divelab/Sys2Bench huggingface dataset:
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
Options:
A)13
B)31
C)49
D)53
E)67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
53
Answer: D
Answer: D
Question: A cube of side 1.5 meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)2878
B)3375
C)1000
D)2997
E)2701
Rationale: Along one edge, the number of small cubes that can be cut
= 150/10 = 15
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 15 * 15 * 15= 3375
Answer: B
Answer: B
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.5 years, The ratio of the number of boys to the number of girls in the class is
Options:
A)1 : 2
B)2 : 3
C)9 : 3
D)6 : 3
E)2 : 5
Rationale: Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.5 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.5) <=> k = 0.3/0.6 = 1/2.
Required ratio = 1/2 : 1 = 1 : 2.
Answer: A
Answer: A
Question: Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $50 per month and Plan B costs $150 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?
Options:
A)25%
B)50%
C)37.5%
D)56.25%
E)75%
Rationale: We can show this algebraically:
If there are A customers with plan A, and B customers with plan B, then the total revenue is $50A + $150B.
Since the average customer pays $100, we know that
$100 = ($50A + $150B) / (A + B)
$100(A + B) = ($50A + $150B)
$100A + $100B = $50A + $150B
$50A = $50B
A = B.
Since there are Equal times as many $50 clients as $150 clients, for every $150 received from Plan B customers, $50 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$50/($50 + $150) = $50/$200 = 25%.
The correct answer is choice (A).
Answer: A
Question: There are 456 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
Options:
A)264
B)209
C)57
D)171
E)181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 456 = 264
ANSWER:A
Answer: A
Question: The true discount on a bill of Rs. 540 is Rs. 90. The Banker’s discount is
Options:
A)Rs. 60
B)Rs. 108
C)Rs. 110
D)Rs. 112
E)None of these
Rationale: Answer B
Solution
P.W. = Rs. (540-90) = Rs. 450.
∴ S.I on Rs. 450 = Rs. 90
S.I on Rs. 540 = Rs. (90/450x540 ) = Rs. 108.
∴ B.D. = Rs. 108 Answer B
Answer: B
Question: (1/34)+(1/35)+……+(1/64)+(1/65) is including in which of the following ranges?
Options:
A)1/2~1
B)1
C)2
D)3
E)4
Rationale: Number of terms in the given series = 32.
The lowest term is 1/65 , the largest being 1/34.
Thus, the sum of the given series will be more than
1/65 + 1/65.....1/65 (32 times)
---> 32*(1/65) = 32/65 and
less than 1/34 + 1/34...... 1/34 (32 times)
---> 32*(1/34) = 32/34 = 1 (approx)
Ans 1/2~ 1
A
Answer: A
Question: The S.I. on a certain sum of money for 2 years at 4% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Options:
A)5250
B)1267
C)5750
D)2267
E)5262
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 5250
Answer:A
Answer: A
Question: The speed of a boat in still water is 90kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)40, 68 kmph
B)110, 70 kmph
C)90, 60 kmph
D)40, 60 kmph
E)20, 60 kmph
Rationale: Speed downstream = 90 + 20 = 110 kmph
Speed upstream = 90 - 20 = 70 kmph
Answer: B
Answer: B
Question: If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
Options:
A)0.49
B)0.48
C)0.41
D)0.482
E)0.411
Rationale: Explanation:
Probability that A speaks truth is 80/100 = 0.8
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.8 × 0.6 = 0.48
Answer: B
Answer: B
Question: In the third grade of Windblown School there are 78 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
Options:
A)0.
B)6.
C)8.
D)10.
E)12.
Rationale: Total = 78
failed in math = 78/3=26
failed in literature=78/6=13
the least failed in both can be 0
while max can be 13
Answer A
Answer: A
Question: If 1535/1038 = a+1/[b+1 /{c+(d+1/e)}]. Find a*b*c*d*e?
Options:
A)165/2
B)175/2
C)178/3
D)187 by 2
E)197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+ 1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: D
Question: (469 + 174)(power 2) - (469 - 174)(power 2) / (469 x 174) = ?
Options:
A)174
B)178
C)171
D)176
E)170
Rationale: Formula = (a + b)(power 2) - (a - b)(power 2) / ab
= 4ab/ab
= 4 (where a = 469, b = 174.)
