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# If a and b are integers of opposite signs such that (a + 3)^2 : b^2

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Director
Joined: 19 Oct 2018
Posts: 970
Location: India
If a and b are integers of opposite signs such that (a + 3)^2 : b^2  [#permalink]

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Updated on: 29 May 2019, 07:47
4
00:00

Difficulty:

55% (hard)

Question Stats:

47% (03:43) correct 53% (02:49) wrong based on 15 sessions

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If a and b are integers of opposite signs such that $$(a + 3)^2 : b^2$$ = 9 : 1 and $$(a - 1)^2 : (b - 1)^2$$ = 4 : 1, then the ratio $$a^2 : b^2$$ is

A. 1:4
B. 9:4
C. 25:4
D. 49:4
E. 81:4

Originally posted by nick1816 on 28 May 2019, 21:45.
Last edited by nick1816 on 29 May 2019, 07:47, edited 1 time in total.
Director
Joined: 20 Jul 2017
Posts: 913
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a and b are integers of opposite signs such that (a + 3)^2 : b^2  [#permalink]

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28 May 2019, 23:23
1
1
nick1816 wrote:
If a and b are integers of opposite signs such that $$(a + 3)^2 : b^2$$ = 9 : 1 and $$(a - 1)^2 : (b - 1)^2$$ = 4 : 1, then the ratio a : b is

A. 1:4
B. 9:4
C. 25:4
D. 49:4
E. 81:4

Hey nick1816 Isn't the question supposed to be ratio $$a^2$$ : $$b^2$$ ?

a and b are integers of opposite signs --> If a>0, b<0 or if a<0, b>0

$$(a + 3)^2 : b^2$$ = 9 : 1
$$\frac{(a + 3)}{b}$$ = 3 or -3

$$\frac{(a + 3)}{b}$$ = -3 only satisfies as the ratio can never be +3 when one of a and b is negative
or
a + 3b = -3 ----- (1)

Similarly, $$(a - 1)^2 : (b - 1)^2$$ = 4 : 1
$$\frac{(a - 1)}{(b - 1)} = -2$$ (+2 is not possible when one of a and b is negative)
or
a + 2b = 3 ----- (2)

Solving (1) & (2) using simultaneous equations, we get a = 15 and b = -6

So, a:b = 15:-6 or -5:2

Ratio of $$a^2$$ : $$b^2$$ = 25:4

IMO Option C.

Hit Kudos if you like my solution
Re: If a and b are integers of opposite signs such that (a + 3)^2 : b^2   [#permalink] 28 May 2019, 23:23
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