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05 Mar 2020, 08:04
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The symbol \(*\) represents the third digit in the 5-digit number \(62,*79\). What number does \(*\) represent?
(1) \(62,*79\) is a multiple of 3.
(2) The sum of the digits of \(62,*79\) is divisible by 4.
(1) \(62,*79\) is a multiple of 3.
(2) The sum of the digits of \(62,*79\) is divisible by 4.
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05 Mar 2020, 23:18
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The symbol ∗ represents the third digit in the 5-digit number 62,∗79. What number does ∗ represent?
(1) 62,∗79 is a multiple of 3.
(2) The sum of the digits of 62,∗79 is divisible by 4.
statement 1: 24 + x = 3k
x = [0,3,6,9]; not sufficient
statement 2: 24 + x = 4k
x = [0,4,8]; not sufficient
combining both statements,
24 + x is divisible by 12.
x = 0, (24 + 0) is divisible by 12.
next multiple of 12 is 36 and x can not be greater than 9.
so the only possible value for x is 0.
Ans: C
(1) 62,∗79 is a multiple of 3.
(2) The sum of the digits of 62,∗79 is divisible by 4.
statement 1: 24 + x = 3k
x = [0,3,6,9]; not sufficient
statement 2: 24 + x = 4k
x = [0,4,8]; not sufficient
combining both statements,
24 + x is divisible by 12.
x = 0, (24 + 0) is divisible by 12.
next multiple of 12 is 36 and x can not be greater than 9.
so the only possible value for x is 0.
Ans: C
06 Mar 2020, 08:11
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From the question statement, we know that the symbol * represents a single digit.
From statement I alone, we know that 62*79 is a multiple of 3.
A number is a multiple of 3 if the sum of all of its digits is divisible by 3.
The sum of the digits of 62*79 is 24+*. If 24+* has to be a multiple of 3, 24+* has to be either 24 itself or 27 or 30 or 33 since * is a single digit and the greatest single digit number is 9.
From the above, we may conclude that * can be 0 or 3 or 6 or 9. Statement I alone is insufficient to find a unique value for the symbol *.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we know that the sum of the digits of 62*79 is divisible by 4. This means 24+* is divisible by 4. * can be 0 or 4 or 8. Statement II alone is insufficient to find a unique value for the symbol *.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements, I and II, the only value of * that satisfies both the statements is 0. Therefore, * HAS TO be 0. The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
Did you see how 0 could have been easily missed out if you did not pay attention to the sum of the other 4 digits? The sum of 6,2,7 and 9 here gave us 24 and that’s what makes 0 a possible value. So you’ll have to be alert about this fact that you already have the sum of the digits to be a multiple of 3 or 4 and therefore 0 can be a possible value for *. Additionally, 0 is a single digit value, so it fits the bill this way too.
Hope that helps!
From statement I alone, we know that 62*79 is a multiple of 3.
A number is a multiple of 3 if the sum of all of its digits is divisible by 3.
The sum of the digits of 62*79 is 24+*. If 24+* has to be a multiple of 3, 24+* has to be either 24 itself or 27 or 30 or 33 since * is a single digit and the greatest single digit number is 9.
From the above, we may conclude that * can be 0 or 3 or 6 or 9. Statement I alone is insufficient to find a unique value for the symbol *.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we know that the sum of the digits of 62*79 is divisible by 4. This means 24+* is divisible by 4. * can be 0 or 4 or 8. Statement II alone is insufficient to find a unique value for the symbol *.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements, I and II, the only value of * that satisfies both the statements is 0. Therefore, * HAS TO be 0. The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
Did you see how 0 could have been easily missed out if you did not pay attention to the sum of the other 4 digits? The sum of 6,2,7 and 9 here gave us 24 and that’s what makes 0 a possible value. So you’ll have to be alert about this fact that you already have the sum of the digits to be a multiple of 3 or 4 and therefore 0 can be a possible value for *. Additionally, 0 is a single digit value, so it fits the bill this way too.
Hope that helps!
