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A positive integer Y is a six digit number of the form

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A positive integer Y is a six digit number of the form  [#permalink]

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New post 08 Aug 2018, 22:10
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Question Stats:

43% (01:42) correct 57% (01:21) wrong based on 37 sessions

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A positive integer Y is a six digit number of the form pqqqqp where p and q are distinct digits. What is the value of p?

(1) Y is divisible by 5.

(2) The integer Y-1 is divisible by 8.

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Re: A positive integer Y is a six digit number of the form  [#permalink]

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New post 09 Aug 2018, 00:24
amanvermagmat wrote:
A positive integer Y is a six digit number of the form pqqqqp where p and q are distinct digits. What is the value of p?

(1) Y is divisible by 5.

(2) The integer Y-1 is divisible by 8.

Posted from my mobile device
digits


pqqqqp is 6-digit number where p and q are distinct


(1) Y is divisible by 5.
so p can be 0 or 5..
but if p is 0, the number becomes 0qqqq0, which is a five digit number and NOT six-digit
hence p is 5
suff

(2) The integer Y-1 is divisible by 8.
just tells us that p is an ODD number
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A positive integer Y is a six digit number of the form  [#permalink]

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New post 09 Aug 2018, 00:44
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amanvermagmat wrote:
A positive integer Y is a six digit number of the form pqqqqp where p and q are distinct digits. What is the value of p?

(1) Y is divisible by 5.

(2) The integer Y-1 is divisible by 8.

Posted from my mobile device


Another great question.

Y =pqqqqp

(1) Y is divisible by 5.

P could be either 0 or 5. But in case P=0, the number is 0qqqq0 = qqqq0 which means only five digits as last zero is meaningless.

Only P =5

Sufficient

(2) The integer Y-1 is divisible by 8.

If Y-1 is divisible by 8, it means that Y-1 is even.....So Y is odd number. It means p is odd number. Let's see

Let's Y =56665...Y-1= 56664........it is divisible by 8..........P =5

Let's Y= 18881...Y-1= 18880........it is divisible by 8..........P = 1

Let's Y= 18889...Y-1= 18888........it is divisible by 8..........P = 9

Different values means no clear cut answer

Insuffcient

Answer: A
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Re: A positive integer Y is a six digit number of the form &nbs [#permalink] 09 Aug 2018, 00:44
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A positive integer Y is a six digit number of the form

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