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29 Jan 2025, 01:30
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D
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Difficulty:
85%
(hard)
Question Stats:
54% (02:33) correct
46%
(02:34)
wrong
based on 171
sessions
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If 917p4q6 is a 7-digit positive integer that is divisible by both 8 and 9 then which of the following can be possible values of p/q?
I. 0
II. 8
III. 9
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
I. 0
II. 8
III. 9
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
29 Jan 2025, 02:25
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Divisibility rule of 8: Last 3 digits should be divisible by 8. By this way, there are three numbers possible for \(q\) \(1, 5, 9\).
Divisibility rule of 9: Sum of the digits should be divisible by 9. Sum of known digits is 27. So \(p+q\) should be divisible by 9.
From both of these conditions, there are 3 possible combinations for \((p,q)\): \((8,1)\), \((4,5)\), \((0,9)\)
\(\frac{p}{q}\) can be \(8\), \(\frac{4}{5}\), or \(0\)
Out of the given options, only \(I\) & \(II\) are possible
Answer: D
Divisibility rule of 9: Sum of the digits should be divisible by 9. Sum of known digits is 27. So \(p+q\) should be divisible by 9.
From both of these conditions, there are 3 possible combinations for \((p,q)\): \((8,1)\), \((4,5)\), \((0,9)\)
\(\frac{p}{q}\) can be \(8\), \(\frac{4}{5}\), or \(0\)
Out of the given options, only \(I\) & \(II\) are possible
Answer: D
29 Jan 2025, 03:18
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917p4q6
integer that is divisible by both 8 and 9
values of p/q?
Checking divisibility by 9:
Sun of the digits shoul be a multiple of 9.
The sum of known digits = 27
Hence p+q = 9
Hence possible combinations:
0+9,9+0,1+8, 8+1, 2+7, 7+2, 3+6, 6+3, 4+5, 5+4
Checking divisibility by 8
Las 3 digits of the number should be multiple of 8
Hence,
4q6 should be divisible by 8
Hence possible q values be 9, 1,5
Hence possible p,q combinations:
(0,9), (8,1), (4,5)
Hence possible p/q = 0, 8, 4/5
Hence IMO Ans D
integer that is divisible by both 8 and 9
values of p/q?
Checking divisibility by 9:
Sun of the digits shoul be a multiple of 9.
The sum of known digits = 27
Hence p+q = 9
Hence possible combinations:
0+9,9+0,1+8, 8+1, 2+7, 7+2, 3+6, 6+3, 4+5, 5+4
Checking divisibility by 8
Las 3 digits of the number should be multiple of 8
Hence,
4q6 should be divisible by 8
Hence possible q values be 9, 1,5
Hence possible p,q combinations:
(0,9), (8,1), (4,5)
Hence possible p/q = 0, 8, 4/5
Hence IMO Ans D
