Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
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x > 10^10
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j_shreyans
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Brent@GMATPrepNow
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Target question: Is x > 10^10?Is x > 10^10?
1) x > 2^34
2) x = 2^35
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
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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GMATGuruNY
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We need to compare POWERS OF 2 to a POWER OF 10.Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
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:
https://www.beatthegmat.com/comparing-va ... 13293.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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[email protected]
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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
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
