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Re: a = 2b = 4c and a, b, and c are integers. [#permalink]
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sandy wrote:
Explanation

Since a is common to both quantities, it can be ignored. The comparison is really between b and c.

Because 2b = 4c, it is true that b = 2c, so the comparison is really between 2c and c. Watch out for negatives. If the variables are positive, Quantity A is greater, but if the variables are negative, Quantity B is greater.



So, the comparison is really between 2c and c.

Why not we cancel both C from both side and rest we get 2 and 1. So A is greater !!!!!!!!!!!!!!!!
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Re: a = 2b = 4c and a, b, and c are integers. [#permalink]
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sandy wrote:
a = 2b = 4c and a, b, and c are integers.

Quantity A
Quantity B
\(a + b\)
\(a + c\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Sometimes a quick approach is looking for values that make the two quantities equal (see video below).

So, for example, it could be the case that a = b = c = 0, In which case the two quantities are equal.
It could be the case that a = 4, b = 2 and c = 1, In which case the two quantities are NOT equal.

Answer: D

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Re: a = 2b = 4c and a, b, and c are integers. [#permalink]
huda wrote:
sandy wrote:
Explanation

Since a is common to both quantities, it can be ignored. The comparison is really between b and c.

Because 2b = 4c, it is true that b = 2c, so the comparison is really between 2c and c. Watch out for negatives. If the variables are positive, Quantity A is greater, but if the variables are negative, Quantity B is greater.



So, the comparison is really between 2c and c.

Why not we cancel both C from both side and rest we get 2 and 1. So A is greater !!!!!!!!!!!!!!!!


Because \(c\) can be negative or positive. You can cancel \(c\) from both sides only when you are hundred percent sure the value of \(c\) is positive.
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a = 2b = 4c and a, b, and c are integers. [#permalink]
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If \(a,b \text{ and } c \text{ are positive }\), then

\(a=2b\)

\(b = \frac{a}{2}\)

\(a = 4c \)

\(c = \frac{a}{4}\)

\(Quantity A = a + \frac{a}{2}\)

\(Quantity B = a + \frac{a}{4}\)

Clearly \(Quantity A > Quantity B\)

But if \(a,b \text{ and } c \text{ are negative }\), we are going to get the opposite

\(Quantity A = -a -\frac{a}{2}\)

\(Quantity B = -a -\frac{a}{4}\)

Clearly \(Quantity B > Quantity A\)

The answer is D. There exists no relationship between the two quantities.
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