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by fskilnik@GMATH » Sun Mar 17, 2019 1:06 pm

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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

Answer: [spoiler]_____(E)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Sun Mar 17, 2019 4:40 pm
fskilnik@GMATH 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
$$4 \cdot 1 + 4 \cdot 2 + \ldots + 4 \cdot N = 612$$
$$? = N\,\,\,\,\left( {N \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\left( * \right)$$
$$612 = 4(1 + 2 + \ldots + N)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.Seq}}} \,\,\,4\left[ {{{N\left( {N + 1} \right)} \over 2}} \right]\,\, = \,\,2N\left( {N + 1} \right)$$
$$N\left( {N + 1} \right) = 306 = 2 \cdot {3^2} \cdot 17\,\,\left[ { = 17 \cdot 18} \right]\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,N = 17$$

The correct answer is (E).


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

Regards,
Fabio.
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