Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT
Re: If a, b, and c are integers and abc ≠ 0, is a2 – b2 a multiple of 4?
[#permalink]
Show Tags
11 Dec 2014, 22:03
Question can be written as a^2 - b^2 or (a-b)*(a+b) is a multiple of 4 STAT1 alone is not sufficient as we don't know anything about b STAT2 alone is not sufficient as we don't know anything about a Taking both together
If c is odd then c-1 will be even and c*c-1 will be a multiple of 2 else if c i even then again c*c-1) will be a multiple of 2
So, in both the cases c*(c-1) is a multiple of 2. So, -2*(c^2)*((c-1)^2) will be a multiple of 4 (Actually will be a multiple of 8 too) So, Answer will be C
Hope it helps!
viktorija wrote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?
(1) a = (c – 1)^2 --> a=c^2-2c+1.
(2) b = c^2 – 1.
How about this approach? If I simplify question stem to best possible, what am I asked? Is a / b even?
Why? a. A multiple pf 4 is always even b. Squaring of odd / even is always odd /even c. Even - Even = Even. or Odd - Odd = Even
I did above in my head. Essentially, either of statements is clearly insuff since I need to know both a and b.
What happens when I combine and simplify \(a^2\) - \(b^2\) I get -2c + 1.
Even if I do not know value of c, I know -2 will always be even Even + Odd = Odd. So, we do get an unique ans: NO
Hello
Its NOT necessary for a & b to be even for this to be true. a & b could be both odd also. Eg, a=5, b=3, here a^2 - b^2 = 25-9 = 16, which is a multiple of 4.
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2
[#permalink]
Show Tags
22 Apr 2018, 09:54
The math on the previous posts is clear, so I can't add anything to that. That's a surefire way of getting the problem correct.
I took a different approach in plugging in numbers to the prompts. It was obvious right away that 1 and 2 alone are insufficient because they don't give full details about the variables.
After combining, start picking smart numbers for C and work out what A and B would be. I made C = 2, 3, and 4, and then worked out what that would make A and B equal to. This gave me a good enough sample size to test divisibility of 4 and to feel comfortable enough in picking answer choice C.
Is this a perfect approach? No, but I got to the right answer in well under 2 minutes with a high probability of being correct.
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2
[#permalink]
Show Tags
22 Feb 2019, 09:01
Top Contributor
mun23 wrote:
If a, b, and c are integers and abc ≠ 0, is a² – b² a multiple of 4?
(1) a = (c – 1)² (2) b = c² – 1
Given: a, b, and c are integers and abc ≠ 0
Target question:Is a² – b² a multiple of 4?
Statement 1: a = (c – 1)² No information about b. NOT SUFFICIENT
If you're not convinced, let's TEST some values. There are several values of a, b and c that satisfy statement 1. Here are two: Case a: a = 4, b = 2 and c = 3. In this case, a² – b² = 4² – 2² = 12. So, the answer to the target question is YES, a² – b² IS divisible by 4 Case b: a = 4, b = 3 and c = 3. In this case, a² – b² = 4² – 3² = 7. So, the answer to the target question is NO, a² – b² is NOT divisible by 4 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b = c² – 1 No information about a. NOT SUFFICIENT
If you're not convinced, let's TEST some values. There are several values of a, b and c that satisfy statement 2. Here are two: Case a: a = 10, b = 8 and c = 3. In this case, a² – b² = 10² – 8² = 36. So, the answer to the target question is YES, a² – b² IS divisible by 4 Case b: a = 9, b = 8 and c = 3. In this case, a² – b² = 9² – 8² = 17. So, the answer to the target question is NO, a² – b² is NOT divisible by 4 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that a = (c – 1)², so a² = (c – 1)⁴ Statement 2 tells us that b = c² – 1, so b² = (c² – 1)²
This means that: a² - b² = (c – 1)⁴ - (c² – 1)² KEY: the right side is a DIFFERENCE OF SQUARE, which means we can factor it We get: a² - b² = [(c – 1)² + (c² – 1)][(c – 1)² - (c² – 1)] Expand and simplify to get: a² - b² = [(c² - 2x + 1) + (c² – 1)][(c² - 2x + 1) - (c² – 1)] Simplify to get: a² - b² = [2c² - 2x][-2x + 2] Factor out some 2's to get: a² - b² = [2(c² - x)][2(-x + 1)] Simplify to get: a² - b² = 4(c² - x)(-x + 1) We can see that a² - b² is clearly divisible by 4 So, the answer to the target question is YES, a² – b² IS divisible by 4
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
close
72% (02:07) correct 
