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# There are many boxes in a certain room, and each box has a label attac

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
There are many boxes in a certain room, and each box has a label attac  [#permalink]

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17 Mar 2019, 14:17
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:38) correct 50% (02:31) wrong based on 20 sessions

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GMATH practice exercise (Quant Class 17)

There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels form a sequence of the first N consecutive positive multiples of 4, the value of N is:

(A) divisible by 3
(B) divisible by 7
(C) divisible by 11
(D) divisible by 13
(E) prime

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: There are many boxes in a certain room, and each box has a label attac  [#permalink]

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17 Mar 2019, 17:57
fskilnik wrote:
GMATH practice exercise (Quant Class 17)

There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels form a sequence of the first N consecutive positive multiples of 4, the value of N is:

(A) divisible by 3
(B) divisible by 7
(C) divisible by 11
(D) divisible by 13
(E) prime

$$4 \cdot 1 + 4 \cdot 2 + \ldots + 4 \cdot N = 612$$

$$? = N\,\,\,\,\left( {N \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\left( * \right)$$

$$612 = 4(1 + 2 + \ldots + N)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.Seq}}} \,\,\,4\left[ {{{N\left( {N + 1} \right)} \over 2}} \right]\,\, = \,\,2N\left( {N + 1} \right)$$

$$N\left( {N + 1} \right) = 306 = 2 \cdot {3^2} \cdot 17\,\,\left[ { = 17 \cdot 18} \right]\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,N = 17$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: There are many boxes in a certain room, and each box has a label attac   [#permalink] 17 Mar 2019, 17:57
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