divelab/Sys2Bench huggingface dataset:
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?
Options:
A)90%
B)99%
C)100%
D)101%
E)110%
Rationale: Let the number of employees before Jul 1 be 100
Then Av sal1 = Total1/100
After Jul 1 employees = 90
Av Sal2 = Total 2/90
Now from the question
Av2 = Av1 + 10%
Total 2/90 = Total1/100 + 1/10 * Total1/100
Total 2/90 = 11 Total1/1000
Total 2 = 99 total1/100
Now Percent = Total2/Total1 * 100
= 99 Total1/Total1
= 99
ANSWER:B
Answer: B
Question: The probability that a visitor at the mall buys a pack of candy is 60%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
Options:
A)0.284
B)0.326
C)0.432
D)0.548
E)0.652
Rationale: One case is: candy - candy - no candy
The probability is 6/10*6/10*4/10 = 144/1000
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 144/1000 * 3 = 432/1000 = 0.432
The answer is C.
Answer: C
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 84. what is sum of the numbers?
Options:
A)49
B)56
C)76
D)84
E)85
Rationale: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 84
=> 12x =84
=> x = 84/12 = 7
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 7 = 49
Answer: Option A
Answer: A
Question: Annie has 100 cards numbered 1 through 100. If she deals six cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
Options:
A)95!/100!
B)96!/100!
C)(95! X 6!)/100!
D)(96! X 5!)/100!
E)(97! X 4!)/100!
Rationale: Alex to get 6 consecutive cards in ascending order, to have 6 consecutive at the end is good enough.
There are 95 consecutive numbers in 100: {1, 2, 3, 4, 5,6}, {2, 3, 4, 5, 6,7}, ..., {95,96, 97, 98, 99, 100};
Total ways to pick 6 cards out of 100 is {6!*95!}{100!}.
Answer: C
Answer: C
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Options:
A)399
B)240
C)882
D)378
E)2131
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer: B
Answer: B
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 12 years now, the son's age five years back was:
Options:
A)3 years
B)7 years
C)1 years
D)6 years
E)5 years
Rationale: Let the son's present age be x years.
Then, (12 - x) = x
2x = 12 => x = 6
Son's age 5 years back = (6 - 5) = 1 years.
ANSWER:C
Answer: C
Question: Convert 200 inches into centimeter?
Options:
A)512cm
B)520cm
C)508cm
D)510cm
E)554cm
Rationale: 1 inch = 2.54cm
200 inches = 200*2.54 = 508cm
Answer is C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)180m
B)180m
C)287m
D)216m
E)865m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: B
Question: A seller of used cars has 18 cars to sell and each of his clients selected 3 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
Options:
A)8
B)10
C)12
D)18
E)16
Rationale: IfNo caris selected more than once then the number of clients = 18/3 = 6
But since every car is being selected three times so No. of Clients must be thrice as well = 6*3 = 18
Answer: option D
Answer: D
Question: A train 400 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)22 kmph
B)77 kmph
C)54 kmph
D)71 kmph
E)90 kmph
Rationale: S = 400/16 * 18/5 = 90 kmph
Answer:E
Answer: E
Question: Every length in a 45°-45°-90° triangle increases by 20%. By what percent does the area of the triangle increase?
Options:
A)20%
B)25%
C)40%
D)44%
E)80%
Rationale: The irony of this question is, of course, the specifics of the shape don’t matter at all. Yes, in general it is a good idea to be familiar with the 45°-45°-90° triangle —- if you’re not, see this post —– but none of that matters here.
We have a 20% increase, so that’s a multiplier of 1.2, which means k = 1.2. The multiplier for area would be k^2 = (1.2)^2 = 1.44, which is the multiplier for a 44% increase. That’s the percent increase in area. Answer = D
Answer: D
Question: fill in the blank space.
2, 7, 14, 23, ?, 47
Options:
A)31
B)28
C)34
D)38
E)42
Rationale: The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Missing Number = 23 + 11 = 34.
Answer : C.
