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

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Director
Joined: 29 Nov 2012
Posts: 706
The middle two digits of the following numbers are hidden. W  [#permalink]

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17 Aug 2013, 07:45
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Difficulty:

35% (medium)

Question Stats:

69% (01:30) correct 31% (02:01) wrong based on 147 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.
Director
Joined: 14 Dec 2012
Posts: 705
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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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.

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Senior Manager
Joined: 10 Jul 2013
Posts: 289
Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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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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Asif vai.....
Intern
Joined: 07 Feb 2019
Posts: 14
The middle two digits of the following numbers are hidden. W  [#permalink]

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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
Manager
Joined: 19 Jan 2019
Posts: 88
Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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08 Mar 2019, 20:12
2
[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...
Intern
Joined: 07 Feb 2019
Posts: 14
Re: The middle two digits of the following numbers are hidden. W  [#permalink]

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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.
Re: The middle two digits of the following numbers are hidden. W   [#permalink] 08 Mar 2019, 20:20
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