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04 Dec 2019, 02:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
42% (01:44) correct
58%
(01:43)
wrong
based on 149
sessions
History
Date
Time
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Not Attempted Yet
If x is a positive integer, is (10x - 1) divisible by the positive integer y ?
(1) x is a multiple of y
(2) y is a prime number
Are You Up For the Challenge: 700 Level Questions
(1) x is a multiple of y
(2) y is a prime number
Are You Up For the Challenge: 700 Level Questions
firas92
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Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
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04 Dec 2019, 05:23
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(1) x is a multiple of y
If x=2, y=1, 10x-1 is divisible by y
If x=3, y=3, 10x-1 is not divisible by y
1 is insufficient
(2) y is a prime number
If x=3, y=3, 10x-1 is not divisible by y
If x=4, y=3, 10x-1 is divisible by y
2 is not sufficient
(1)+(2) x is a multiple of y and y is a prime number
If x is a multiple of y, 10x is a multiple of y and since y cannot be 1 (y is prime), 10x-1 cannot be a multiple of y
(1)+(2) is sufficient
Answer is (C)
If x=2, y=1, 10x-1 is divisible by y
If x=3, y=3, 10x-1 is not divisible by y
1 is insufficient
(2) y is a prime number
If x=3, y=3, 10x-1 is not divisible by y
If x=4, y=3, 10x-1 is divisible by y
2 is not sufficient
(1)+(2) x is a multiple of y and y is a prime number
If x is a multiple of y, 10x is a multiple of y and since y cannot be 1 (y is prime), 10x-1 cannot be a multiple of y
(1)+(2) is sufficient
Answer is (C)
31 Jan 2020, 04:56
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Bunuel
Solution
Step 1: Analyse Question Stem
- • x and y are positive integers.
• We need to find, if \((10x-1)\) is divisible by y
- o Or, if \(\frac{(10x – 1)}{y }= k\) , where k is positive integer.
o Or, if \(\frac{10x}{y }-\frac{1}{y} = k\)
- Hence, for k to be a positive integer either both \(\frac{10x}{y}\) and \(\frac{1}{y}\) have to be integers or both have to be fractions.
Step 2: Analyse Statements Independently
Statement 1: x is a multiple of y
- • According to this statement, \(\frac{x}{y} \) is an integer
- o \(\frac{10x}{y }\) is an integer
- o Let’s take two simple cases to understand the above statement:
- Case 1: If \(y = 1\) then \(\frac{1}{y }=1\) is an integer
Case 2: If \(y ≠ 1\) then \(\frac{1}{y}\) is not an integer.
The results of above two cases are not same. Therefore, we cannot conclude about the nature of 1/y.
Statement 2: y is a prime number
- • According to this statement, \(y ≠ 1 \)
- o \(\frac{1}{y }\)is a fraction
Step 3: Analyse Statements by combining.
- • According to statement 1: \(\frac{10x}{y }\)is an integer
• According to statement 2: \(\frac{1}{y} \)is a fraction
• On combining both, we get
- o \(\frac{10x}{y} - \frac{1}{y }\)is not an integer i.e. \(\frac{10x}{y} - \frac{1}{y }≠ k\)
