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A person travelled 300 km by train and another 200 km by bus. The journey took a total time of 5 hours and 30 minutes. However, if the person had travelled 260 km by train and 240 km by bus, the journey would have taken a total time of six more minutes than the original time. What was the speed of the train in km per hour?

(A) 80

(B) 100

(C) 110

(D) 120

(E) 130
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Hovkial
A person travelled 300 km by train and another 200 km by bus. The journey took a total time of 5 hours and 30 minutes. However, if the person had travelled 260 km by train and 240 km by bus, the journey would have taken a total time of six more minutes than the original time. What was the speed of the train in km per hour?

(A) 80

(B) 100

(C) 110

(D) 120

(E) 130
Show more

Let speed of train = V, speed of bus = W

Then:

(300/V) + (200/W) = 11/2 ......................... (Equation 1)

(260/V) + (240/W) = 336/60 ....................... (Equation 2)

Solving:

V = 100 km/hr

ANSWER: (B)
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Users' Self Made Questions 13 Oct 2019, 05:28
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All the positive integers less than 1000 but not containing the digit '5' are arranged horizontally in descending order. What is the 555th number on the list?

A. 209
B. 210
C. 211
D. 212
E. 213
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All the positive integers less than 1000 but not containing the digit '5' are arranged horizontally in descending order. What is the 555th number on the list?

A. 209
B. 210
C. 211
D. 212
E. 213
Show more

giving a try
for a range of no from 0-99 ; we have 1+(8*10) ; 81 values without '5'
since the arrangement of no is done in descending order so
from 600 to 999 we have ; 81* 4 ; 324 positions
400 to 499 ; 81 positions ; 324+81 ; 405
200 to 399 ; 81*2 ; 162 +405 ; 567 postions
so no 200 is 567th
555th no ; 567-555 ; 12th from 200 + 1 missing 205 ; i.e 213 shall be 555th term
IMO E
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Solution of the Question shall be as per attached sketch
Attachment:
Solution.jpeg
Solution.jpeg [ 78.51 KiB | Viewed 2817 times ]


gmatbusters
Hi math experts, try this question and provide feedback...

Janvisahu

Triangle ABC is a right angled triangle with right angle at Vertex B. Triangle DEF is an equilateral triangle with side 10 cm. The lengths of sides (in cm) are marked in the Drawing. What is the area of the polygon ABFEGA?

(1) The length of CD (overlap of sides) is 3 cm.
(2) The length of altitude (GH) of triangle GDC is 2.598 cm.


Show SpoilerOA
D

Show Spoiler
Attachment:
The attachment Triangle.jpg is no longer available
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If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

(1) The tens digit of x is NOT equal to the sum of the tens digits of y and z.
(2) The units digit of x is equal to the sum of the units digits of y and z.

Show Spoiler
Modified Question:
Correct choice C, according to me
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Tom goes to the supermarket to buy an equal amount of small and large cucumbers. He receives an additional 30 small cucumbers as a gift. This makes the ratio of small to large cucumbers 6:5. How many cucumbers did Tom buy initially?
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What is the remainder when 1234569 is divided by 2^51?
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VeritasKarishma

Hello,

Part of the integral solutions

Question: A boy goes to a supermarket and buys some pencils and erasers . The cost of each pencil is $0.3 and cost of each eraser is $0.6. If he bought at least one pencil and at least one eraser, how many pencils did he buy?

(1) He paid a total of $4

(2) He bought three erasers.

I was inspired for this by Veritas ... can someone help plz

Topic is integral solutions to an equation in two variables
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Users' Self Made Questions 18 Jun 2020, 22:25
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VeritasKarishma

Hello,

Part of the integral solutions

Question: A boy goes to a supermarket and buys some pencils and erasers . The cost of each pencil is $0.3 and cost of each eraser is $0.6. If he bought at least one pencil and at least one eraser, how many pencils did he buy?

(1) He paid a total of $4

(2) He bought three erasers.

