Maths Problem

[OlderButNotWiser]

7 times X times a 5 figure number always gives an answer consisting of Xs, and it dosn't matter what number is used for the X. What is the 5 figure number?
Anybody any ideas on this one please

[Old_Geezer]

00000 ?

[Old_Geezer]

I'm unsure I understand the question, to be honest.

[elliemay1]

Don't understand it either!

[Old_Geezer]

So...

xxxxx / x = 7 times abcde

11111 = 7(abcde)

abcde = 11111 / 7 = 1587.286, which isn't a 5 digit number.

[Gizmonster]

I don't understand the question as well ??
7 x a 5 figure number (ABCDE) always gives an answer consisting of X's. Does the answer contain one X, or all 5 X's, or any number of X's ??

[Old_Geezer]

Ok your answer might not be xxxxx as it doesn't specify how many digits the answer is.

But is will still be string of 1s when (both sides of the equation is) divided by x.

No; I think I'm going to bow out at this point.

[Buenchico]

15873

[BlackadderV]

7x times abcde will give an answer consisting entirely of x's. What is abcde? they don't necessarily all have to be different digits.

[Gizmonster]

Chris - the question says "what is the 5 figure number".
If you understand the question, please explain lol :)

[Old_Geezer]

Hmm so close and yet. I should deal only with integers or something.

[Old_Geezer]

Use A instead if X

7 x A x abcde = AAAAAA

Much less confusing.

[Old_Geezer]

... instead *OF* X

like I typed

[gingejbee]

How is it that Chris (and myself) understands the question and nobody else does?

[Old_Geezer]

Because of all the "times" and X. Leaves things open to interpretation.

[Gizmonster]

I get it now - and I agree with Chris' answer of 15873 - even though the OP asks "what is the 5 digit number"?

[Buenchico]

GM - The question says:
"There's a mystery 5-figure number which, when multiplied both by 7 and by any single-digit number, always produces an answer where every digit is the same as that single-digit number. What's that mystery 5-figure number?"

Taking 4 as an example for the single-digit number, that means that 28 (= 7 x 4) times the mystery number must come to 4 or 44 or 444 or 4444, etc. But since a 5 digit number must be between 10000 and 99999, the required string-of-4s number must be between 280,000 and 2,800,000, i.e. 444,444

Dividing 444,444 by 28 gives 15873.

Checking other examples confirms the answer. e.g.
7 times 8 x 15873 = 888,888.

That way of proving it (by exhaustion) would score poorly in a maths exam (because it lacks 'elegance') but it's the simplest way of finding the required answer here.

[Gizmonster]

LMAO - why did I think TWICE, that 15873 was 6 digits - I'm going blind lol !!!!

[Gizmonster]

Yea I got it Chris .... for some reason I counted 15873 as 6 digits, even on the 2nd count lol :P

[Buenchico]

Actually, starting from Divebuddy's approach (of the importance of 111,111 as a multiplied of x) would give a simple, yet elegant, mathematical proof.