Answer is A.
Answer: A
Question: Which of the following numbers is divisible by 11?
Options:
A)4424
B)2232
C)1522
D)8524
E)9515
Rationale: 9515. This is the only option with last two digits divisible by 11
Answer:E
Answer: E
Question: A no. Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
Options:
A)1/5
B)2/5
C)3/7
D)3/11
E)2/7
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
C
Answer: C
Question: Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 2. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Options:
A)3, 8, 24
B)7, 9, 17
C)6, 9, 12
D)5, 15, 18
E)9, 10, 13
Rationale: I didnt get your point on eliminating B.
The number of stamps only one purchased was divisible by 2.Could that not be Cecilia with 7 stamps.
I choose this and marked B.
Answer: B
Question: Two partners in a business (James and Kelly) invested $900 and $1600 in a business respectively. At the end of the year they made a profit of $950. Find share of each partner?
Options:
A)$352,$657
B)$392,$608
C)$342,$408
D)$342,$608
E)$347,$608
Rationale: A:B = 900:1600
A:B = 9 : 16
A's share = 950*9/25 = $342
B's share = 950*16/25 = $608
Answer is D
Answer: D
Question: Jason flips a coin three times. What is the probability X that the coin will land on the same side in all three tosses?
Options:
A)1/16
B)1/8
C)1/4
D)1/3
E)1/2
Rationale: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability X is 2/8 or 1/4.C
Answer: C
Question: The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
Options:
A)15
B)29
C)64
D)39
E)35
Rationale: 29 matches
because each match will result in removing a player.
ANSWER:B
Answer: B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)228
B)240
C)887
D)166
E)1811
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: B
Question: IN Common Wealth Games an athlete runs 200 meters in 30 seconds. Hisspeed is ?
Options:
A)24 km/hr
B)27 km/hr
C)30 km/hr
D)32 km/hr
E)None of these
Rationale: Explanation :
(200/1000)/(30/3600)=24 km/hr
Answer : A
Answer: A
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children A & B must sit next to each other, and child C must be somewhere to the right of A & B. How many possible configurations are there for the children?
Options:
A)600
B)720
C)1440
D)4320
E)4800
Rationale: First, consider the restriction of A & B. As with problem #1 above, there are 12 possibilities for A & B, counting both position and order.
Now, put the other five in any order — that’s 120 possibilities, for a total number of configurations of 1440. That number does not take into account the restriction with C.
Think about those 1440 configurations. In exactly half of them, C will be to the right of A & B, and exactly half, C will be to the left of A & B. Therefore, in (1/2)*1440 = 720 configurations, C will be to the right of A & B.
Answer = B
Answer: B
Question: January 25, 2014, fell on a Saturday. On which day of the week did January 25, 2016, fall? (Note: 2016 was a leap year.)
Options:
A)Sunday
B)Monday
C)Tuesday
D)Wednesday
E)Thursday
Rationale: There are 365 days in a non-leap year, and 366 in a leap year.
365 / 7 = 52 remainder 1, so for every non-leap year the day of the week advances by 1.
January 25, 2014 = Saturday
January 25, 2015 = Sunday
January 25, 2016 = Monday
Even though 2016 is a leap year, with 366 days, the extra day does not come into play until February 29. Since the date range in question did not contain February 29, 2016, the day of the week only advances 1 day for 2016.
The answer is B.
Answer: B
Question: A person buys an article at $800. At what price should he sell the article so as to make a profit of 12%?
Options:
A)896
B)890
C)990
D)789
E)740
Rationale: A
896
Cost price = $800
profit = 12% of 800 = $96
Selling price = Cost price + Profit
= 800 + 96 = 896
Answer: C
Question: How many T ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
Options:
A)120
B)240
C)360
D)540
E)720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways T=> 2*5*4*3*2*1 = 240.B
Answer: B
Question: If the sum of all consecutive integers from A to B (A<B), inclusive, is S and the average (arithmetic mean) of these integers is M, then, in terms of A, B, and S, what is the value of M?
Options:
A)2S/(A+B+1)
B)2S/(A+B)
C)(B−A)/2
D)S/(B−A+1)
E)(B−A)/(2S)
Rationale: Mean=sum of all the terms /number of terms
We already know the sum which is given as S.
