)29.2
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer:D
Answer: D
Question: Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
Options:
A)1/36
B)1/18
C)1/32
D)1/37
E)None of these
Rationale: Probability of getting yellow color = P(Y) = 3/6 = 1/2
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 2/6=1/3
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 = 1/18
ANSWER:B
Answer: B
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 81 more than n. What is y in terms of x ?
Options:
A) 10 - x
B) 9 - x
C) x + 9
D) x - 1
E) x + 1
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 9 more than 10x+y
10x+y+81=10y+x
10x-x+81=10y-y
9x+81=9y
x+9=y
OR
y=x+9
Ans:C
Answer: C
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)10%
E)none of the above
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680
Gain = (80/1600 * 100)% = 5%
Answer = B
Answer: B
Question: how many such letters pairs r in word FRONTIER having same no. of letters left between them in the word as they have in the series
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: the no of letters between the specific two letters when we write in the alphabetical order should be same as the number of letters between those two letters in the given word
two are possible
1)letters 'o' and 'n'
2)'n' and 'r'......( middle letters are o,p,q i.e 3 letters in alphabetical order & in the given word t,i,e i.e 3 letters)
so 2 such pairs are possible
ANSWER:B
Answer: B
Question: convert 100 miles into inches?
Options:
A)6336000
B)6542000
C)5462300
D)6213000
E)6120330
Rationale: 1 feet = 12 inches
1 mile = 5280 feet
100 mile = 5280*12*100 = 6336000
Ans: A
Answer: A
Question: curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: curie made 5*5 cookies = 25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends.
9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same.
The nearest multiple of 2 is 8.
9-8=1
A is the correct answer
Answer: A
Question: A person want to give his money of $12000 to his 5 children A,B,C,D,E in the ratio 2:4:3:1:5. What is the D+E share?
Options:
A)$1800
B)$2800
C)$3800
D)$5800
E)$4800
Rationale: D's share = 12000*1/15 = $800
D's share = 12000*5/15 = $4000
A+D = $4800
Answer is E
Answer: E
Question: Albert invested amount of 12000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
Options:
A)Rs. 8510
B)Rs. 8620
C)Rs. 8730
D)Rs. 13230
E)None of these
Rationale: Explanation:
=>(12000×(1+5/100)2)
=>12000×21/20×21/20
=>13230
Option D
Answer: D
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 11 and 12. The larger of the two numbers is:
Options:
A)338
B)276
C)322
D)231
E)121
Rationale: Clearly, the numbers are (23 * 11) and (23 * 12). Larger number
= (23 * 12) = 276.
Answer: B
Answer: B
Question: The ratio of buses to cars on River Road is 1 to 3. If there are 20 fewer buses than cars on River Road, how many cars are on River Road?
Options:
A)100
B)120
C)140
D)30
E)150
Rationale: B/C=1/3
C-B=20.........> B=C-20
(C-20)/C=1/3
Testing answers. Clearly Eliminate ABCE
Put C=30.........> (30-20)/30=10/30=1/3
Answer: D
Answer: D
Question: A man can row downstream at 16 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)3
B)5
C)6
D)4
E)9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 16 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 26=> x = 13, y = 3. Answer: A
Answer: A
Question: Agatha has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
Options:
A) 32
B) 30
C) 29
D) 28
E) 27
Rationale: 5n + 10m = 460
n > m
Pick an easy number to work with.
suppose n=30.
Then you have 150.
You need another 310 and that means you need m=31 which is greater than n.
Therefore, n > 30.
The only answer choice where n> 30 is if n = 32.
A is the answer.
Answer: A
Question: A grocery store bought some mangoes at a rate of 4 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
Options:
A)1:4
B)1:5
C)2:3
D)1:2
E)1:2
Rationale: The cost price of a mango = 1/4 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/4 = 1/12 dollars.
The selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/3 - 1/6 = 1/6 dollars.
The profit from one mango from the first stack is 4 times the loss from one mango from the second stack.
the ratio is 1/12*6/1 = 1/2 =1:2
E
Answer: E
Question: The profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?
Options:
A)Rs. 40
B)Rs. 50
C)Rs. 49
D)Rs. 59
E)Rs.64
Rationale: S.P 1- C.P = C.P – S.P 2
86 - C.P = C.P - 42
2 C.P = 86 + 42;
C.P = 128/2 = 64
ANSWER:E
Answer: E
Question: 85 80 25 70 55 25 35 ? ?
