divelab/Sys2Bench huggingface dataset:
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds.If the speed of the train is 15m/sec,what is the length of the train?
Options:
A)150m
B)200m
C)300m
D)240
E)None
Rationale: Length of the train= (15*20)m=300m
Let the length of the platform be x meters.
Then, (x+300)/36=15
x=240m
Answer:Option D
Answer: D
Question: How many seconds will a 100 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)6
B)30
C)8
D)12
E)1
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 100 * 3/50 = 6 sec.
Answer: Option A
Answer: A
Question: A cricket bat is sold for $900, making a profit of $300. The profit percentage would be
Options:
A)24%
B)25%
C)30%
D)50%
E)40%
Rationale: 300/(900 - 300) = 50%.
Answer: D
Answer: D
Question: How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm2 for each plant ?
Options:
A)18
B)750
C)24
D)120
E)None of these
Rationale: Circumference of circular bed = 30 cm
Area of circular bed = (30)2⁄4π
Space for each plant = 4 cm2
∴ Required number of plants
= (30)2⁄4π ÷ 4 = 17.89 = 18(approx)
Answer A
Answer: A
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)12 min
B)10 min
C)11 min
D)10 min
E)17 min
Rationale: A
12 min
T = 9/45 * 60 = 12
Answer: A
Question: A random number is picked following which, five guesses are to be made in order to find the correct number. All the guessed numbers are noted down in a paper. On another paper, all the differences between the guessed numbers and the picked numbers are written down by subtracting the smaller one from the bigger one.
Now, one number each is erased from both of the papers. As a result, four numbers remain on each paper:
Guesses: 27, 32, 44, 45
Differences: 5, 7, 10, 13
If this is all the information you need, can you find out what number was picked?
Options:
A)33
B)37
C)55
D)79
E)83
Rationale: B
The number is 37.
The missing guess can be either 24 or 50 and the missing difference is 8.
Answer: B
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)69.5 km/hr
B)70 km/hr
C)79 km/hr
D)79.2 km/hr
E)62.2 km/hr
Rationale: Answer: Option D
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
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 108 kmph, how much time it took in doing so?
Options:
A)8 sec
B)5 sec
C)6 sec
D)1 sec
E)9 sec
Rationale: D = 180
S = 108 * 5/18 = 30 mps
T = 180/30 = 6 sec
Answer:C
Answer: C
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 40 candies for the discounted price of 14 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?
Options:
A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
E
Answer: E
Question: he average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
Options:
A)75 kg
B)55 kg
C)45 kg
D)80 kg
E)25 kg
Rationale: Explanation:
Total weight increased = (6 x 2.5) kg = 15 kg.
Weight of new person = (65 + 15) kg = 80 kg.
Answer: D
Answer: D
Question: P and Q had the same number of candies. P gave Q 20 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-20) = Q+20
5(Q-20) = Q+20
4Q = 120
Q = 30
Now person Q has 30+20 candies which is 50 candies.
The answer is A.
Answer: A
Question: What will be the compound interest on Rs. 50000 after 3 years at the rate of 12 % per annum
Options:
A)Rs 20123.20
B)Rs 20246.4
C)Rs 20123.40
D)Rs 20123.50
E)None of these
Rationale: Explanation:
(50000×(1+12/100)3)
=>50000×28/25×28/25×28/25
=>70246.4
So Compound interest will be 70246.4 - 50000
= Rs 20246.4
Option B
Answer: B
Question: A large research project was scheduled over the course of a 30-month period, and a budget of $90,000 was allotted for the course of the entire project. After seven months, the project had spent $20,000. Was the project at this point over budget or under budget, and by how much?
Options:
A)under, $4200
B)under, $1200
C)under, $1000
D)over $1800
E)over $5800
Rationale: cost per month = 90,000/30 = 3,000.
Now, multiply by seven months: 7*($3000) = $21,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is less than this, so it is under budget.
