Hi, this is my first question post. The question comes from the first CAT from the mba.com site. I don't believe there are explanations out there for these problems, but please correct me if I'm wrong. Similarly, I had trouble searching the forum to see if my question (or a similar one) had already been posted. Is there a recommended way to search? I'd hate post a bunch of repeats.
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5.
1. 5^6
2. 13^5
3. 2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
The official answer is option 3. I recognize now that this is the case, but I haven't identified a noncalculation intensive method to solve the problem. What am I missing?
question from mba.com CAT
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saritalr wrote:
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5.
1. 5^6
2. 13^5
3. 2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
The official answer is option 3. I recognize now that this is the case, but I haven't identified a noncalculation intensive method to solve the problem. What am I missing?
2^5 + 2^5 + 3^5 + 3^5 + 3^5
take 2^5 and 3^5 common you will get
2^5 (1+1) + 3^5 (1+1+1)
= 2^5 (2) + 3^5 (3)
= 2^6 + 3^6

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Thanks for your response. Would you mind elaborating a little more? How did you determine that both powers would be 6?RumpelThickSkin wrote:saritalr wrote:
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5.
1. 5^6
2. 13^5
3. 2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
The official answer is option 3. I recognize now that this is the case, but I haven't identified a noncalculation intensive method to solve the problem. What am I missing?
2^5 + 2^5 + 3^5 + 3^5 + 3^5
take 2^5 and 3^5 common you will get
2^5 (1+1) + 3^5 (1+1+1)
= 2^5 (2) + 3^5 (3)
= 2^6 + 3^6

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= 2^5 (2) + 3^5 (3)
multiply 2^5(2) = 2^6 + multiply 3^5 (3) = 3^6
answer 2^6 + 3^6 .. that's all there is to it!
multiply 2^5(2) = 2^6 + multiply 3^5 (3) = 3^6
answer 2^6 + 3^6 .. that's all there is to it!

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Okay, thanks for clarifying. I'd originally considered that method to be more calculation intensive, but I suppose if I memorized 2^2 through 2^10 I'd have a clearer idea of the right answer straight off the bat.RumpelThickSkin wrote:= 2^5 (2) + 3^5 (3)
multiply 2^5(2) = 2^6 + multiply 3^5 (3) = 3^6
answer 2^6 + 3^6 .. that's all there is to it!
Mostly I was concerned that there was a simpler method that I was missing  but I guess that isn't the case. Thanks again!
 Abhishek009
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Normally CAT test takers follow an approach of Cyclicity of numbers.saritalr wrote:Hi, this is my first question post. The question comes from the first CAT from the mba.com site. I don't believe there are explanations out there for these problems, but please correct me if I'm wrong. Similarly, I had trouble searching the forum to see if my question (or a similar one) had already been posted. Is there a recommended way to search? I'd hate post a bunch of repeats.
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5.
1. 5^6
2. 13^5
3. 2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
The official answer is option 3. I recognize now that this is the case, but I haven't identified a noncalculation intensive method to solve the problem. What am I missing?
I am providing a link for the same : https://takshzilabeta.com/index.php?opti ... &Itemid=5
This is just for reference but I personally feel that the solution provided by deeyah is the best and quickest method for solving this problem.
Abhishek

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I just read something in my number properties review book that made the problem above snap into place. RumpleThickSkin  it may have been what you were trying to explain but I just didn't understand because I didn't know the exponent rule.saritalr wrote:Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5.
1. 5^6
2. 13^5
3. 2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
The official answer is option 3. I recognize now that this is the case, but I haven't identified a noncalculation intensive method to solve the problem. What am I missing?
Exponent rule: a^x + a^x + a^x = 3a^x
Example: 3^4 + 3^4 + 3^4 = 3 "¢ 3^4 = 3^5
Example 2: 3^x + 3^x + 3^x = *3 "¢ 3^x = 3^1 "¢ 3^x* = 3^(x +1)
Example 3: 2^3 + 2^3 = 2(2^3) = 2^4
*note that any number that does not have an exponent implicitly has an exponent of 1.
3 "¢ 3^x = 3^1"¢ 3^x = 3^(x + 1)*
Thanks everyone!
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Hi,saritalr wrote:Okay, thanks for clarifying. I'd originally considered that method to be more calculation intensive, but I suppose if I memorized 2^2 through 2^10 I'd have a clearer idea of the right answer straight off the bat.RumpelThickSkin wrote:= 2^5 (2) + 3^5 (3)
multiply 2^5(2) = 2^6 + multiply 3^5 (3) = 3^6
answer 2^6 + 3^6 .. that's all there is to it!
Mostly I was concerned that there was a simpler method that I was missing  but I guess that isn't the case. Thanks again!
you don't need to do any calculations with the method provided  you just need to understand how exponents work.
An exponent signifies how many times to multiply a number by itself.
For example, 2^5 = 2*2*2*2*2
Accordingly, when we multiply two terms with the same base, we add the exponents:
2^5 * 2^6 = (2*2*2*2*2)*(2*2*2*2*2*2) = 2^(5+6) = 2^11
So, back to the question you posted:
2^5 + 2^5 = 2 * 2^5 = 2*(2*2*2*2*2) = 2^6
(As another poster noted, a nonvisible exponent is really an exponent of 1, so 2^1 * 2^5 = 2^(1+5) = 2^6.)
Similarly:
3^5 + 3^5 + 3^5 = 3 * 3^5 = 3*(3*3*3*3*3) = 3^6
(Or, again, 3^1 * 3^5 = 3^(1+5) = 3^6.)
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Great thread, everyone! You've all worked the problem out nicely, but it also brings up a pretty key takeaway that's worth mentioning.
I talk to my students about "finding opportunities to do what you do well", kind of like the business concept of "core competencies" (if you're, like Amazon.com, great at distribution of media, then find opportunities like the Kindle to continue to do it even better; Amazon, however, isn't great at brickandmortar setups, so you won't see them partnering with Starbucks to create inperson stores with cafes, etc.).
On the GMAT, there are things that you should be good at, and some things that you can probably recognize right away that you're not good at (at least not in ~2 minutes per question without a calculator).
This is a great example of that  we're awful at adding and subtracting exponents, but we're pretty good at multiplying them. When you see a series of exponents added together, you probably need to find a way to use your "core competency" of multiplication. The easiest way to do that is typically to factor, which allows you to turn addition into multiplication.
When you see complex problems on the GMAT, ask yourself how to turn what you see into something that you do well. With core competencies like prime factorization, factoring, using number properties, etc., you should be able to solve any problem as long as you can get that problem on your terms.
I talk to my students about "finding opportunities to do what you do well", kind of like the business concept of "core competencies" (if you're, like Amazon.com, great at distribution of media, then find opportunities like the Kindle to continue to do it even better; Amazon, however, isn't great at brickandmortar setups, so you won't see them partnering with Starbucks to create inperson stores with cafes, etc.).
On the GMAT, there are things that you should be good at, and some things that you can probably recognize right away that you're not good at (at least not in ~2 minutes per question without a calculator).
This is a great example of that  we're awful at adding and subtracting exponents, but we're pretty good at multiplying them. When you see a series of exponents added together, you probably need to find a way to use your "core competency" of multiplication. The easiest way to do that is typically to factor, which allows you to turn addition into multiplication.
When you see complex problems on the GMAT, ask yourself how to turn what you see into something that you do well. With core competencies like prime factorization, factoring, using number properties, etc., you should be able to solve any problem as long as you can get that problem on your terms.
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