divelab/Sys2Bench huggingface dataset:
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 49 grams of protein daily, how many grams of food X are in the mixture?
Options:
A)160
B)180
C)200
D)220
E)240
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 49
0.05x = 11
x = 220
The answer is D.
Answer: D
Question: A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. However, already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately, he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90.
What is the overall profit the man makes?
Options:
A)$10
B)$60
C)$20
D)$50
E)$60
Rationale: C
$20
In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10.
In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.
Conclusion: The man makes an overall profit of $10 + $10 = $20.
You can also look at the problem as follows: the total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140 = $20.
Answer: C
Question: A given positive integer is divided by 9 with a remainder of 5. The same integer when divided by 12 has a remainder of 3. What is the remainder if the it integer is divided by 35.
Options:
A)Between 1 and 4, inclusive
B)Between 5 and 7, inclusive
C)Between 8 and 10, inclusive
D)5
E)1
Rationale: Put in real numbers.
Let the integer be x
9x+5= 12x+3
Start 9x+5 -->14, 23, 32,....41...
Of these only 41 fit the description 12x+3. The remainder when divided by 35 is 6. So answer is B).
Answer = B)
Answer: B
Question: In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
Options:
A)15
B)21
C)25
D)30
E)36
Rationale: Total number of entries 6*6(6rows*6columns) =36
Now 6 entries are representing mileage with the city itself so subtract that => 36-6
Minimum entries required = half the Total = 30/2 = 15
ANSWER:B
Answer: B
Question: Which is not a leap year?
Options:
A)2004
B)2012
C)1700
D)1704
E)2008
Rationale: the answer is 1700,
becz if the year is centurial ,that should be divisible by 400 for leap year
ex:400,800,1200
ANSWER:C
Answer: C
Question: Of the 800 employees of Company X, 80 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 70 percent ?
Options:
A)200
B)266.67
C)112
D)80
E)56
Rationale: The # oflong-termemployees is 80%*800=640.
After y of them retire new # oflong-termemployees would become 640-y.
Total # of employees would become 800-y.
We want 640-y to be 70% of 800-y --> 640-y=(800 -y)*70% --> y = 266.67.
Answer: B.
Answer: B
Question: What is the average of 1/2, 4/5 and 7/10?
Options:
A)1/5
B)3/10
C)2/3
D)1/2
E)6/5
Rationale: Sum of 1/2,4/5,7/10 =20/10
Average = 20/10*1/3 =2/3
Answer C 2/3
Answer: C
Question: add 10% of 30 and 15% of 50.
Options:
A)9.5
B)10.5
C)11.5
D)12
E)15
Rationale: 10% of 30 + 15% of 50
30*10/100+50*15/100
3+7.5=10.5
answer B
Answer: B
Question: What annual payment will discharge a debt of Rs. 6450 due in 4 years at 5% per annum?
Options:
A)1500
B)1400
C)1700
D)1800
E)1600
Rationale: Explanation :
he amount needs to be repaid in 4 years = Rs.6450
Suppose Rs.x is paid annually to repay this debt
Then, amount paid after 1st year = Rs.x
Interest for this Rs.x for the remaining 3 years = x × 5×3/100=15x/100
Then, amount paid after 2nd year = Rs.x
Interest for this Rs.x for the remaining 2 years = x × 5 × 2 /100=10x/100
Amount paid after 3rd year = Rs.x
Interest for this Rs.x for the remaining 1 year = x × 5 ×1/100=5x/100
Amount paid after 4th year = Rs.x and this closes the entire debt
=>x+15x/100+x+10x/100+x+5x/100+x=6450
=>4x+30x/100=6450
=>4x+3x/10=6450
=>40x+3x=64500
=>43x=64500
=>x=1500
Answer : Option A
Answer: A
Question: What is the greatest of 3 consecutive integers whose sum is 33 ?
Options:
A)12
B)7
C)8
D)9
E)5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 33;
=> 3n = 30;
=> n = 10
The greatest of the three numbers is therefore 10+ 2 = 12 Answer: A
Answer: A
Question: It was calculated that 75 men could complete a piece of work in 25 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
Options:
A)28 days.
B)30 days.
C)37.5 days.
D)40 days.
E)36 days.
Rationale: One day work = 1 / 25
One man’s one day work = 1 / ( 25 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 25 * 75)
The total no. of days required to complete the work = (75 * 25) / 50 = 37.5
Answer:C
Answer: C
Question: In a 100 m race,A covers the distance in 30 seconds and B in 45 second.In this race A beats B by :
Options:
A)33.33 m
B)25 m
C)45 m
D)30 m
E)None of these
Rationale: Solution
Distance covered by B in 15 sec. = (100/45x15)m =33.33m.