I was inspired for this by Veritas ... can someone help plz

Topic is integral solutions to an equation in two variables
Show more

The numbers you have taken do not give a possible scenario:

0.3P + 0.6E = 4
3P + 6E = 40
3*(P + 2E) = 40
P + 2E = 40/3

If P and E are integers, their sum cannot be a fraction.

Instead of $4, take $4.2 and you will get your solution.
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New question:

A man sells seven different sized balls. each ball costs $n more than the next one below it in size, and the price of the biggest ball is $46. if the sum of the prices of seven different balls is $196, what is the value of n?

a.6 b.7 c.8 d.9 e.none of these
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\( x \) is an even integer. If \( |x-1| \geq 9 \) then which of the following must be true?

A. \( \sqrt{|x|} \) is not a prime number.
B. \( x \geq 10\).
C. When x is divided by its greatest factor, the remainder is 1.
D. x is not a multiple of \( \frac{23}{10}\).
E. \( \frac{1}{x} \) hundredth digit is not greater than 2 if the tenth digit is 1.

Posted from my mobile device
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Users' Self Made Questions 30 Nov 2020, 12:08
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TheUltimateWinner
If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

(1) The tens digit of x is NOT equal to the sum of the tens digits of y and z.
(2) The units digit of x is equal to the sum of the units digits of y and z.

Show Spoiler
Modified Question:
Correct choice C, according to me
Show more

Interesting twist to the original Question and I agree with the answer.
With 1 alone it is possible that the sum of tens digit do not give a carry over and the sum of tens is not equal to tens digit of z, only if it receives a carryover from Units digit. Statement 2 confirms that there is no carryover from units digit and hence C should be the answer.

Another question that makes you think when you add a twist to the original question:
If \(x,y\) belong to set of integers, is \(x^y\) odd?
(1) \(x\) is odd
(2) \(y\) is even

Show Spoiler
Modified Question:
Correct choice E, according to me.

If \(x \)is odd and\( y\) is -ve (even or odd) integer then \(x^y\) is not Integer and hence not odd.
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If a line l passes through points (1,2) & (3,4) which of the lines is pendendicular to it.

A. x + y = 6
B. x - y = 3
C. x + 2y = 7
D. x - 2y = 5
E. y = x + 3

Bunuel

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Users' Self Made Questions 03 May 2021, 19:20
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Given: A person travelled 300 km by train and another 200 km by bus. The journey took a total time of 5 hours and 30 minutes. However, if the person had travelled 260 km by train and 240 km by bus, the journey would have taken a total time of six more minutes than the original time.

Asked: What was the speed of the train in km per hour?

Let the speed of the train in kmh be t kmh and speed of the bus be b kmh.

A person travelled 300 km by train and another 200 km by bus. The journey took a total time of 5 hours and 30 minutes.
300/t + 200/b = 5.5 (1)

However, if the person had travelled 260 km by train and 240 km by bus, the journey would have taken a total time of six more minutes than the original time.
260/t + 240/b = 5.6 (2)

(1) * 6 - (2) * 5
(1800-1300)/t = 33 - 28 = 5
500/t = 5
t = 100 kmh

Speed of the train = 100 kmh

IMO B
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20% of a 25% ethanol solution is replaced with a 50% ethanol solution. From the resulting solution, again 20% is replaced with the 50% ethanol solution. What is the concentration of ethanol in the final solution obtained?
a) 32%
b) 34%
c) 36%
d) 38%
e) 40%


Solution: B
Original concentration = 25%
1st iteration concentration = 25% – 0.2(25%) + 0.2(50%) = 30%
2nd iteration concentration = 30% – 0.2(30%) + 0.2(50%) = 34%
In the first iteration, we are taking out 20% of the 25% original ethanol concentration. Then we are adding in 20% from the 50% ethanol concentrated solution. The resulting concentration is 30%.
Now we start with 30% in the second iteration. We take out 20% of the 30% ethanol concentration and again add in 20% from the 50% ethanol concentrated solution. The resulting concentration is 34%.

