**Economist GMAT**

How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120

B. 148

C. 360

D. 540

E. 720

OA E

00:00

**A**

**B**

**C**

**D**

**E**

How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120

B. 148

C. 360

D. 540

E. 720

OA E

- GMATGuruNY
- GMAT Instructor
**Posts:**15495**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1877 members**GMAT Score:**790

Let the 3 math books = A, B, C and the remaining 4 books = D, E, F, G.AAPL wrote:Economist GMAT

How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120

B. 148

C. 360

D. 540

E. 720

Since the 3 math books must be next to one another, put them together in a block:

[ABC].

The number of ways to arrange the 5 elements [ABC], D, E, F and G = 5! = 120.

Since A, B and C can swap positions within the [ABC] block, the result above must be multiplied by the number of ways to arrange A, B and C within the block (3!):

120 * 3! = 720.

The correct answer is E.

Mitch Hunt

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- Scott@TargetTestPrep
- GMAT Instructor
**Posts:**3997**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**20 members

Let's think of the three math books as a single group. Then, the four non-math books together with the group of math books can be arranged in 5! = 120 ways. Within the group, the three math books can be arranged in 3! = 6 ways; therefore, a total of 120 x 6 = 720 arrangements are possible.AAPL wrote:Economist GMAT

How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120

B. 148

C. 360

D. 540

E. 720

OA E

Answer: E

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