∴ A beats B by33.33 metres.
Answer A
Answer: A
Question: A bowl contains many kinds of fruit. In the bowl there are twice as many apples then there are bananas, and three times as many oranges as bananas. If the total number of pieces of fruit is X, then how many apples are in the bowl as a fraction of X
Options:
A)X/2
B)X/3
C)2*X
D)X/6
E)X/4
Rationale: Since X is the total number of fruit: X = apples + bananas + oranges.
Since there are three times as many oranges as bananas then 1*orange = 3*bananas
Thus X = apples + bananas + (3*bananas); which simplifies to X = apples + 4*bananas
Since there are twice as many apples as bananas then 1*apple = 2*bananas; which converts to bananas=apple/2
Thus X = apples + 4*(apples/2); which simplifies to X = 2*apples.
Thus apples = X/2
Answer: A
Answer: A
Question: If x : 0.25 : : 3 : 5, then x is equal to :
Options:
A)0.25
B)0.15
C)0.2
D)0.3
E)None of these
Rationale: Explanation :
Solution: x : 0.25 : : 3 : 5
=> x*5 = 3*0.25 => x = 0.75/5 = 0.15
Answer : B
Answer: B
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)16 sec
B)12 sec
C)41 sec
D)09 sec
E)15 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20
=12 sec.
Answer: B
Answer: B
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 5% dividend at the end of the year,then how much does he get ?
Options:
A)Rs. 500
B)Rs. 600
C)Rs. 650
D)Rs. 720
E)None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(5/100x12000) = Rs. 600.
Answer B
Answer: B
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 105?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 105
5x -20 = 105
5x = 125
x = 25
The answer is B.
Answer: B
Question: if radius of a circle is reduced by 10%,then how much % of its area will be reduced?
Options:
A)10%
B)19%
C)20%
D)36%
E)30%
Rationale: let initial radius=a then,area=πa^2.
new radius=90% of a=9a/10.new area=π*81a^2/100=81/100πa^2
reduce in area=[πa^2-81/100πa^2]=19/100πa^2
% reduce=[(19*πa^2/100)*(1*100/πa^2)]%=19%
answer B
Answer: B
Question: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability G that the first ball picked up is odd numbered?
Options:
A)	0
B)	1/3
C)	1/2
D)	2/3
E)	1
Rationale: Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability G is 2/3.D
Answer: D
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
Options:
A)1/48
B)5/16
C)11/12
D)11/16
E)23/48
Rationale: Probability of event not happening is equal to (1 - Probability of event happening)
So, Probability NO heads=1/2
Probability NO number 6 =5/6
Probability NO picking a spades card =3/4
so, Probability NO winning = 1/2*5/6*3/4 = 15/48=5/16
Probability NO winning = 1 - 5/16 = 11/16 .
answer is D
Answer: D
Question: In a library, there are certain number of books on a shelf, ranging between 75 and 100. 1/6th of them are fiction and 12.5% of them are non-fiction. Find the number of books.
Options:
A)376
B)96
C)26
D)198
E)178
Rationale: Explanation:
12.5% can be written as 1/8th
Since 1/6th of the books are fiction and 1/8th are non-fiction, the total number of books must be exactly divisible by 6 and 8 and should be between 75 and 100.
Therefore, 96 is the only number, which fulfills the above criteria.
Note that the question doesn't imply that there are ONLY two varieties of books.
ANSWER: B
Answer: B
Question: There are 16 bees in the hive , then 9 more fly. How many bees are there in all?
Options:
A)7
B)33
C)12
D)17
E)25
Rationale: 16+9=25 . Answer is E.
Answer: E
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)289
C)267
D)261
E)552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 841 = 261
Answer: D
Answer: D
Question: Of the 100 people in a room, 4/5 are women. If 3/5 of the people are married, what is the maximum number of women in the room who could be unmarried?
Options:
A)32
B)34
C)36
D)38
E)40
Rationale: women = 4/5 * 100 = 80
married = 3/5 * 100 = 60
unmarried = 40
max(un-married women) = 40
E
Answer: E
Question: Alfred buys an old scooter for $4400 and spends $800 on its repairs. If he sells the scooter for $5800, his gain percent is?