We need the number of terms which needs to be calculated.
Since this is evenly placed set (set of consecutive numbers forms an AP with common difference of 1)
Number of terms in an AP is given by : Last term−first term common difference+1
Using this , we get the number of terms as : B - A + 1 (d = 1 in this case)
Hence the answer is: M=S/(B−A+1);
ANSWER:D
Answer: D
Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one third that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
Options:
A) d
B) 1/3*d
C) 1/2*d
D) 3/4*d
E) 2/3*d
Rationale: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d/3
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (d+d/3)/2
= 4/6*d= 2/3 * d
We find that option E is the answer as it gives the same expression as found in our calculation above. Answer option E.
Answer: E
Question: What is the place value of 4 in the numeral 488?
Options:
A)40
B)400
C)4
D)4000
E)20
Rationale: place value of 4 = 4 * 100 = 400
Answer is B
Answer: B
Question: If x <<< 1000, then the value of (x-1)/(3x+1) is closest to?
Options:
A)1/5
B)1/7
C)1/2
D)1/3
E)1/4
Rationale: since x <<< 1000
assume x = 400
(x-1)/(3x+1) = 399 / (400*3+1)
=399 / 1201
= = 1/3
Ans - D
Answer: D
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages.
Options:
A)20,35,45
B)8,20,28
C)16,28,36
D)16,28,46
E)None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 56
20K = 80
K = 4
Therefore, then present ages are 16,28,36.
ANSWER:C
Answer: C
Question: Two trains 100 meters and 120 meters long are running in the same direction with speeds of 100 km/hr, 82 km/hr. In how much time will the first train cross the second
Options:
A)37 sec
B)35 sec
C)48 sec
D)44 sec
E)36 sec
Rationale: Explanation:
Relative speed of the trains = (100 - 82) km/hr = 18 km/hr
= (18Ã— 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.
Answer: Option D
Answer: D
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.20000, my total savings for the two-year is
Options:
A)s. 8000
B)s. 9000
C)s. 9900
D)s. 9990
E)s. 11000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (20000 + 35000)
= 66000 - 55000 = Rs. 11000
E
Answer: E
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
Options:
A)7000
B)8000
C)9000
D)10000
E)11000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer: B
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
Options:
A)42
B)20
C)72
D)54
E)43
Rationale: The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
ANSWER C 72
Answer: C
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
Options:
A)100% decrease
B)50% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: CA: Concentration A
CB: Concentration B
R: Reaction rate
Formula for reaction rate:
R = (CA^2) / CB
Thus if CB is increased by 100% >> means concentration doubles >> 2xCB
Thus, for R to remain the same (CA^2) also has to double.
>> 2 x (CA^2) >> to see what happens to CA, take the 2 into the bracket by taking its root
>> (SQRT 2 CA)^2
SQRT 2 is roughly 40% >> answer D
Answer: D
Question: A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction?
Options:
A)10%
B)5%
C)12%
D)6%
E)4%
Rationale: In such a case there is always a loss
Loss% = (20/10)^2 = 4%
Answer is E
Answer: E
Question: 3/5 of all married couples have more than one child. 1/4 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?
Options:
A)1/5
B)B.1/4
C)7/20
D)3/5
E)It cannot be determined from the given information.
Rationale: Plug in simple numbers. Take 100 couples for example.
3/5 of 100 couples have more than one child = 60 couples.
1/4 of 100 couples have more than 3 kids = 25 couples.
This implies that 25 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 40 couples have either one or no kids at all.
We need to find couples that have 2 or 3 kids, so essentially, it is 60 - 25 = 35. Fraction will be 35/100 = 7/20.
Option C
Answer: C
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 1:2. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
Options:
A)7:18
B)9:23
C)10:17
D)23:54
E)31:77
Rationale: M = 4/9 of total games
N = 5/9 of total games
Wins = 1/3*4/9 + 2/5*5/9 = 4/27 + 6/27 = 10/27
Losses = 1 - 10/27 = 17/27
The ratio of wins to losses is 10:17.
The answer is C.
Answer: C
Question: If Clara owns 7 boxes of cardboard of the 12 boxes placed on a table, and 2 boxes are to be picked from the table at random, what is the probability that the boxes picked at random are not Clara's?.
