BTGmoderatorLU wrote: ↑

Fri Jun 19, 2020 5:08 am

Source: Manhattan Prep

Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old?

1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children's age
2) Sarah is not the oldest child in the room

The OA is C

Sum of the six children = 42.

Let's take each statement one by one.

1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children's age.

Case 1: Say Sara is 7 years old.

We see that the age of the fourth oldest child is also 7 years.

=> 7 = (42 + 7)/7 => 5 = 7. The answer is yes.

Case 2: Say Sara is x years old, where x < 5.

We see that the age of the fourth oldest child is 5 years.

=> 5 = (42 + x)/7 => x = negative number. Not a valid case. Sara is not less than 5 year old.

Case 3: Say Sara is x years old, where x > 8.

We see that the age of the fourth oldest child is 8 years.

=> 8 = (42 + x)/7 => x = 14. Sara is not 7 year old. The answer is no.

No unique answer. Insufficient.

2) Sarah is not the oldest child in the room.

Certainly insufficient.

(1) and (2) together

Case 3 in statement 1 is not applicable. So, only statement 1 is applicable. Sufficient.

Correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan GMAT | GRE Practice Questions | LSAT Practice Test | SAT Info | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.