Options:
A)5.45%
B)6.23%
C)7%
D)8.12%
E)11.5%
Rationale: C.P. = 4400+800 = $5200
S.P. = $5800
Gain = 5800-5200 = $600
Gain% = 600/5200 * 100 = 11.5%
Answer is E
Answer: E
Question: In a mayoral election, Candidate X received 2/3 more votes than candidate Y, and Candidate Y received 1/3 fewer votes than Z. If Z received 27,000 votes how many votes did candidate X received?
Options:
A)18000
B)22000
C)24000
D)26000
E)30000
Rationale: Z=27 --> Y received 2/3 fewer votes than Z --> Y=Z-1/3*Z=18;
X received 2/3 more votes than Y --> X=Y+2/3*Y=30.
Answer: E.
Answer: E
Question: The grade point average of the entire class is 88. If the average of one third of the class is 94, what is the average of the rest of the class?
Options:
A)82
B)83
C)84
D)85
E)86
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
88x = (1/3)94x + (2/3)(P)x
264 = 94 + 2P
2P = 170
P = 85.
The answer is D.
Answer: D
Question: If the cost of 15 kgs of rice is Rs.780/-, what is the cost of 112 kgs of rice?
Options:
A)Rs.5824/-
B)Rs.5720/-
C)Rs.5616/-
D)Rs.5512/-
E)None of these
Rationale: Explanation:
Cost of 1 kg of rice = Rs.780/15 = Rs.52.
Therefore, cost of 112 kgs. = Rs.52x112 = Rs.5824/-
Answer: Option A
Answer: A
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)17%
C)78%
D)13%
E)19%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: A
Question: A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?
Options:
A)162
B)216
C)272
D)360
E)414
Rationale: The total number of ways to choose and arrange 4 flags out of 6 is C^46∗4!=360(or directly P^46).
We cannot have Liverpool and Arsenal flags at the same time. The number of ways to have and arrange Liverpool and Arsenal flags at the same time is C24∗4!=144 (choosing 2 flags out of 4 remaining, without Liverpool and Arsenal, and then arranging 4 flags with 4!);
Total - Restriction = 360 - 144 = 216.
Answer: B.
Answer: B
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.02 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
Options:
A)1-0.02^10
B)1-0.98^10
C)(1-0.98)^10
D)0.06
E)1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.98^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: B
Question: 15 years hence, Karthik will be just Quadrice as old as he was 15 years ago, How old is Karthik at now? [ Quadrice = 4 Times ]
Options:
A)25
B)26
C)22
D)29
E)28
Rationale: A
25
Let the current age of Karthikh = A years
Then, A+15 = 4(A – 15)
Therefore A = 25
Answer: A
Question: If the 11th day of a month is three days earlier than Friday, What day will it be on the 20th day of the month?
Options:
A)Thursday
B)Monday
C)Sunday
D)Wednesday
E)Friday
Rationale: Explanation:
Given that 11th day of a month is three days earlier than Friday
=> 11th day is Tuesday
=> 18th is Tuesday
=> 20th is Thursday
Answer: Option A
Answer: A
Question: Twenty times a positive Integer is less than its square by 96. What is the integer?
Options:
A)4
B)25
C)24
D)16
E)27
Rationale: Let the Integer be x.
Then X2 - 20X = 96
X2 - 20X - 96 = 0
X2 + 4X - 24X - 96 = 0 ===> X(X + 4) -24(X + 4)
===> (X + 4)(X-24)
X = -4 or 24. as the Integer is positive the correct answer is
option C)24
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
Options:
A)200 metres
B)180 metres
C)324 metres
D)150 metres
E)100 meters
Rationale: Speed=60 x5/18m/sec=50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50/3	x 12m = 200 m.
ANSWER:A
Answer: A
Question: In Badminton game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
A)1/3
B)4/9
C)5/9
D)2/3
E)3/4
Rationale: In Badminton game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Answer: C.
Answer: C
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 70% profit?
Options:
A)277
B)1088
C)277
D)266
E)121
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 170% of Rs. 640 = 170/100 * 640 = Rs. 1088.
Answer: B
Answer: B
Question: 1100 male students and 700 female students are examined in a monthly test; 42% of the male students and 30% of the female students only pass in the examination. Find the percentage of the total failed?
Options:
A)62*2/3
B)40*2/3
C)55*2/3
D)50*2/3
E)35*2/3
Rationale: Total number = 1100 + 700 = 1800.
tot students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.
Number of failures = 1800-672 = 1128.
Percentage of failure = (1128/1800 * 100 )% = 62 * 2/3 %.
