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a and b are positive. (a + 6) : (b + 6) = 5 : 6
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14 Apr 2019, 10:17
14 Apr 2019, 10:17
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a and b are positive. (a + 6) : (b + 6) = 5 : 6
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.
Quantity A |
Quantity B |
\(\frac{a+10}{b+10}\) |
1 |
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.
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a and b are positive. (a + 6) : (b + 6) = 5 : 6
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22 Apr 2019, 17:38
22 Apr 2019, 17:38
1
Carcass wrote:
a and b are positive. (a + 6) : (b + 6) = 5 : 6
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.
Quantity A |
Quantity B |
\(\frac{a+10}{b+10}\) |
1 |
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.
Since b is positive, we know that b+10 is POSITIVE
So, we can safely multiply both quantities by b+10 to get:
QUANTITY A: a + 10
QUANTITY B: b + 10
Subtract 10 from both quantities to get:
QUANTITY A: a
QUANTITY B: b
At this point, we'll need to use the given information: (a + 6) : (b + 6) = 5 : 6
Rewrite as: (a + 6)/(b + 6) = 5/6
Cross multiply to get: 6(a + 6) = 5(b + 6)
Expand to get: 6a + 36 = 5b + 30
Subtract 30 from both quantities: 6a + 6 = 5b
Divide both sides by 5 to get: b = 6a/5 + 6/5
Replace b with 6a/5 + 6/5 to get:
QUANTITY A: a
QUANTITY B: 6a/5 + 6/5
At this point, we can continue the solution in TWO ways
Approach #1: number sense
Since a is positive, we know that 6a/5 is greater than a, which means 6a/5 + 6/5 is definitely greater than a
In other words, Quantity A is greater
Answer: A
Approach #2: matching operations
Take:
QUANTITY A: a
QUANTITY B: 6a/5 + 6/5
Subtract a from both quantities to get:
QUANTITY A: 0
QUANTITY B: a/5 + 6/5
Subtract 6/5 from both quantities to get:
QUANTITY A: -6/5
QUANTITY B: a/5
Since a is positive, we know that a/5 is POSITIVE. So, we have:
QUANTITY A: -6/5
QUANTITY B: some POSITIVE number
So, Quantity A is greater
Answer: A
Cheers,
Brent
RELATED VIDEO
Re: a and b are positive. (a + 6) : (b + 6) = 5 : 6
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12 Jun 2020, 21:09
12 Jun 2020, 21:09
1
please correct me if I am wrong
from the stem it is clear that a is less than b
so (a + N)/(b+N) is always less than 1 for any positive integer N
so answer is B
from the stem it is clear that a is less than b
so (a + N)/(b+N) is always less than 1 for any positive integer N
so answer is B
