If Adam is a centimeters tall, Alfredo is b centimeters tall, and Davi

Question

If Adam is  a  centimeters tall, Alfredo is  b  centimeters tall, and David is  c  centimeters tall, is  b  equal to the median of  a ,  b , and  c  ?

(1) Adam and Alfredo are exactly the same height.

(2) David is 5 centimeters taller than Alfredo.

This is a  CR Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

gmatophobia · Answer

Statement 1

(1) Adam and Alfredo are exactly the same height.

There are three possibilities -

1) The height of Adam and Alfredo is less than that of David. If that was the case, the height can be represented in increasing order as -

a \quad b \quad c

2) The height of Adam and Alfredo is more than that of David. If that was the case, the height can be represented in increasing order as -

c \quad b \quad a

3) The height of Adam, Alfredo, and David are the same. If that was the case, the height can be represented in increasing order as -

a \quad b \quad c

In all three cases,  b  is equal to the median of  a ,  b , and  c . The statement is sufficient, and we can eliminate B, C, and E.

Statement 2

(2) David is 5 centimeters taller than Alfredo.

1) David is the tallest and Alfredo is the shortest

b \quad a \quad c=b+5

2) David is the tallest and Adam is the shortest

a \quad b \quad c=b+5

As we have two conflicting answers to the question, the statement is not sufficient.

Option A

Beko · Answer

Hello gmatophobia,

couldn't we arrange it in statement 1 as

" c a b " too if Adam and Alfredo are equally tall and taller than david?

Thank you very much in advance!

Best regards

gmatophobia · Answer

Hello  Beko ,

Yes, we can do so. But as the heights represented by a and b are the same it doesn't matter if the arrangement is -

c a b or c b a or otherwise.

The value represented by b will always be at the median.

For example say a = b = 5; c = 10

b a c → 5 5 10
a b c → 5 5 10

Hence, the value 5 is always the median.

Hope this clarifies.

If Adam is a centimeters tall, Alfredo is b centimeters tall, and Davi

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If Adam is a centimeters tall, Alfredo is b centimeters tall, and Davi

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards