a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of

Question

a, b, c, and d are all positive integers. If  \frac{ab}{c + d} = 3.7 , which of the following statements must be true ?

I. ab is divisible by 5
II. c + d is divisible by 5
III. If c is even, then d must be even

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

LeoN88 · Answer

a,b,c and d >0 Integers

10 (ab) = (c+d)*37
I. ab can also be a number not divisible by 5.
e.g. 10(37)= (c+d)*37

II. c+d must have 2 and 5 prime factors for the equation to hold true.

III. c+d must be 10k which is even so if c is even then d has to be even.

II and III  D

GMATWhizTeam · Answer

Solution:  
 • We can right the relation given as shown below:
 \frac{ab}{(c+d)}=\frac{37}{10} 
• Let  37k  and  10k  be the value of ab and  (c+d) , respectively, where  k  is an integer.
 o  \frac{ab}{(c+d)}=\frac{37k}{10k}=\frac{37*k}{2*5*k} 
   Statement 1:   ab  is divisible by  5 
 •  ab = \frac{37*k}{2*5*k}*(c+d) 
 o If  c = d =5 , then  ab = 37 
o Which is not a multiple of  5 .
  Hence, statement 1 is not true.
 Statement 2:   c + d  is divisible by  5 
 •  c + d = 2*5*k 
 o  \frac{(c + d)}{5} = 2*k = integer .
o  c + d  is divisible by  5 .  
Hence, statement 2 is always true.
 Statement 3:  If  c  is even, then  d  must also be an even number.
 •  c + d = 2*5*k 
•  even + d = even 
 o  d = even – even 
o  d =even ,   
 Hence, statement 3 is also always true.
Thus, the correct answer is  Option D .

Sparta_750 · Answer

ab= (c+d)3 +0.7(c+d)

A simple equation can be derived for the remainder

R/(c+d) = 7/10

So II has to be true since (c+d) is necessarily a multiple of 10
And III has to be true because if c is even, d has to be even in order for c+d to be a multiple of 10 (or even)

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a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of

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a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of

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