$21,000 â€“ #20,000 = $1000
Answer = (C)
Answer: C
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)28 cm2
B)26 cm2
C)20 cm2
D)86 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 28/2
= 35 cm2
Answer: E
Answer: E
Question: If n is a 25-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 5
II. n is divisible by 10
III. n is divisible by 25
Options:
A)I only
B)I and II only
C)I and III only
D)II and III only
E)I, II and III only
Rationale: Rule for divisibility by 5: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 10: The sum of the nos digits of the number should be divisible by 5 or the number should be divisible by 5 two times.
Rules for divisibility by 25: The sum of the digits should a multiple of 25
Consider no 11111111...25 times = The sum 25*1=25----> divisbible by 5,10 and 25
consider number to be 222....25 times, then sum of the no. 25*2=50 divisibly by 5,10 and 25
So why so because when you sum the numbers either you can add the digits 25 times or multiply the digit *25..
Note that since 25 is divisble by 25,10 and 5 and thus the sum of the nos will be divisible by all the nos.
Ans is E
Answer: E
Question: Enrollment in City College in 1980 was 25 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
Options:
A)100%
B)300 %
C)200%
D)250%
E)183 1/3%
Rationale: Assume 100 enrollments present in 1990
25 % of 1990 = enrollments on 1980
enrollments on 1980 = 25
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 25) *100 / 25
= 7500 / 25
= 300 %
Ans - B
Answer: B
Question: 8!/(8-2)!=?
Options:
A)36
B)46
C)56
D)66
E)96
Rationale: 8!/(8-2)!=8!/6!=8*7=56. Hence, the correct answer is C.
Answer: C
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
Options:
A)6 PM
B)7 PM
C)8 PM
D)5 PM
E)9 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Answer: D
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 9 minutes by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Options:
A) 3%
B) 5%
C) 8%
D) 10%
E) 12%
Rationale: Bob's time = 600 secs.
His sis' time = 540 secs.
Percent increase needed = (600-540/600) * 100 = 60/600 * 100 = 10%. Ans (D).
Answer: D
Question: A jogger running at 9 km/hr along side a railway track is 120 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)89
B)20
C)36
D)24
E)34
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 120 + 120 = 360 m.
Time taken = 240/10 = 24 sec.
Answer: Option D
Answer: D
Question: Three students shared a group project, jack claimed that he do the project by himself in 20 hours, and Jane in 30 hours. Jack started working on the project for 10 hours, then Jane continued working on it another 10 hours. Lastly, Julie joined the team and working 10 hours, the project was completed. How many hours it takes Julie to finish the project by herself?
Options:
A)70 hours
B)60 hours
C)50 hours
D)40 hours
E)30 hours
Rationale: 10/20 + 10/30 + 10/x = 1x = 60 hoursANSWER:B
Answer: B
Question: What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?
Options:
A)6
B)8
C)9
D)10
E)11
Rationale: Such kind of combinations problems are always about a pattern recognition.
Maximum pieces:
0 line gives 1 whole piece;
1 line will gives 2 pieces: 1+1=2;
2 lines will give 4 pieces: 2+2=4;
3 lines will give 7 pieces: 4+3=7;
4 lines will give 7+4=11 pieces.
ANSWER:E
Answer: E
Question: What is 15 percent of Rs. 34 ?
Options:
A)Rs. 3.40
B)Rs. 3.75
C)Rs. 4.50
D)Rs. 5.10
E)None
Rationale: Sol.
15% of Rs. 34
= Rs. (15 / 100 x 34)
= Rs. 5.10
Answer D
Answer: D
Question: From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?
Options:
A)2
B)4
C)6
D)8
E)Cannot be determined
Rationale: solution:
At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.
Let, total candidates = n
according to the question,
nCx = nC(x+2)
or, nCn-x = nCx+2 [nCr = nCn-r]
or, n-x = x+2
so, n = 2x+2
Remember total least number should be 8? So below 8 we can't expect anything.
Put x=2, then n=6 that is unacceptable.
so x is not equal to 2 . Answer: A
Answer: A
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40% while buying and by 10% while selling. What is his percentage profit?
Options:
A)10.22%
B)20.22%
C)21.22%
D)40%
E)Can't be calculated
Rationale: The owner buys 100kg but actually gets 140kg;
The owner sells 100kg but actually gives 90kg;
Profit: (140-90)/90*100=40%
Answer: D.
