Problem Solving

LUANDATO wrote:Which number is divisible by 2, 3, 4, and 6 but is not divisible by 5?

A. 138
B. 644
C. 1,020
D. 1,428
E. 4,620

The OA is D.

Can any expert help me with this PS question please? Thanks.

Since LCM of 2, 3, 4 and 6 is 12, we must find the number that is divisible by 12 but not divisible by 5.

A number is divisible by 5 if its unit digit is either 0 or 5. Thus, the correct answer must be one among A, B and D.

Among these, the only number divisible12 is 1428.

The correct answer: D

Hope this helps!

-Jay

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BTGmoderatorLU wrote:Which number is divisible by 2, 3, 4, and 6 but is not divisible by 5?

A. 138
B. 644
C. 1,020
D. 1,428
E. 4,620

The OA is D.

Can any expert help me with this PS question please? Thanks.

We see that 138, 644, and 1,428 are not divisible by 5. Of those three numbers, only 1,428 is divisible by 2, 3, 4 and 6 (138 is not divisible by 4 and 644 is not divisible by 3 or by 6).

Answer: D

Hi All,

We're asked which number is divisible by 2, 3, 4, and 6 but is NOT divisible by 5. This question is built around several 'rules of division' patterns - and if you know those patterns, then you can use some 'math shortcuts' on this question and save some calculation time.

To start, we're looking for a number that is NOT divisible by 5.... so if a number 'ends' in a 0 or 5, then we can eliminate it. Eliminate Answers C and E.

Next, any number that is divisible by 4 is ALSO divisible by 2.... and any number that is divisible by 6 is ALSO divisible by 2 and 3. This ultimately means that we need to check 3 of the answers (Answers A, B and D) and find the one that is divisible by both 4 and 6...

Answer A: 138/4 = 34.5.... not evenly divisible by 4. Eliminate Answer A

Answer B: 644/4 = 161...... 644/6 = 107.333.... not evenly divisible by 6. Eliminate Answer B

You might also recognize that you can use the "rule of 3" to eliminate Answer B. The digits of 644.... 6, 4 and 4 add up to 6+4+4 = 14. Since 14 is NOT divisible by 3, 644 is NOT divisible by 3 either.

There's only one answer left...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich