Answer to Question #286960 in Algebra for shine

Question

Direction: In this section, the question is based on a set of conditions. In answering the question, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answer the question.

A government department labels its files according to these guidelines:

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 Each label should be a five digit number

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 Can use only the digits 0 to 4. Digits 5 to 9 are not allowed.

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 No digit is repeated.

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 The 1st digit should be half of the 2nd digit.

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 The 5th digit should always be greater than the 3rd digit.

If a file's label's last digit is 1, then

(A) first digit is 2

(B) second digit is 0

(C) third digit is 3

(D) fourth digit is 4

(E) fourth digit is 0

Answer 1

 Each label should be a five digit number

$$abcde$$

Can use only the digits 0 to 4. Digits 5 to 9 are not allowed.

$$0,1,2,3,4$$

No digit is repeated.

$$a\not=b, a\not=c,a\not=d,a\not=e,b\not=c,$$

$$b\not=d,b\not=e,c\not=d,c\not=e,d\not=e$$

The 1st digit should be half of the 2nd digit.

$$b=2a$$

The 5th digit should always be greater than the 3rd digit.

$$e>c$$

If a file's label's last digit is 1, then

$$e=1, e>c=>c=0$$

$$b=2a=>a=2, b=4, d=3$$

$$24031$$

(A) first digit is 2