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Manager  Joined: 21 Mar 2007
Posts: 56
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5  [#permalink]

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6
31 00:00

Difficulty:   5% (low)

Question Stats: 83% (00:51) correct 17% (01:20) wrong based on 492 sessions

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

Originally posted by japped187 on 07 Mar 2008, 02:53.
Last edited by Bunuel on 08 Oct 2019, 07:12, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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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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13
5
Rs1991 wrote:
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

$$(2^5+2^5) + (3^5+3^5+3^5)$$
$$= 2*2^5 + 3*3^5$$ (You have two 2^5 so you club them as 2*2^5. Similarly for 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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3
3
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^(1+5) + 3^(1+5)
= 2^6 + 3^6

Ans: 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]

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2
7
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]

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2
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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1
Top Contributor
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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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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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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E-mail : kinshook.chaturvedi@gmail.com Re: Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5   [#permalink] 08 Oct 2019, 07:28
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