Options:
A)10 25
B)25 85
C)35 25
D)85 35
E)25 75
Rationale: 85-5=80
again 25
80-10=70
70-15=55
again 25
55-20=35
35-25=10
again 25
then answer is 10 ,25
ANSWER:A
Answer: A
Question: When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let the number be
2 + 1/2[1/3(a/5)] = a/15
=> 2 = a/30 => a = 60
ANSWER:C
Answer: C
Question: x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: Since smallest possible prime factor is required.
Let x = 2 then --> 2# = 2
x#+7 ==> 2#+7 = 2+7 = 9 = 3*3.
Thus 3 is the smallest possible Prime Factor
2 cannot be the possible prime factor because --> x# is always even since it is product of even numbers
Even +7 = Odd. Hence 2 cannot be prime factor of this result
ANSWER:B
Answer: B
Question: Rs. 875 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 875 become in 3 years ?
Options:
A)Rs. 1020.80
B)Rs. 1025
C)Rs. 1061
D)Data inadequate
E)None of these
Rationale: Solution
S.I. = Rs.(956-875 )=Rs.81
Rate = (100x81/875x3) = 108/35%
New rate = (108/35 +4)% = 248/35%
New S.I. = Rs.(875 x 248/35 x 3/100) Rs. 186.
∴ New amount = Rs.(875+186)= Rs. 1061.
Answer C
Answer: C
Question: 3/4 of 5/7 of a number is greater than 2/3 of 4/7 of the same number by 26. What is half of that number?
Options:
A)32
B)78
C)92
D)84
E)96
Rationale: Let no. be x
3/4*5/7*x - 2/3*4/7*x = 26
by further solving
15x/28- 8x/21= 26
13x/84= 26
x=168
we have to find x/2
=168/2=84
ANSWER:D
Answer: D
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Options:
A)14
B)15
C)16
D)18
E)19
Rationale: Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
5 : 4 :: 20 : x
x = (4 x 20)/5
x = 16 days.
Hence, Tanya takes 16 days to complete the work.
ANSWER:C
Answer: C
Question: The Least Common multiple of 2^6−1 and 2^9−1 is
Options:
A)2^12+27*2^9-217
B)2^ 12 +63*2^3-1
C)2^12+5^29-1
D)2^12+9*2^8 -1
E)None of these.
Rationale: The best approach in my opinion is what Zarroli has suggested above.
LCM * GCF = Product of the numbers = (2^6−1)∗(2^9−1)=(2^3−1)(2^3+1)∗(2^3−1)(2^6+1+2^3)
Notice that the only common factor between them is (23−1)(23−1) so this must be the GCF. Hence LCM will be the rest of the product.
LCM=(2^3+1)∗(2^3−1)(2^6+1+2^3)=(2^6−1)(2^6+1+2^3)
Now how do you get it in the format in the options? Almost all options have 2^12 and 1 so retain those two and club everything else together.
LCM=2^12−1+(2^6+2^9−2^6−2^3)=2^12−1+2^3(2^6−1)=2^12−1+2^3∗63
Answer (B)
Answer: B
Question: Of the diplomats who attended a summit conference: 20 spoke Japanese, 32 did not speak Russian and 20% of the diplomats spoke neither Japanese nor Russian. If 10% of the diplomats spoke both Japanese and Russian, then how many diplomats attended the conference?
Options:
A)70
B)96
C)108
D)120
E)150
Rationale: 2X2 matrix will be the easiest way to calculate this.
Text in black: given statements
Text in red: calculated values
Thus D=120 is the correct answer
Answer: D
Question: A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.
Options:
A)1/7
B)1/2
C)3/7
D)2/3
E)1/3
Rationale: Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2
ANSWER:B
Answer: B
Question: A train 220 m long passed a pole in 12 sec. How long will it take to pass a platform 600 m long?
Options:
A)80
B)45
C)49
D)50
E)56
Rationale: Speed = 220/12 = 18 m/sec.
Required time = (220 + 600)/18 = 45 sec.
Answer: Option B
Answer: B
Question: There are 11 baskets numbered from 1 to 11 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
Options:
A)180
B)220
C)260
D)300
E)340
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8+9+10+11 = 11*12/2 = 66 apples.
The total number of apples taken by 10 children is 10*66 = 660
The number of apples left in the end is 1000 - 660 = 340 apples.
The answer is E.
Answer: E