Answer: C
Question: In a river flowing at 2 km/hr, a boat travels 56 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
Options:
A)10 hours
B)12 hours
C)14 hours
D)21 hours
E)None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 56 km
Total time taken = Time taken downstream + Time taken upstream
= (56/8) + (56/4) = 21 hr. Answer : Option D
Answer: D
Question: If x/y = 5/z, then 25y^2 =
Options:
A)x²z²
B)3x²
C)(1/9)x²z²
D)x²z
E)x²/9
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 25y²:
x/y = 5/z
x = 5y/z
5y = xz
y = xz/5.
If we substitute xz/5 into the expression for y, we get:
25(xz/5)² = 25(x²z²/25) = x²z².
The correct answer is choice (A)
Answer: A
Question: he number of sequences in which 3 players can throw a ball, so that the youngest player may not be the last is?
Options:
A)81
B)10
C)4
D)6
E)8
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 2 players. The first 6 players can throw the ball in 2P2 ways.
The required number of ways = 2(2!) = 4
Answer:C
Answer: C
Question: Mary and John can do a piece of work in 24 day; John and Vino in 30 days;Vino and Mary in 40 days. If Mary, John and Vino work together they will complete work in ?
Options:
A)77
B)20
C)27
D)19
E)17
Rationale: Explanation:
Given that
Mary and John take 24 days; i.e., (Mary + John)'s 1 day's work = 124124
John and Vino take 30 days; i.e., (John + Vino)'s 1 day's work = 130130
Vino and Mary take 40 days; i.e., (Vino + Mary)'s 1 day's work = 140140
Adding above 3 equations, we get,
[(Mary + John) + (John + Vino) + (John + Vino)]'s 1 day's work = 124+130+140124+130+140
2((Mary + John + Vino)'s 1 days work = 124+130+140124+130+140
2(Mary + John + Vino)'s 1 days work = 5+4+31205+4+3120 = 110110
Therefore, (Mary + John + Vino)'s 1 days work = 120120
i.e., Mary, John and Vino together can complete the work in 20 days.
Answer: B
Answer: B
Question: The main line train starts at 5.00AM and the harbor line train starts at 5.02AM.Each train has the frequency of 10 minutes. If a guy goes in the morning at a random time what is the probability of he getting main line train?
Options:
A).5
B)0.6
C)0.4
D)0.7
E)0.8
Rationale: out of 10 minutes there is only 2 minutes chance of getting harbour line train and there is 8 minutes chance for getting main line train.
So, probability = 8/10 = 0.8
ANSWER:E
Answer: E
Question: Simplify 64552 * 999
Options:
A)12456899
B)23647895
C)64487448
D)03688445
E)23614895
Rationale: Explanation:
Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
64552 * (1000 - 1) = 64552000 - 64552 = 64487448
Answer: Option C
Answer: C
Question: How many pieces of 0.42 meteres can be cut from a rod 36.5 meteres long
Options:
A)30
B)40
C)86
D)89
E)95
Rationale: Explanation:
We need so simple divide 36.5/0.42,
=(3650/42) = 86
Option C
Answer: C
Question: The third largest prime number is?
Options:
A)11
B)13
C)5
D)7
E)23
Rationale: The third largest prime number is 11.
A)
Answer: A
Question: Albert borrowed a total of $ 6000 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
Options:
A)$210
B)$630
C)$441
D)$694
E)$684
Rationale: Money from Brian = x
Money from Charlie = 6000 -x
1494 = 3 [ x (0.07) + (6000-x) (0.09)]
Solve for x, x = 2100
Interest paid to Brian = 2100 * 0.07 * 3 = 441
ANSWER:C
Answer: C
Question: In a rectangular coordinate system, if a line passes through the points (-15,-18), (15,22) and (x,2) then what is the value of x?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: The slope of the line m is rise/run = 22-(-18) / 15-(-15) = 4/3
4/3 = 22-2 / 15-x
60-4x = 66-6
x = 0
The answer is C.
Answer: C
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.400 more. What was the Sum?
