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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Sep 08, 2014 10:19 pm
Is x > 10^10?

1) x > 2^34
2) x = 2^35
Target question: Is x > 10^10?

Statement 1: x > 2^34
NOTE: if 2^34 > 10^10, then x will be greater than 10^10, in which case the statement is sufficient.
If 2^34 < 10^10, then x may or may not be greater than 10^10, in which case the statement is not sufficient

Since the statement is sufficient only if 2^34 > 10^10, we can reword the target question as Is 2^34 > 10^10?
- Apply exponent laws to rewrite both sides: Is (2^10)(2^24) > (2^10)(5^10)?
- Divide both sides by 2^10 to get: Is 2^24 > 5^10?
- Apply exponent laws to rewrite both sides: Is (2^12)² > (5^5)²?
- Take the square root of both quantities to get: Is 2^12 > 5^5?

This is pretty manageable.
- Rewrite both sides to get: Is (2^6)(2^6) > (5^4)(5)?
- Evaluate to get: Is (64)(64) > (625)(5)?
- Estimate to get: Is 3600+ > ≈3000?
The answer is a definite YES
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 2^35
If I wanted to, I could evaluate 2^35, and then determine whether or not x is greater 10^10
So, since I could use statement 2 to answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by GMATGuruNY » Tue Sep 09, 2014 1:09 am
Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35
We need to compare POWERS OF 2 to a POWER OF 10.
Every test-taker should know the following:
2¹� = 1024 ≈ 10³.

Statement 1: x > 2³�
Is 2³� > 10¹�?

(2¹�)(2¹�)(2¹�)(2�) > 10¹�

(10³)(10³)(10³)(16) > 10¹�

(10)�(16) > (10�)(10).

Since the lefthand side is greater than the righthand side, 2³� > 10¹�.
Thus:
x > 2³� > 10¹�
x > 10¹�.
SUFFICIENT.

Statement 2: x = 2³�
Since the value of x is known, we can determine whether x > 10¹�.
SUFFICIENT.

The correct answer is D.

Check here for a similar problem:

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by [email protected] » Tue Sep 09, 2014 4:16 pm
Hi j_shreyans,

As Brent and Mitch have shown, these type of questions aren't really about performing a big calculation, they're more about finding a logical way to compare values. This usually involves breaking a big number down into smaller pieces. Here's another way to do it....

We're asked if X > 10^10. This is a YES/NO question.

Fact 1: X > 2^34

We need to compare 2^34 to 10^10

First, let's break down 10^10 into (2x5)^10

So we have 2^34 vs. (2^10(5^10)

We can divide both by 2^10, which leave us....

2^24 vs. 5^10

Now, let's try to find a set of smaller values that are close....

2^7 = 128
5^3 = 125

2^24 = (2^7)(2^7)(2^7)(2^3) = (128)(128)(128)(8)
5^10 = (5^3)(5^3)(5^3)(5^1) = (125)(125)(125)(5)

Without actually multiplying those numbers, we can see that 2^24 is BIGGER than 5^10.

Since X > 2^34, we now know that it's ALSO > 10^10 and the answer to the question is YES.
Fact 1 is SUFFICIENT

Fact 2: X = 2^35

Since we COULD calculate this, we would eventually be able to figure out if X > 10^10 or not and there would be one definitive answer to the question. As it stands, we know that the answer would be YES, but we don't need to do that math.
Fact 2 is SUFFICIENT

Final Answer: D

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