Options:
A)5/33
B)4/33
C)7/33
D)2/7
E)7/12
Rationale: Since Clara owns 7 of the boxes, the subset from which the boxes should be chosen are the 5 pictures not owned by clara from the universe of 12.
The first picture can be one of the 5 from the 12 with probability 5/12
The second picture can be one of the 4 from the 11 remaining with probability 4/11
The total probability will be 5/12 × 4/11. On cancellation, this comes to 5/33.
Thus, the answer is A - 5/33.
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 45% but the selling price
remains constant, approximately what percentage of the selling price is the profit
Options:
A)65%
B)80%
C)90%
D)100%
E)None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 145% of Rs. 100 = Rs. 145
New S.P. = Rs. 420.
Profit = Rs. (420 - 145) = Rs. 275
Required percentage = (275/420) * 100
= 65.4% = 65%(approx)
Answer: A
Answer: A
Question: A and B invest money in the ratio 3:4 and they has loss of Rs.7000 at the end of year. what is the share of loss of B?
Options:
A)Rs.4000
B)Rs.3000
C)Rs.7000
D)Rs.2000
E)None of the above
Rationale: et ratio of A and B be 3x & 4x
so net loss = 3x+4x= 7000
x=1000
A=3x=3(1000)=3000
B= 4x=4(1000)=4000
so, B= 4000
ANSWER:A
Answer: A
Question: If a man lost 4% by selling oranges at the rate of 60 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)11
B)28
C)39
D)40
E)43
Rationale: 96% ---- 60
144% ---- ?
96/144 * 60 =40
Answer: D
Answer: D
Question: One decade ago, X was half of Y in age. If the proportion of their current ages is 3:4, what will be the overall of their current ages?
Options:
A)35 years
B)44 years
C)76 years
D)55 years
E)43 years
Rationale: A
35 years
Let the ages of X and Y 1 decade ago be A and 2A years correspondingly.
Then, [ (A +10)/2A+10) ] = (3/4)
4 (A – 10) = 3(2A – 10)
2A = 10
A = 5
Therefore,
Sum of theircurrent ages = (A + 10) + (2A + 10) = (3A + 20)
= 35 years.
Answer: A
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
Options:
A)$500
B)$600
C)$700
D)$800
E)$900
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800
correct answer D
Answer: D
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly 6 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.
(x+1.5x)*6 = 2.5x*6 = 15x, which is the capacity of the whole pool.
Working alone:
1.5x*Time = 15x
Time = 15/1.5 = 10 hours
The answer is D.
Answer: D
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 48¢?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 48, the ratio should be 2:3.
Mary must put back 5 oranges.
The answer is E.
Answer: E
Question: Find large number from below question The difference of two numbers is 250. On dividing the larger number by the smaller, we get 5 as quotient and the 14 as remainder
Options:
A)120
B)135
C)140
D)309
E)369
Rationale: Let the smaller number be x. Then larger number = (x + 250).
x + 250= 5x + 14
4x = 236
x = 59
Large number = 59+250 = 309
D
Answer: D
Question: Entry fee in an exhibition is $1. Later this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is?
Options:
A)20%
B)40%
C)50%
D)60%
E)100%
Rationale: Let the total original sale be $100
Then original number of visitors = 100
New number of visitors = 120/0.75 = 160
Increase % = 60%
Answer is D
Answer: D
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)17 Kmph
B)26 Kmph
C)72 Kmph
D)66 Kmph
E)41 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Answer: C
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability R that Kate has more than $10 but less than $15?
Options:
A)5/16
B)1/2
C)R=12/30
D)R=15/32
E)R=3/8
Rationale: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32.D
Answer: D
Question: An escalator moves towards the top level at the rate of 8 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.
Options:
A)14 sec
B)10 sec
C)16 sec
D)8 sec
E)9 sec
Rationale: Time taken to cover the entire length = tot.dist/resultant speed
= 160/ (8+2)
= 16sec
ANSWER:C
Answer: C
Question: Evaluate: 10010 - 12*3*2 = ?
Options:
A)30002
B)70002
C)50002
D)90002
E)10002
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
10010 - 12*3*2 = 10010 - 8 = 10002
correct answer E
Answer: E