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19 Nov 2021, 04:45
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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:
25%
(medium)
Question Stats:
71% (01:20) correct
29%
(01:26)
wrong
based on 89
sessions
History
Date
Time
Result
Not Attempted Yet
If X is a digit, 369X70 cannot be divided by which of the following numbers?
A. 15
B. 7
C. 4
D. 6
E. 9
A. 15
B. 7
C. 4
D. 6
E. 9
19 Nov 2021, 05:15
Kudos
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C.(this is my first time giving a comment here, am so excited,☺️ tihihihi)
I cannot tell for sure if the number is divisible by the other numbers But am sure it is not divisible by 4 because the last two digits form a number that is not divisible by 4, so the number is not.
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I cannot tell for sure if the number is divisible by the other numbers But am sure it is not divisible by 4 because the last two digits form a number that is not divisible by 4, so the number is not.
Posted from my mobile device
PyjamaScientist
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19 Nov 2021, 05:33
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To do this you need to know the divisibility rules of all the digits.
The number is \(369X70\).
Checking divisibility by \(2 \) & \(5\),
Since, the no. ends with a 0 it will be divisible by 2 and 5.
Checking divisibility by \(3 \) and \(9\),
Summation of all digits of the number is \(= 3+6+9+7+0+X = 25 + X\). So, for \(X = 2\). Sum can be equal to \(27 \) and thus divisible by \(3 \) and 9.
Thus, we can eliminate choices, \(15\), \(6\), and \(9 \) safely.
Checking for divisibility by \(7 \) and \(4\),
As Juliter has rightly pointed out that since the last two digits ain't divisible by \(4\), \(4\) can not be a divisor of the number \(369X70 \) for any value of \(X\).
Let's see why-
\(369X70\) can be written as- \(360000 + 9000 + X00 + 70.\) If we divide this 4, you can see that all the first three terms can be divisible by \(4\), but \(70 \) is not divisible by \(4\). Thus, it is can not be a divisor of \(369X70 \) for any \(X\).
For \(7\), You can see that the last \(70\) will be divisible by \(7 \) and thus you can choose \(X = 6\) to make the first 4 digits of the number divisible by \(7\), i.e, \(\frac{369670}{7} = 52810\). Answer (C)
The number is \(369X70\).
Checking divisibility by \(2 \) & \(5\),
Since, the no. ends with a 0 it will be divisible by 2 and 5.
Checking divisibility by \(3 \) and \(9\),
Summation of all digits of the number is \(= 3+6+9+7+0+X = 25 + X\). So, for \(X = 2\). Sum can be equal to \(27 \) and thus divisible by \(3 \) and 9.
Thus, we can eliminate choices, \(15\), \(6\), and \(9 \) safely.
Checking for divisibility by \(7 \) and \(4\),
As Juliter has rightly pointed out that since the last two digits ain't divisible by \(4\), \(4\) can not be a divisor of the number \(369X70 \) for any value of \(X\).
Let's see why-
\(369X70\) can be written as- \(360000 + 9000 + X00 + 70.\) If we divide this 4, you can see that all the first three terms can be divisible by \(4\), but \(70 \) is not divisible by \(4\). Thus, it is can not be a divisor of \(369X70 \) for any \(X\).
For \(7\), You can see that the last \(70\) will be divisible by \(7 \) and thus you can choose \(X = 6\) to make the first 4 digits of the number divisible by \(7\), i.e, \(\frac{369670}{7} = 52810\). Answer (C)
