Is the radius of circle with center O a whole number? (I)

Question

Is the radius of circle with center O a whole number?
(I) The circumference of the circle is 16 * (22/7)
(II) The ratio of the circumference of the circle to the area of the circle is ¼

(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient

(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

(D) Each statement ALONE is sufficient

(E) Statements (I) and (II) TOGETHER are NOT sufficient

Bunuel · Answer

This is a flawed question.

(1) The circumference of the circle is 16 * (22/7) -->  circumference=2\pi{r}=16*\frac{22}{7}  -->  r=8*\frac{22}{7*{\pi}}
eq{ineger} . Sufficient.

(2) The ratio of the circumference of the circle to the area of the circle is ¼ -->  \frac{circumference}{area}=\frac{2\pi{r}}{\pi{r^2}}=\frac{1}{4}  -->  r=8=integer . Sufficient.

Now, technically answer should be D, as  EACH statement ALONE is sufficient to answer the question .

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as:  on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other .

So we can not have answer NO from statement (1) and answer YES from statement (2), as in this case statements would contradict each other.

Also note that 22/7 is only approximation of  \pi  and not its exact value. If statement (1) were: The circumference of the circle is  16*\pi  then we would have  circumference=2\pi{r}=16*\pi  -->  r=8=integer . Sufficient. So in this case answer would be D and the question wouldn't be flawed.

Is the radius of circle with center O a whole number? (I)

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