Options:
A)s.1200
B)s.800
C)s.1400
D)s.1000
E)s.920
Rationale: At 5% more rate, the increase in S.I for 10 years = Rs.400 (given)
So, at 5% more rate, the increase in SI for 1 year = 400/10 = Rs.40/-
i.e. Rs.40 is 5% of the invested sum
So, 1% of the invested sum = 40/5
Therefore, the invested sum = 40 × 100/5 = Rs.800 Answer: B
Answer: B
Question: Two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)22 sec
B)23 sec
C)76 sec
D)20 sec
E)66 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 180 + 280 = 400 m.
The time required = d/s = 460/20 = 23 sec.
Answer:B
Answer: B
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord E, in feet?
Options:
A)30
B)25
C)15
D)10
E)5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
E=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D
Answer: D
Question: Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
Options:
A)360 cc
B)60 cc
C)300 cc
D)36 cc
E)39 cc
Rationale: r1 = x r2 = 3x
Π * x2 * h = 40
Π9 x2h = 40 * 9 = 360
ANSWER:A
Answer: A
Question: Tough and Tricky questions: Number Properties.
If (z + 3)/7 is an integer, what is remainder when z is divided by 7?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Assume the answer choices as the value of z
7/7=1
Ans D
Answer: D
Question: K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?
Options:
A)16
B)20
C)25
D)40
E)It cannot be determined from the information given.
Rationale: K = 1000a + 100b + 10c + d
L = 1000p + 100q + 10r + s
also W = 16 = 2^4 now when u equate this value
u will get a=p c=r d=s and b-q = 4 as u will have to equate the powers.
now put that in value of z you will get 10*4 = 40
ANSWER:D
Answer: D
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)1 years
B)7 years
C)6 years
D)8 years
E)9 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
Answer: C
Answer: C
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 30 ?
Options:
A)4
B)5
C)3
D)2
E)1
Rationale: Denote |x - 3| as y: y^2 + y = 30 --> y = -6 or y = 5. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.
y = |x - 3| = 5 --> x = 8 or x = -3. The sum = 5.
Answer: B.
Answer: B
Question: A collection of books went on sale, and 2/3 of them were sold for $4.25 each. If none of the 30 remaining books were sold, what was the total amount received for the books that were sold?
Options:
A)$260
B)$255
C)$285
D)$290
E)$275
Rationale: If 30 books constitute 1/3rd of the total, then 2/3rd of the total = 60 books
Amount received for sold books = 60 * 4.25 = $255
Answer : B
Answer: B
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 2 club members, how many members does the club have?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let, Total members = n
@n=2, no. of ways to select 2 out of 2(A,B) = (AB) = 1
@n=3, no. of ways to select 2 out of 3(A,B,C) = (AB, AC, BC) = 2+1 = 3
@n=4, no. of ways to select 2 out of 4(A,B,C,D) = (AB, AC, AD, BC, BD, CD) = 3+2+1 = 6
i.e. @n=5, Total Selection of 2 = 4+3+2+1 = 10
i.e. @n=6, Total Selection of 2 = 5+4+3+2+1 = 15
i.e. @n=7, Total Selection of 2 = 6+5+4+3+2+1 = 21
i.e. @n=8, Total Selection of 2 = 7+6+5+4+3+2+1 = 28
i.e. @n=9, Total Selection of 2 = 8+7+6+5+4+3+2+1 = 36
Answer: Option E
Answer: E
Question: If abc ≠ 3 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
Options:
A)(1 + bc)/(b + c)
B)(1 – bc)/(b + c)
C)(1 + b + c)/(bc)
D)(1 – b – c)/(bc)
E)(1 – b – c)/(b + c)
Rationale: Answer is D though it took me around 4 minutes to get that.
Answer: D
Question: Ashley and Vity work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vity will be chosen?
Options:
A)1/10
B)3/28
C)2/9
D)1/4
E)1/2
Rationale: I did slightly different and hence obviously ended up with the answer 2/9.
I assumed that because Ashley and Vity have to be chosen, the remaining selection is 3 people from 8.