Anyone have a different method ;)?
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Users' Self Made Questions 18 Jan 2022, 05:05
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For a certain cube, 3 different edges that do not all meet at a single vertex are to be painted red. How many different selections of the 3 different edges to be painted red are possible?

A. 56
B. 112
C. 120
D. 212
E. 504
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(Q):
Is P divisible by 10?

(1) 6P is divisible by 10
(2) 15P is divisible by 10


Thanks
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New Question

Trains A and B travel at constant speeds from destinations X and Y, respectively to their destinations Y and X, respectively. After crossing each other, Train A reaches Y after 12 hours, while Train B reaches X after 27 Hours. If the speed of A is 30 miles/hour more than that of B, find out the speed of A (in miles/hour)

A. 40
B. 50
C. 70
D. 90
E. 100
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Users' Self Made Questions 04 Aug 2022, 13:55
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Here is a self-made question that is an adaption of this official question.

This is a very challenging question and I hope you have a fun time solving this. I am including the correct answer choice and the detailed step-by-step explanation to arrive at the same, however, please feel free to let me know in case you need any further help on this.

Question: If \(x\) is an integer, is \(\frac{(x^2 + 1)}{(x + 5)}\) an even number? (Given \(x ≠ -5\))

Statement 1: \(x\) is an odd number
Statement 2: Each prime factor of \(x^2\) is greater than \(7\)

Show SpoilerCorrect answer:
D
Show SpoilerExplanation:


Let's start by assuming that \(\frac{(x^2 + 1)}{(x + 5)}\) is an even number. Therefore \(\frac{(x^2 + 1)}{(x + 5)}=2p\) for some integer \(p\). Cross-multiplying and forming a quadratic, we get:

\(x^2-2px+1-10p=0\)

Solving for \(x\) using the Quadratic formula, we get \(x = p ± \sqrt{p^2+10p-1}\)

Now since we have been given that \(x\) is an integer, it is necessary that \(\sqrt{p^2+10p-1}\) is an integer as well. Let's assume \(p^2+10p-1=m^2\) for some integer \(m\). Rearranging and forming a quadratic, we get:

\(p^2+10p-1-m^2=0\)

Solving for \(p\) using the Quadratic formula, we get \(p = -5 ± \sqrt{26+m^2}\)

But since we had assumed initially that \(p\) is an integer, therefore \(\sqrt{26+m^2}\) must also be an integer. Let's assume \(26+m^2=k^2\) for some integer \(k\). Rearranging, we get:

\(k^2-m^2=26\) which can further be written as \((k+m)(k-m)=26\) where both \(k\) and \(m\) are integers.

In order for this to hold, \((k+m)\) and \((k-m)\) must be of the same even/odd nature. But from factorization of \(26\) we know that \(26\) cannot ever have a pair of integral factors such that they are of the same even/odd nature. (\(26\) and \(1\) are different in their even/odd nature, and so are \(2\) and \(13\))

Thus,

1. There is no \(k\) for which \(\sqrt{26+m^2}\) is an integer. This implies that
2. There is no \(m\) for which \(\sqrt{p^2+10p-1}\) is an integer. This implies that
3. There is no \(p\) for which \(\frac{(x^2 + 1)}{(x + 5)}\) is an integer.

Thus, this contradicts our initial assumption and proves that for no \(x\) can \(\frac{(x^2 + 1)}{(x + 5)}\) ever be an even integer.

We can confidently say that Statement 1 is sufficient.

From here it is a simple step to observe that all elements in Statement 2 are indeed a subset of elements in Statement 1 and thus our conclusion holds true for Statement 2 as well.

Therefore, either statement is sufficient in answering the question (the answer is NO, the given fraction cannot be an even integer for any integer \(x\)) and hence option D is our correct option choice for this question.

This brings us to the end of this super long post. I hope you guys had fun! :) Suggestions and feedback are welcome.

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