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)

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

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

Solution of the Question shall be as per attached sketch




_________________

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.

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?

What is the remainder when 1234569 is divided by 2^51?

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

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.
_________________

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

\( x \) 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

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