8C3/10C5= 2/9. Option C.
Answer: C
Question: A women purchased a sofa and a bed for Rs. 12000 &Rs. 8000 respectively. He sold the sofa at a loss of 9% and the bed at a profit of 14%. Overall how much he make a profit.
Options:
A)20
B)10
C)30
D)50
E)40
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 12000(1 - 9/100) = 12000 - 1080
m = 8000(1 + 14/100) = 8000 + 1120
Total SP - Total CP = r + m - (12000 + 8000) = -1080 + 1120 = Rs.40
As this is positive, an overall profit of Rs. 40 was made.
B
Answer: B
Question: An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
Options:
A)5:8
B)3:2
C)6:1
D)8:7
E)5:6
Rationale: Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be 4y and y.
2(3x + 2x) = 2(4y + y)
5x = 5y
x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : 4y * y
= 6x^2 : 4y^2
= 6x^2 : 4x^2
= 6 : 4
= 3 : 2
The answer is B.
Answer: B
Question: A boy has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)30
B)110
C)140
D)130
E)120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30.
A
Answer: A
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)30%
B)35%
C)40%
D)45%
E)None of these
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
ANSWER:C
Answer: C
Question: How many multiples of 9 are there between 18 and 270 ?
Options:
A)12
B)27
C)42
D)61
E)60
Rationale: It should be mentioned whether 18 and 270 are inclusive.
If 18 and 270 are inclusive, then the answer is (270-18)/9+1=29.
If 18 and 270 are NOT inclusive, then the answer is (261-27)/9+1=27.
Since OA is B, then we have NOT inclusive case.
Answer: B
Question: Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
Options:
A)113 miles
B)432 miles
C)456miles
D)887 miles
E)767 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer B
Answer: B
Question: A train covers a distance in 50 min ,if it runs at a speed
of 48kmph on an average.The speed at which the train must run
to reduce the time of journey to 40min will be.
Options:
A)60kmph
B)63kmph
C)57kmph
D)70kmph
E)61kmph
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer is A.
Answer: A
Question: Each child has 2 pencils and 13 Skittles. If there are 15 children, how many pencils are there in total?
Options:
A)30
B)12
C)18
D)22
E)08
Rationale: 2*15=30.Answer is A.
Answer: A
Question: What is the least number which should be added to 2982 so that the sum is exactly divisible by 5, 6, 4, and 3?
Options:
A)14
B)18
C)22
D)26
E)30
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 2982 by 60, the remainder is 42.
The number to be added = 60 - 42 = 18.
The answer is B.
Answer: B
Question: A can finish a work in 18 days and B can do same work in half the time taken by A. then working
together, what part of same work they can finish in a day
Options:
A)1\5
B)1\6
C)1\7
D)1\8
E)None of these
Rationale: Explanation:
Please note in this quesƟon, we need to answer part of work for a day rather than complete work. It was
worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half Ɵme than A]
(A+B)'s one day work =
(118+19)=(1+218)=16
So in one day 1/6 work will be done
Answer: B
Answer: B
Question: A and B can do a piece of work in 7 days, B and C in 8 days, C and A in 9 days. How long will C take to do it?
Options:
A)14.1 days
B)18.8 days
C)21.4 days
D)24.3 days
E)26.5 days
Rationale: 2c = 1/8 + 1/9 – 1/7 = 47/504
c = 47/1008 => 1008/47 = 21.4 days
The answer is C.
Answer: C
Question: If the radius of a circle is decreased by 50%, find the percentage decrease
Options:
A)22
B)099
C)75
D)26
E)18
Rationale: Let original radius = R.
New radius = =
Original area = and new area =
Decrease in area = = 75%
Answer: C
Answer: C
Question: The batting average of a particular batsman is 63 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Options:
A)179
B)208
C)210
D)223
E)248
Rationale: Explanation:
Total runs scored by the batsman = 63*46 = 2898 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2898 – 2552 = 346 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 346
2x = 496
x = 248 runs
ANSWER E
Answer: E
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $203?
