A sequence consists of the consecutive integers from 1 through m. Does

Question

A sequence consists of the consecutive integers from 1 through m. Does m equal to 49?

(1) The average of the integers in the sequence is not an integer.
(2) The median of the integers in the sequence is not an integer.

ashudhall · Answer

Sum of 49 terms/ 49 is an integer hence m can't be 49. Sufficient
B. Median is not an integer, sonumber of terms must be even.hence m can't be 49
Hence answer is D

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abhishekdadarwal2009 · Answer

IMO : D

A sequence consists of the consecutive integers from 1 through m. Does m equal to 49?

(1) The average of the integers in the sequence is not an integer.
(2) The median of the integers in the sequence is not an integer.

The avg of the sequence that consist of consecutive integers= (first+last)/2.

1) so (1+49)/2=50/2=25 ; which is an integer, that means m is not equal to 49.

Sufficient.

2) the median of the sequence from 1 to 49 =25, which is again a integer, so sufficient m is not =49.

D

merajul · Answer

A sequence consists of the consecutive integers from 1 through m. Does m equal to 49?

(1) The average of the integers in the sequence is not an integer.
(2) The median of the integers in the sequence is not an integer.

(1) Sum can be calcualted from n/2   =1225, which divided by 49 will give average as 25. Thus, it is found average is infact Integer. SUFFICIENT.

(2) Median = Middle Number of a set of numbers. Thus S=  when m=49, the median would be 25. Thus it is found median is in fact integer. SUFFICIENT

Thus correct option is D, both are sufficient

Edskore · Answer

Key concept: Properties of Average and Median for Consecutive Integer Sequences

This is a great Data Sufficiency question because both statements look similar on the surface but force you to think through the same underlying property twice — from slightly different angles.

One key fact to anchor on: For consecutive integers from 1 to m, both the average and the median equal (1 + m) / 2. This is the same formula — because consecutive integers are symmetric around their middle value.

Evaluate Statement (1): "The average is not an integer."
Average = (1 + m) / 2. For this NOT to be an integer, (1 + m) must be odd, which means m must be even. If m is even, then m ≠ 49 (since 49 is odd). We get a definitive "NO" to the question — SUFFICIENT.

Evaluate Statement (2): "The median is not an integer."
For consecutive integers 1 through m, the median is also (1 + m) / 2. Same logic: not an integer → m is even → m ≠ 49. Again a definitive "NO" — SUFFICIENT.

Answer: (D) — each statement alone is sufficient.

Common trap: Students sometimes worry that a "NO" answer isn't really sufficient — they think sufficiency only applies when the answer is "YES." That's wrong. In Data Sufficiency, a clear and definitive "NO" is just as sufficient as a clear "YES." The question is whether you can answer the yes/no question, not whether the answer happens to be yes.

A second trap: seeing that both statements give the same result and assuming you must be making an error. You're not — it just means the GMAT designed the question so (D) is the answer.

Takeaway: In DS problems involving sequences or sets, immediately write down the formula for average and median — they're often the key that unlocks both statements at once.

— Kavya | 725 (99th percentile), GMAT Focus Edition

A sequence consists of the consecutive integers from 1 through m. Does

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GMAT Data Sufficiency (DS) Questions

A sequence consists of the consecutive integers from 1 through m. Does

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