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If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 02:38
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If a and b are integers, is \(a^5 < 4^b\) ? (1) \(a^3 = –27\) (2) \(b^2 = 16\) DS38502.01 OG2020 NEW QUESTION
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 11:17
I thought statement 1 is sufficient. My answer is A.
Statement 2 is clearly insufficient.
Statement 1 establishes that a is negative.
No matter what integer you put as b in 4^b, it wouldnt return a negative value: Ex: 4^4 = large positive number (256) 4^0 = 1 (still positive) 4^2 = small fraction, but still positive (1/16)
Thus proving the inequality sound.
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 10:33
From S1: \(a^{3} = 27\) a = 3 But, No info about b. Insufficient. From S2: \(b^2 = 16\) b = +4 or 4 No info about a. Insufficient. Combining both: 243 < 4^4 243 < 256 Yes \(a^5 < 4^b\) If b = 4 \(243 < 4^{4}\) 243 < 1/256 Yes \(a^5 < 4^b\) C is the answer.
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 11:35
Chethan92 wrote: From S1:
\(a^{3} = 27\) a = 3 But, No info about b. Insufficient.
From S2:
\(b^2 = 16\) b = +4 or 4 No info about a. Insufficient.
Combining both:
243 < 4^4 243 < 256 Yes \(a^5 < 4^b\) If b = 4 \(243 < 4^{4}\) 243 < 1/256 Yes \(a^5 < 4^b\)
C is the answer. Can you give me a scenario where 4^b will yield a negative value... I feel that A is sufficient because no matter what value b takes, 4^b will always be greater than 0 ... Take extreme case , b = 1000/3 .. 4^1000/3 = 4^1/3(1000) = (1/4^1/3)^1000... I need to know what's a and statement 1 gives me value of a... Or atleast sign of a. Which is sufficient to tell that LHS<RHS... I would go with a... Am I missing something?? Posted from my mobile device



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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 11:37
Chethan92 wrote: From S1:
\(a^{3} = 27\) a = 3 But, No info about b. Insufficient.
From S2:
\(b^2 = 16\) b = +4 or 4 No info about a. Insufficient.
Combining both:
243 < 4^4 243 < 256 Yes \(a^5 < 4^b\) If b = 4 \(243 < 4^{4}\) 243 < 1/256 Yes \(a^5 < 4^b\)
C is the answer. Can you provide me a scenario where 4^b will yield a negative value... I have been trying soo hard to figure out the RHS... My reasoning  A look at RHS  4^b... If b = 0.. 4^0 = 1, if b = 1/2.. 4^1/2 = 2.. if b = 1/2 ... 4^1/2 = 1/4^1/2 = 1/2... Take extreme case b= 1000/3 .. then 4^1000/3 = 4^1/3(1000)= {1/4^1/3}^1000....in every case, no Matter whether b is a negative integer, a positive integer, a fractional value... I get 4^b > 0... Soo I just need to know whether a is positive or negative... By statement 1 , a is negative... Which means LHS is <0 ... Which implies that LHS<RHS... sufficient... In statement 2  b^2 = 16... As explained earlier 4^b > 0... Nothing is mentioned about a... If a is negative integer, LHS < RHS... If a is positive integer LHS>RHS... I get two possibilities... Not sufficient... I would go with A... I don't know whether I missed out something.... I would appreciate if someone explain me what I did wrong??... Posted from my mobile device



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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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26 Apr 2019, 11:38
Yes, correct. I missed it Posted from my mobile device
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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27 Apr 2019, 06:23
If base is negative & power is odd, resulting number must be negative.
And if base is positive, whatever the power, the resulting number must be POSITIVE. Statement one is SUFFICIENT.
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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27 Apr 2019, 06:32
Learning points: If BASE is POSITIVE whatever the power (positive/negative/zero), the resulting number must be POSITIVE.
If base is Negative, there are two situations: 1. If power is ODD, the resulting number is NEGATIVE. 2. if power is EVEN, the resulting number is POSITIVE.
That means, there is a SINGLE situation in which the resulting number is NEGATIVE, BASE IS NEGATIVE & POWER IS ODD. In all other cases, the resulting number is POSITIVE.
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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27 Apr 2019, 06:35
NEGATIVE POWER implies that the resulting number is FRACTION. (NEGATIVE POWER DOES NOT SAY ANYTHING WHETHER the resulting number is NEGATIVE or POSITIVE.)
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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07 May 2019, 14:57
Bunuel wrote: If a and b are integers, is \(a^5 < 4^b\) ?
(1) \(a^3 = –27\)
(2) \(b^2 = 16\)
Target question: Is a^5 > 4^b Statement 1: a³ = 27Solve to get: a = 3 So, a^5 = (3)^5 = 243 Since 4^b will be POSITIVE for all values of b, the answer to the target question is NO, a^5 is definitely NOT greater than 4^bSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: b^2 = 16 Solve to get: EITHER b = 4 OR b = 4 Let's test some possible cases: Case a: a = 1 and b = 4. In this case, a^5 = 1^5 = 1, and 4^b = 4^4 = 256. Here, the answer to the target question is NO, a^5 is definitely NOT greater than 4^bCase b: a = 10 and b = 4. In this case, a^5 = 10^5 = 100,000, and 4^b = 4^4 = 256. Here, the answer to the target question is YES a^5 is greater than 4^bSince we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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07 May 2019, 18:34
We need to determine whether a^5 is less than 4^b. Statement One Alone: a^3 = 27 We see that a is 3; so a^5 is negative. However, 4^b is always positive regardless of the value of b. Therefore, a^5 is indeed less than 4^b. Statement one alone is sufficient to answer the question. Statement Two Alone: b^2 = 16 So we see that b = 4 or 4. However, without knowing anything about the value of a, we cannot determine whether a^5 is less than 4^b. For example, if a < 0, then a^5 < b^4. However, if a > 0, then a^5 might be greater than b^4 (for example, a = 5). Statement two alone is not sufficient to answer the question. Answer: A
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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10 May 2019, 16:26
Hi All, We're told that A and B are INTEGERS. We're asked if A^5 is less than 4^B. This question can be approached with a mix of Number Properties and TESTing VALUES. To start, it's worth noting that raising +4 to ANY power will lead to a POSITIVE value (for example, 4^0 = 1, 4^1 = 1/4, etc.). (1) A^3 = 27 Fact 1 tells us that A = 3, although once you realize that A is a NEGATIVE value, you can stop working. By extension, A^5 would be a NEGATIVE value  and since 4^B is a POSITIVE value, we know that A^5 will ALWAYS be less than 4^B. Thus the answer to the question is ALWAYS YES. Fact 1 is SUFFICIENT (2) B^2 = 16 Fact 2 tells us that B = 4, but we don't know anything about the value of A. 4^4 = 16^2 = 256 IF... A = 1, then A^5 = 1 and the answer to the question is YES. A = 4, then 4^5 is clearly GREATER than 4^4, so the answer to the question is NO. Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If a and b are integers, is a^5 < 4^b ? (1) a^3 = –27 (2) b^2 = 16
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