Answer: D
Question: Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 2. What is P(A and B)?
Options:
A)1/8
B)1/6
C)1/5
D)1/3
E)1/2
Rationale: P(A and B) = 1/3*1/2 = 1/6
The answer is B.
Answer: B
Question: The expression 10^14−110 is divisible by all of the following integers EXCEPT
Options:
A)2
B)3
C)4
D)7
E)11
Rationale: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (D) is correct.
Answer: D
Question: Tom drives from town Q to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between Q and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
Options:
A)12
B)20
C)24
D)30
E)36
Rationale: Let's assume that it takes 4 hours to go from point Q to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Answer: B
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder X when N is divided by 30?
Options:
A)(a) 4
B)(b) 7
C)(c) 11
D)(d) 13
E)(e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder X when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: C
Question: Set Q includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First, reach to the point of getting the equation Q: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: D
Question: In how many ways a committee, Consisting of 4 men and 5 women can be formed from 8 men and 10 women?
Options:
A)2660
B)3360
C)11760
D)17640
E)17200
Rationale: To choose Required number of ways to form a committee:
Select 4 men out of 8 men and 5 women out of 10 women.
That is 8C4 * 10C5.
8C4=8!/4!*4!=70
10C5=10!/5!*5!=252
The Required number of ways=70*252=17640
D
Answer: D
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour
of the stream. The ratio of the speed of the boat in still water and stream is
Options:
A)3:1
B)1:3
C)2:4
D)4:2
E)None of these
Rationale: Explanation:
Let speed downstream = x kmph
Then Speed upstream = 2x kmph
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
Answer: A
Answer: A
Question: 24 people can write 48 book in 6 days working 8 hour a day.then in how many day 192 can be written by 50 people?
Options:
A)223/26
B)288/27
C)309/22
D)288/26
E)288/25
Rationale: work per day epr hour per person= 48/(6*8*24) // eq-1
people= 50; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 192/(p*8*50) // eq-2
eq-1==eq-2;
p= 288/25
ANSWER:E
Answer: E
Question: Eight kilograms of rice costing Rs. 16 per kg is mixed with four kilograms of rice costing Rs. 22 per kg. What is the average price of the mixture?
Options:
A)20
B)18
C)16
D)19
E)17
Rationale: P1 = Rs.16 per kg, p2 = Rs. 22 per kg, q1 = 8 kg, q2 = 4 kg
Now , p = (p1q1+p2q2)/(q1+q2)
Average price of the mixture = 8*16+4*22/12
= 128+88/12
= 216 /12 = 18
ANSWER:B
Answer: B
Question: If x and y are nonzero integers and 450x = 120y then which of the following must be an integer?
I. xy/60
II. 15x/4y
III. 4x/15y
Options:
A)I only
B)II only
C)I and III
D)I and II
E)I, II, and III
Rationale: 450x=120y reduce by 30 --> 15x=4y --> x is a multiple of 4 (y=15x/4 so x must be multiple of 4 for y to be an integer) and y is a multiple of 15 (x=4y/15y must be multiple of 15 for x to be an integer).
I. xy/60 --> always true, as xy will be multiple of 4*15=60;
II. 15x/4y --> as 4y=15x then 15x/4y=15x/15x=1=integer so this option is also always true;
III. 4x/15y --> as x=4y/15 then 4x/15y=16/225≠integer, so this option is never true.
Answer: I and II (only).
ANSWER:D
Answer: D
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 33,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
Options:
A)Rs. 4000
B)Rs. 4008
C)Rs. 4002
D)Rs. 4003
E)Rs. 4001
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 33,000 = Rs. 11,000
Salary of A = Rs. (15000 – 11000) = Rs. 4000
ANSWER: A
Answer: A
Question: How many even integers from 1 to 50 (both inclusive) have even number of factors?
Options:
A)3
B)14
C)5
D)6
E)7
Rationale: Integers having even number of factors will be perfect squares. even numbers will have even perfect squares. Thus, the possible values for the perfect squares are :
4,16,36 and the corresponding integers are 2,4,6 (more than 2). Thus A is the correct answer .
