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If P represents a single digit in the four digit number x=17P6, how ma

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New post 11 Aug 2015, 14:20
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If P represents a single digit in the four digit number x=17P6, how many different values of P are there such that x is divisible by 8?

A. 0
B. 1
C. 2
D. 3
E. 4

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If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 11 Aug 2015, 14:30
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reto wrote:
If P represents a single digit in the four digit number x=17P6, how many different values of P are there such that x is divisible by 8?

A. 0
B. 1
C. 2
D. 3
E. 4


Recognise that the p[ossible values are : 1706 , 1716, 1726....1796.

Now, 1706 is NOT divisble by 8 and thus this also rules out 1746 and 1786 as well (1746-1706 =40 a multiple of 8, so if 1706 is not divisble by 8 then 1706 + multiple of 8 will not be divisble by 8).

Similarly, 1716 is not divisible by 8 and thus this eliminates 1756 and 1796 as well.

1726 is not divisible by 8 ---> eliminate 1766

Remaining values, 1736 and 1776 are both divisible by 8 . Hence C,2 is the correct answer.
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If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post Updated on: 22 Sep 2015, 17:34
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A number is divisble by 8 if the last three digits of that number are divisible by 8.

Without much thinking we know that 720 is a multiple of 8.

From there it is obvious that 706, 716, 726, 746, 756, 786, and 796 are not multiples of/divisible by 8.

We're left with 736 and 776 - hence the answer is C.

Originally posted by Marchewski on 29 Aug 2015, 05:35.
Last edited by Marchewski on 22 Sep 2015, 17:34, edited 1 time in total.
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If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 22 Sep 2015, 10:56
when checking from 1706, 1716, 1726, 1736, we got that 1736 is divisible by 8. we know the unit digit is 6, so we need to add a no which should be multiple of 8 and after adding that, it must have the same unit digit 6. so add 40 with 1736, as 40 is one of the multiples of 8, which will give the ans in a required unit digit also a multiple of 8.

Ans C.
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Re: If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 23 Sep 2015, 05:03
Hi,

Start with 1706. The remainder is 2. Hence 1704 is divisible.

Now if we add... 2 to the units digit of 1704(number divisible).. the units digit of the 4 digit number will be 6.

We know 32 is divisible by 8.. Hence 1736 is divisible.. Similarly add.. 72..

Hence answer is C.

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If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 28 Mar 2016, 07:42
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If P represents a single digit in the four digit number x=17P6, how many different values of P are there such that x is divisible by 8?

Method1:
x/8=17P6/8= 1000/8+700/8+10P/8+6/8 = 125+ 87+ 4/8 + 2p/8 +6/8

=Some value+ (4+6)/8 + 2p/8 = some value + (2+2p)/8 => divisible by 8 for p=3 and p=7. Therefore 2 is the answer.

Method2: the last three digits must be divisible by 8
7P6
8*2=16
8*7=56
We have 6 only in these two terms.
Therefore two is the answer.
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If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 20 Dec 2018, 10:02
All the above solutions are too time consuming.

The best solution:

Rule for 8: N is divisible by 8 if its last three digits in conjunction are.

Hence, we take 7P6. We intuitively know that 72*10 is divisible by 8. We also know that the only two products of 8 which have a 6 as unit digit are 16 and 56. Hence, we add those numbers to 720 and move on.
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Re: If P represents a single digit in the four digit number x=17P6, how ma  [#permalink]

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New post 20 Dec 2018, 21:46
reto wrote:
If P represents a single digit in the four digit number x=17P6, how many different values of P are there such that x is divisible by 8?

A. 0
B. 1
C. 2
D. 3
E. 4


1700/8 leaves a remainder of 4
so, in order for x to be divisible by 8,
P6/8 must also leave a remainder of 4
only 36 and 76 do this
2
C
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Re: If P represents a single digit in the four digit number x=17P6, how ma   [#permalink] 20 Dec 2018, 21:46
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