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The middle two digits of the following numbers are hidden. W

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Director
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The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 17 Aug 2013, 07:45
2
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:29) correct 31% (02:02) wrong based on 140 sessions

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The middle two digits of the following numbers are hidden. Which of the following could be the total number of oranges in a storage room that has X cartons, where each carton has 12 oranges?

\(a) 50**22\)
\(b) 56**06\)
\(c) 45**20\)
\(d) 26**43\)
\(e) 27**90\)

The total no of oranges = X*12. Thus,\(\frac{# of oranges}{12}\)= X(An Integer)

Thus, the no of oranges has to be a multiple of 12, and thus, must be divisible by 4. The last 2 digits should be divisible by 4 \(\to\) Only C satisfies.
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Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 17 Aug 2013, 08:12
1
fozzzy wrote:
The middle two digits of the following numbers are hidden. Which of the following could be the total number of oranges in a storage room that has X cartons, where each carton has 12 oranges?

\(a) 50**22\)
\(b) 56**06\)
\(c) 45**20\)
\(d) 26**43\)
\(e) 27**90\)

The total no of oranges = X*12. Thus,\(\frac{# of oranges}{12}\)= X(An Integer)

Thus, the no of oranges has to be a multiple of 12, and thus, must be divisible by 4. The last 2 digits should be divisible by 4 \(\to\) Only C satisfies.


theory:
a number is divisible by 4 when last 2 digit of that number is divisible by 4.

QUESTION: Which of the following could be the total number of oranges?

NOTE: COULD BE and MUST BE are different.

let say there are\(n\) number of cartons
therefore total oranges = \(12n\) (since each carton has \(12\) oranges)

so it means total number of oranges is that number which is divisible by \(12\)....or we can say that divisible by \(4.\)

now using the above stated theory we have to check divisibility of only last 2 digits.

clearly option C having \(20\) as last two digit is divisible by \(4.\)

rest all numbers are not divisible by 4.

hence answer C.
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Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 17 Aug 2013, 10:23
fozzzy wrote:
The middle two digits of the following numbers are hidden. Which of the following could be the total number of oranges in a storage room that has X cartons, where each carton has 12 oranges?

\(a) 50**22\)
\(b) 56**06\)
\(c) 45**20\)
\(d) 26**43\)
\(e) 27**90\)

The total no of oranges = X*12. Thus,\(\frac{# of oranges}{12}\)= X(An Integer)

Thus, the no of oranges has to be a multiple of 12, and thus, must be divisible by 4. The last 2 digits should be divisible by 4 \(\to\) Only C satisfies.



Anything that is divisible by 12, must be divisible by 4.

And the last two digits can fix this riddle.

i see 20, so (C) is the Answer
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The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 08 Mar 2019, 19:53
Why didn't we chose option B? As we kno if a number divided by 12 also divided by 3. In option B 06 also divided by 3.Clarify me giving further explanation .

Posted from my mobile device
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Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 08 Mar 2019, 20:12
1
[quote="Talha95"]Why didn't we chose option B? As we kno if a number divided by 12 also divided by 3. In option B 06 also divided by 3.Clarify me giving further explanation .

[size=80][b][i]Posted from my mobile device[/i][/b][/size][/quote]

If a number is divisible by 3, then the sum of it's digits must be divisible by 3..... We cannot tell whether a number is divisible by 3 just by looking at the last two digits.... In option B , we may not know whether that number is really divisible by 3 or not , and we must not even care really checking about divisibility of 3...
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Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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New post 08 Mar 2019, 20:20
thyagi wrote:
Talha95 wrote:
Why didn't we chose option B? As we kno if a number divided by 12 also divided by 3. In option B 06 also divided by 3.Clarify me giving further explanation .

Posted from my mobile device


If a number is divisible by 3, then the sum of it's digits must be divisible by 3..... We cannot tell whether a number is divisible by 3 just by looking at the last two digits.... In option B , we may not know whether that number is really divisible by 3 or not , and we must not even care really checking about divisibility of 3...


Thank you.i can realise now.
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Re: The middle two digits of the following numbers are hidden. W   [#permalink] 08 Mar 2019, 20:20
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