Answer: A
Question: Two cars start at the same time from opposite ends of a highway that is 60 miles long. One car is riding at 13 mph and the second car is riding at 17 mph. How long after they begin will they meet?
Options:
A)0.75
B)1
C)1.25
D)1.5
E)2.0
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 17+13 = 30 mph
Total distance to be covered = 60 miles.
Time taken would be: 60 miles/30 mph = 2.0 hours
E is the answer.
Answer: E
Question: How many Q 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 Q=> 2*5*4*3*2*1 = 240.B
Answer: B
Question: Solve for x and check: - 200x = 1600
Options:
A)2000
B)2573
C)1600
D)2950
E)None of these
Rationale: Solution : Dividing each side by -200, we obtain
(-200x/-200)=(1600/-200)
Therefore : x=-8
Check :
-200x=1600
(-200*-8)=1600
1600=1600
ANSWER : C
Answer: C
Question: Albert invested amount of 16000 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. 17640
B)Rs. 8620
C)Rs. 8730
D)Rs. 8820
E)None of these
Rationale: Explanation:
=>(16000×(1+5/100)2)
=>16000×21/20×21/20
=>17640
Option A
Answer: A
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. y + z is odd
II. (x+z)/y is an integer
III. xz is not an integer
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II, and III
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. 2x+3+2x+5=4x+8=4(x+1), so divisible by 2 and even - NOT TRUE
II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE
III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so TRUE
ANSWER: D
Answer: D
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)8 sec
B)6 sec
C)3 sec
D)2 sec
E)9 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man
=[110 * 3/55] sec =6 sec
Answer: B
Answer: B
Question: Set A: {1, 3, 4, 6, 9, 12, 15,18}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
Options:
A)3/14
B)2/7
C)5/14
D)5/7
E)11/14
Rationale: using probability you can solve: 6/8*5/7*4/6=5/14
Ans C
Answer: C
Question: A train running at 25 km/hr takes 30 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Options:
A)a) 200/3m175/3m
B)b) 60m130m
C)c) 50m45m
D)d) 100/3 m200/3
E)e) none of these
Rationale: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/30*12=10m so the train covered a distance in 12 sec= 25*5/30*12=50
so the length of the train(Lt) is 10+50=60m
Now crossing the platform means length of train+length of platform(Lt+p)= 30*25*5/30=125m Now the length of platform (Lp) is= 125-60=65m
So answer is 60m and 65m Must beBeven though its mentioned 60m and 130m thinking so typo mistake...........
Answer: B
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
Options:
A)8 years
B)9 years
C)2 years
D)6 years
E)3 years
Rationale: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: D
Answer: D
Question: If (m-8) is a factor of m^2-pm-24, then p=
Options:
A)3
B)5
C)6
D)11
E)16
Rationale: (m-8)(m-a)=m^2-pm-24
A=-3
p=8+a=5=B
Answer: B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)111.18 m
C)111.82 m
D)121.12 m
E)111.11m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Answer: A
Question: The number of people who moved to live in a small town per 200 persons is 10.5. if the number of person who leave the town per 200 persons is 5.5 how long will it take for the population of 1000 people to double.
Options:
A)25
B)30
C)40
D)10
E)2
Rationale: Annual increase is (200 + 10.5 - 5.5)*5=1025
Hence every year there is an increase of 25
for the population to double we needs additional 1000
therefore 1000/25=40
correct option is C)
Answer: C
Question: If the number 892,132,26x is divisible by 11, what must be the value of x?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,132,24x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 6 = 18(ii)
(i) - (ii) = 15 + x - 18 = x - 3
Hence x should be = 3 to make this a multiple of 11 (0) Option C
Answer: C
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.50 per glass on the first day, what was the price per glass on the second day?
Options:
A)$0.15
B)$0.20
C)$0.33
D)$0.40
E)$0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.5=3*x --> x=$0.33.
Answer: C.
Answer: C
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
Options:
A)10
B)11
C)12
D)13
E)15
Rationale: Given that, A + B =12+ B + C
⇒ A - C =12
Therefore, C is younger than A by 12 years
Answer is C.
Answer: C