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Really quick brain teaser problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Coelhothales » Tue Mar 18, 2014 5:47 am
Hey I need help on this problem , does anyone have an idea if there is a correct answer ?

Mike has three children of different ages. How old is the youngest today?
(1) The two older children have, together, 18 years
(2) The two younger children have, together, 7 years

Does it have a possible answer ?

Thanks all !
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Source: — Quantitative Reasoning |

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by [email protected] » Tue Mar 18, 2014 7:49 pm
Hi Coelhothales,

This is a badly-worded DS question, but the math behind it provides enough information to choose an answer.

We're told that there are three children with different ages. We're asked for the age of the youngest child.

I'm going to call the children...

X = youngest
Y = middle
Z = oldest

Fact 1: Y + Z = 18

This tells us NOTHING about the age of the youngest child.
Fact 1 is INSUFFICIENT

Fact 2: X + Y = 7

We could have...
X = 1, Y = 6
X = 2, Y = 5
X = 3, Y = 4
Since we don't know what age the youngest child actually is...
Fact 2 is INSUFFICIENT

Combined, we run into the same problem that we had with Fact 2: multiple answers.

Y + Z = 18
X + Y = 7

We could have...
X = 1, Y = 6, Z = 12
X = 2, Y = 5, Z = 13
Combined, INSUFFICIENT

Final Answer: E

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by Jim@StratusPrep » Tue Apr 01, 2014 8:19 am
The basic thought is you have 3 variables so you will need 3 separate equations to solve for the variables.

*there are rare instances where multiple variables can be cancelled when simplifying expressions, making this rule not a 100% truth. It is an easy check to see that this does not happen in this case.

Again, this is a poorly worded question, so I would look to a different source for material.
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