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Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5

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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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Rs1991 wrote:
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = ?

A. 5^6
B. 13^5
C. 2^6 + 3^6
D. 2^7 + 3^8
E. 4^5 + 9^5

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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
I did it using the answer choices.

After reaching this point:
2^5 + 2^5 + 3^5 + 3^5 + 3^5
= 2 (2^5) + 3 (3^5)

I just took the answer choices from E upwards and rejected them.

E.g E. 4^5 + 9^5, has many more numbers that what we want, because 4^5 is equal to 2^10. No need to check 9^5.
D similarly has more numbers than we want, D. 2^7 + 3^8, since we have 2*2*2*2*2*2*2, so this is 2*2^6.

ANS C, gives as the number we are looking for.
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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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2^5 + 2^5 + 3^5 + 3^5 + 3^5

2^5 (1+1) + 3^5 (1+1+1)

2^5 (2) + 3^5 (3)

2*2*2*2*2*2 + 3*3*3*3*3*3

= 2^6 + 3^6
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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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japped187 wrote:
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5 ?

A. 5^6
B. 13^5
C. 2^6 + 3^6
D. 2^7 + 3^8
E. 4^5 + 9^5

Given: 2^5 + 2^5 + 3^5 + 3^5 + 3^5

Notice that this expression has the same STRUCTURE as x + x + y + y + y
Simplifying, we get: x + x + y + y + y = 2x + 3y

LIKEWISE, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)
= (2^1)(2^5) + (3^1)(3^5)
= 2^6 + 3^6

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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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japped187 wrote:
Which of the following is equal to the value of $$2^5 + 2^5 + 3^5 + 3^5 + 3^5$$ ?

A. $$5^6$$

B. $$13^5$$

C. $$2^6 + 3^6$$

D. $$2^7 + 3^8$$

E. $$4^5 + 9^5$$

2*2^5 + 3*3^5 = 2^6 + 3^6

IMO C

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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
GMATPrepNow wrote:
japped187 wrote:
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5 ?

A. 5^6
B. 13^5
C. 2^6 + 3^6
D. 2^7 + 3^8
E. 4^5 + 9^5

Given: 2^5 + 2^5 + 3^5 + 3^5 + 3^5

Notice that this expression has the same STRUCTURE as x + x + y + y + y
Simplifying, we get: x + x + y + y + y = 2x + 3y

LIKEWISE, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)
= (2^1)(2^5) + (3^1)(3^5)
= 2^6 + 3^6

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Hi

I was just wondering when I made the equation 2^5 (1+1) + 3^5 (1+1+1) ------> 2^5 (2) + 3^5 (3) felt that it should be 4^5 + 9^5 with direct multiplication irrespective of powers. Can you help me understand why it won't be that please?
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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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$$2^5 + 2^5 + 3^5 + 3^5 + 3^5$$

$$=(2^5 + 2^5) + (3^5 + 3^5 + 3^5)$$

$$=2^5 (1+1) + 3^5 (1+1+1)$$

$$=2^5 (2) + 3^5 (3)$$

$$=2^6 + 3^6$$
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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
japped187 wrote:
Which of the following is equal to the value of $$2^5 + 2^5 + 3^5 + 3^5 + 3^5$$ ?

A. $$5^6$$

B. $$13^5$$

C. $$2^6 + 3^6$$

D. $$2^7 + 3^8$$

E. $$4^5 + 9^5$$

Simplifying, we have:

2^5(1 + 1) + 3^5(1 + 1 + 1)

2^5 x 2^1 + 3^5 + 3^1

2^6 + 3^6

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Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 [#permalink]
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japped187 wrote:
Which of the following is equal to the value of $$2^5 + 2^5 + 3^5 + 3^5 + 3^5$$ ?

A. $$5^6$$

B. $$13^5$$

C. $$2^6 + 3^6$$

D. $$2^7 + 3^8$$

E. $$4^5 + 9^5$$

2^5=32
32+32=64=2^6

3^5=243
243+243+243=729=3^6

Therefore 2^6+3^6
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