**GMATH**practice exercise (Quant Class 16)

The sum of all integers between 500 and 2500 that are divisible by both 18 and 75 is:

(A) 6750

(B) 6300

(C) 5400

(D) 4050

(E) 3150

Answer: [spoiler]______(B)__[/spoiler]

- [email protected]
- GMAT Instructor
**Posts:**1449**Joined:**09 Oct 2010**Thanked**: 59 times**Followed by:**33 members

00:00

**A**

**B**

**C**

**D**

**E**

The sum of all integers between 500 and 2500 that are divisible by both 18 and 75 is:

(A) 6750

(B) 6300

(C) 5400

(D) 4050

(E) 3150

Answer: [spoiler]______(B)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)

English-speakers :: https://www.gmath.net

Portuguese-speakers :: https://www.gmath.com.br

English-speakers :: https://www.gmath.net

Portuguese-speakers :: https://www.gmath.com.br

- [email protected]
- GMAT Instructor
**Posts:**1449**Joined:**09 Oct 2010**Thanked**: 59 times**Followed by:**33 members

$$? = \sum N \,\,\,::\,\,\,\left\{ \matrix{[email protected] wrote:GMATHpractice exercise (Quant Class 16)

The sum of all integers between 500 and 2500 that are divisible by both 18 and 75 is:

(A) 6750

(B) 6300

(C) 5400

(D) 4050

(E) 3150

\,500 < N\,\,{\mathop{\rm int}} < 2500\,\,\,\,\left( * \right) \hfill \cr

\,{N \over {2 \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,;\,\,\,{N \over {3 \cdot {5^2}}} = {\mathop{\rm int}} \,\,\,\,\left( {**} \right) \hfill \cr} \right.$$

$$\left( {**} \right)\,\,\,\, \Rightarrow \,\,\,\,N = k \cdot LCM\left( {2 \cdot {3^2};3 \cdot {5^2}} \right) = k \cdot 2 \cdot {3^2} \cdot {5^2} = 450 \cdot k\,\,\,\,\,\left( {k\,\,{\mathop{\rm int}} } \right)$$

$$\left\{ \matrix{

\,450 \cdot 2 = 900 \hfill \cr

\,\left( {450 \cdot 2} \right) \cdot 3 = 2700 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,k = 2,3,4,5$$

$$? = 450\,\left( {2 + 3 + 4 + 5} \right)\,\,\, = \,\,\,6300$$

The correct answer is (B).

We follow the notations and rationale taught in the

Regards,

Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)

English-speakers :: https://www.gmath.net

Portuguese-speakers :: https://www.gmath.com.br

English-speakers :: https://www.gmath.net

Portuguese-speakers :: https://www.gmath.com.br