# GMAT Sample Questions & Answers

## GMAT sample questions and answers written by our admissions experts

**Problem solving: Geometry, Circles**

**Question:**

*In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?*

*(A) 4*

*(B) 3*

*(C) 2*

*(D) √3 *

*(E) √2*

**Answer:**

Before we examine the different approaches to this question, we should have a clear idea of what is happening in this case:

There are two circles; a small one and a big one and the small one is completely contained within the big circle.

The shaded area represents the difference in the area between them:

Area of big circle = Area of small circle + shaded area

The shaded area, according to the question, is 3 times the area of the small circle:

Shaded area = 3 x area of small circle.

Substituting in the above equation:

Area of big circle = Area of small circle + 3 x area of small circle

Thus: area of big circle = 4 x area of small circle

So how many times is the circumference of the big circle greater than circumference of the small circle?

**The academic approach**

We need to recall the basic formulas that relate to circles:

Area of circle: A=πR^2

Circumference of circle: C=2πR

Where r is the radius of the circle.

In terms of the areas, we saw above that: area of big circle = 4 x area of small circle

We can now say that: πR_BIG^2=4× πR_SMALL^2

Cancelling p in both sides, we will have R_BIG^2=4× R_SMALL^2

Taking the square root on both sides: RBIG = 2 x RSMALL

Now, the circumference of big circle is 2πR_BIG

But if we replace RBIG with 2 x RSMALL, we will have:

Circumference of big circle is 2π2×R_SMALL.

However, π2×R_SMALL= 2πR_SMALL, which is the circumference of the small circle.

Therefore, the circumference of the big circle is 2 x the circumference of the small circle and the correct answer is C.

**A simpler approach: similarity**

The small and big circles have identical shape (quite obviously!). We could see the big circle as a ‘magnified version’ of the small circle. When this happens, we have ‘similarity’: all linear measures of both circles are proportional: radii, diameters, circumferences.

That means if the radius of the big circle is k times bigger than the radius of the small circle, then:

The diameter of the big circle will be k times bigger that the diameter of the small circle

The circumference of the big Circle will be k times bigger that the circumference of the small circle

What about the two areas? They will also be proportional, but to k2. Therefore:

The area of the big circle will be k2 times bigger that the area of the small circle.

Thus, in our case, k2 = 4 and k = 2. So, the circumference of the big circle is 2x the circumference of the small one. The correct answer is C.

**Read More: How Can You Score 800 On The GMAT?**

**Problem solving: Algebra, Plug-in numbers, Quant**

**Question:**

*If 1 < x < y < z, which of the following has the greatest value?*

*A. z(x + 1)*

*B. z(y + 1)*

*C. x(y + z)*

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