Options:
A)1,108
B)2,100
C)2,108
D)2,120
E)2,256
Rationale: I think it should be D.
I can buy 8 250-pack for Rs 22.95*8 = $183.60
Now, I can buy 6 20-pack for 3.05*5 = $18.30
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*5 = 2120
Answer: D
Question: If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively.
2(60+p+60+q)= 240 + 2(p + q).
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 40 up to 76.
There can be 4 possibilities for the tens digit.
The answer is C.
Answer: C
Question: The sum of two numbers is 25 and their difference is 13. Find their product.
Options:
A)104
B)114
C)315
D)325
E)335
Rationale: Let the numbers be x and y.
Then x + y = 25 and x - y = 13.
x = 19; y = 6
xy = 19 * 6 = 114
ANSWER: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 14 members of this sequence?
Options:
A)878
B)900
C)560
D)928
E)1022
Rationale: I would split them up like this.
23 28 33 and so on (7 terms)....the 7th term = 23+6*5 = 53
27 32 37 and so on (7 terms)......the 7th term = 27+6*5 = 57
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+53)/2 * 7 =266
(27+57)/2 * 7 = 294
= 560
C
Answer: C
Question: If Jesse flips a coin seven times in a row, what is the probability that the result will not be tails for more than 2 times?
Options:
A)21/128
B)29/128
C)35/128
D)1/16
E)1/4
Rationale: Not more than 2 times tails = at least 5 times heads
Atleast 5 heads in 7 flip.
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHHHHTT
HHHHHHT
HHHHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHHHTT = [7!]/5!*2! = 21
HHHHHHT = [7!]/6! = 7
HHHHHHH = [7!]/[7!] = 1
Sum = 21+7+1 = 29/128
Answer - B
Answer: B
Question: In the xy-coordinate system, if (m, n) and (m + 1, n + k) are two points on the line with the equation x = 2y + 5, then k =
Options:
A)1/2
B)1
C)2
D)5/2
E)4
Rationale: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+1 =2 *(n+k)+5.
By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k+4 ---> 5=2k+4 --->k=1/2.
The answer is, therefore, (A).
Answer: A
Question: Deepa started a business in 2009 by investing Rs.50,000. She invested Rs. 20,000 as additional amount in 2010 and her friend Sushma joined her with an amount of Rs.70,000. Deepa invested another Rs. 20,000 in 2011 and Avanthi joined them with Rs. 70,000. At the end of these 3 years, they earned a profit of Rs. 3,00,000. Find Sushma's share ?
Options:
A)Rs.1,00,229
B)Rs.1,00,209
C)Rs.1,00,012
D)Rs.1,00,000
E)Rs.1,00,109
Rationale: Deepa invested Rs.50,000 for 12 months, Rs.(50000 + 20000) for 12 months and Rs.(50000 + 20000 + 20000) for 12 months.
i.e, she invested Rs.50,000 for 12 months, Rs.70000 for 12 months and Rs.90000 for 12 months.
Sushma invested Rs. 70000 for 2 years; i.e, Rs.70000 for 24 months
And, Avanthi invested Rs.70000 for 1 year; i.e, Rs. 70000 for 12 months.
Their investing ratio:
Deepa : Sushma : Avanthi = (50,000 x 12 + 70000 x 12 + 90000 x 12):(70000 x 24):(70000 x 12)
= (25,20,000):(16,80,000):(8,40,000) = 252:168:84 = 3:2:1
Total profit for 3 years = Rs.3,00,000
Therefore, Sushma's share = Rs.(3,00,000 x 2 /(3+2+1)) = Rs.(3,00,000 x 2/6) = Rs.1,00,000.
Answer: D
Answer: D
Question: The ratio of the volumes of two cubes is 8: 27 What is the ratio of their total surface areas?
Options:
A)2:4
B)3:6
C)4:12
D)4:9
E)1:3
Rationale: Ratio of the sides = Â³âˆš8 : Â³âˆš27
= 2 : 3
Ratio of surface areas =4:9
Answer: D
Answer: D