ANSWER A
Answer: A
Question: The decimal 0.1 is how many times greater than the decimal (0.0001)^3?
Options:
A)10^9
B)10^10
C)10^11
D)10^12
E)10^13
Rationale: 0.1 = 10^-1
(0.0001)^3 = (10^-4)^3 = 10^-12
10^11 * 10^-12 = 10^-1
The answer is C.
Answer: C
Question: John throws a coin until a series of five consecutive heads or three consecutive tails appears. What is the probability that the game will end after the sixth throw?
Options:
A)1/32
B)2/16
C)3/16
D)7/16
E)9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T-T-T ----> P = (1/2)^6 = 1/64
T-H-H-H-H-H ----> P = (1/2)^6 = 1/64
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/64 + 1/64= 2/64 = 1/32
Answer(A).
Answer: A
Question: A can do a work in 8 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?
Options:
A)600,400
B)500,500
C)400,200
D)800,200
E)550,450
Rationale: Ratio of their works A:B = 8:4
Ratio of their wages A:B = 2:1
A's share = (2/5)1000 = 400
B's share = (1/5)1000 = 200
correct option is C
Answer: C
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
Options:
A)16
B)77
C)88
D)26
E)29
Rationale: Explanation:
Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
{\color{Blue} \left.\begin{matrix} weavers &4:8 \\ days& 4:8 \end{matrix}\right\}::4:x}
{\color{Blue}\therefore }4 x 4 x x = 8 x 8 x 4
{\color{Blue}\Rightarrow x=\frac{8\times 8\times 4}{4\times 4} }
{\color{Blue} \Rightarrow }x = 16.
Answer: A) 16
Answer: A
Question: In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by
Options:
A)64
B)8
C)4
D)64
E)1/64
Rationale: Say r=2 => V1 = 1/64
when r=1; V2 = 1/16
V2 = 4*V1.
Answer=C=4
Answer: C
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is?
Options:
A)75%.
B)27%.
C)25%.
D)45%.
E)15%.
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer:C
Answer: C
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
Options:
A)8! * ⁷P₆
B)6! * ⁷P₆
C)9! * ⁷P₆
D)5! * ⁷P₆
E)2! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * ⁷P₆
Answer: B
Answer: B
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 12, what was the speed of the leak, in terms of Vâ€™?
Options:
A)9Vâ€™
B)4Vâ€™
C)Vâ€™/2
D)Vâ€™/4
E)Vâ€™
Rationale: When h=4 v=V'
So V' = k.16
Hence k = V'/16
Now when h=12
v=(V'/16).12^2
v=V'.144/16
v=9V'
Ans : A
Answer: A
Question: If a committee of 3 people is to be selected from among 6 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)20
B)40
C)50
D)80
E)160
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
12*10*8 / 6 = 160. Answer E.
Answer: E
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
A)13 days
B)15 days
C)17 days
D)21 days
E)None
Rationale: A's 2 day's work = 1	x 2 =	1	.
20	10
(A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
Option B
Answer: B
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 30% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Options:
A)$37.80
B)$38.50
C)$39.20
D)$39.50
E)$41
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 30% discount then the original price of it was x*0.7=$14 --> x=$20.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 20+21=$41.
Answer: E.
Answer: E
Question: Lucy's personal library had 1/20 the capacity as the town library. Lucy decided to donate 1/2 of her book collection to the town library. What fraction of the town library's capacity would Lucy's book donation fill?
Options:
A)3/16
B)1/10
C)1/6
D)1/18
E)1/4
Rationale: Assuming that the town library has space for 100 books, that would mean that Lucy's personal library had 20 books. If Lucy donated a 1/2 of her books, that would mean she donated 10 books. Those 10 books would make 10/100 of the town library's collection. 10/100 simplifies to 1/10. (Answer: B)
Answer: B
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 80 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
Options:
A)1 hour
B)1 hour 10 minutes
C)2 hours 30 minutes
D)1 hour 40 minutes
E)2 hours 20 minutes
Rationale: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/80)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 80 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (80+60)=140 minutes on the road.
E. 2 hours 20 minutes
Answer: E
Question: Arithmetic mean and standard deviation of a certain normal distribution are 13 and 1.5. What value is exactly 2 standard deviations less than the mean?
Options:
A) 10.5
B) 10
C) 11.5
D) 12
E) 12.5
Rationale: The value which is exactly two SD below the mean is: mean-2*SD=13-2*1.5=10.
Answer: B.
Answer: B