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# All of the following have the same value EXCEPT?

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All of the following have the same value EXCEPT? [#permalink]

Solution

To find:
• The answer choice, whose value is different from the rest

Approach and Working:

• Option A: $$\frac{15}{3} = 5$$

• Option B: $$(\frac{1}{3}) * 5 = \frac{5}{3}$$

• Option C: $$5* \frac{1}{3} = \frac{5}{3}$$

• Option D: $$(\frac{2}{3}) * 5 * \frac{1}{2} = \frac{5}{3}$$

• Option E: $$\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{5}{3}$$

Hence, the correct answer is option A.

Originally posted by EgmatQuantExpert on 18 Sep 2018, 03:35.
Last edited by EgmatQuantExpert on 18 Sep 2018, 09:40, edited 1 time in total.
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Re: All of the following have the same value EXCEPT? [#permalink]
Bunuel wrote:
All of the following have the same value EXCEPT?

A. $$\frac{1 + 2 + 3 + 4 + 5}{3}$$

B. $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$

C. $$\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$$

D. $$\frac{2}{3}(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2})$$

E. $$\frac{1}{3} + \frac{2}{6} + \frac{3}{9} + \frac{4}{12} + \frac{5}{15}$$

It can be clearly seen that:

B. = $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$
taking common $$\frac{1}{3}$$, C = $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$
Taking 2 inside the bracket , we get D = $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$
Simplifying the fractions we get , E= $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$

Hence, A is the odd one out.

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Re: All of the following have the same value EXCEPT? [#permalink]
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Bunuel wrote:
All of the following have the same value EXCEPT?

A. $$\frac{1 + 2 + 3 + 4 + 5}{3}$$

B. $$\frac{1}{3}(1 + 1 + 1 + 1 +1)$$

C. $$\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$$

D. $$\frac{2}{3}(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2})$$

E. $$\frac{1}{3} + \frac{2}{6} + \frac{3}{9} + \frac{4}{12} + \frac{5}{15}$$

If we use the distributive law in choices B and D and simplify each term in choice E, we see that each term is 1/3 in choices B, C, D, and E. However, if we distribute in choice A, we have: 1/3 + 2/3 + 3/3 + 4/3 + 5/3. All the terms are not equal to 1/3. So the answer is A.

Alternate Solution:

Choice A becomes 1/3 + 2/3 + 3/3 + 4/3 + 5/3.

Choice B becomes 1/3 + 1/3 + 1/3 + 1/3 + 1/3.

Choice C is already 1/3 + 1/3 + 1/3 + 1/3 + 1/3.

Since we are looking for the answer choice that is unlike the others, we see, without going any further with our analysis of the answer choices, that Choice A will not yield the same value as B or C (or D or E). Thus, A is the correct answer.

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Re: All of the following have the same value EXCEPT? [#permalink]
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Although we need to check all 5 options before picking up the answer, in this case as question ask "have the same value EXCEPT", After checking the Option A, B, and C, we can easily pick the Option A, as it doesn't have the same value as Option B, and C.

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All of the following have the same value EXCEPT? [#permalink]
We can mutiple by 3 to avoid confusion with fraction because all the options will yield the same answer after multiplying with 3 except A

choice A - 1 + 2 + 3 + 4 + 5

choice b - 1 + 1 + 1 + 1 + 1

choice c - 1 + 1 + 1 + 1 + 1
All of the following have the same value EXCEPT? [#permalink]
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