GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 06:53 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # There are many boxes in a certain room, and each box has a label attac

Author Message
TAGS:

### Hide Tags

GMATH Teacher P
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]

### Show Tags 00:00

Difficulty:   55% (hard)

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

### HideShow timer Statistics

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 P
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]

### Show Tags

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
Display posts from previous: Sort by

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