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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 [#permalink] New post   28 May 2019, 01:24
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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
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Re: a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of [#permalink] New post   22 Feb 2020, 14:07
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Bunuel wrote:
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



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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Re: a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of [#permalink] New post   28 May 2019, 01:35
Bunuel wrote:
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

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
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Re: a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of [#permalink] New post   18 Feb 2020, 04:01
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Bunuel wrote:
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


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 \(d =even\), [difference of two even number is always even]
Hence, statement 3 is also always true.
Thus, the correct answer is Option D.
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Re: a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of [#permalink] New post   12 Jan 2022, 18:55
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Re: a, b, c, and d are all positive integers. If ab/(c + d) = 3.7 which of [#permalink]
12 Jan 2022, 18:55
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