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# If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?

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Math Expert
Joined: 02 Sep 2009
Posts: 53832
If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?  [#permalink]

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07 Mar 2019, 03:00
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Difficulty:

25% (medium)

Question Stats:

78% (00:43) correct 22% (01:40) wrong based on 18 sessions

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If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?

A. 5/12

B. 2/5

C. 12/5

D. 5/7

E. 7/5

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Math Expert
Joined: 02 Aug 2009
Posts: 7448
If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?  [#permalink]

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07 Mar 2019, 05:31
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Bunuel wrote:
If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?

A. 5/12

B. 2/5

C. 12/5

D. 5/7

E. 7/5

As a+b and ab are related to $$\frac{1}{a}+\frac{1}{b}$$ but the equations look different, so let us modify $$\frac{1}{a}+\frac{1}{b}$$..
$$\frac{1}{a}+\frac{1}{b}=\frac{(a+b)}{ab}=7/5$$

E
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Re: If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?  [#permalink]

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07 Mar 2019, 06:27
Bunuel wrote:
If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?

A. 5/12

B. 2/5

C. 12/5

D. 5/7

E. 7/5

1/a + 1/b
a+b/ab = 7/5
IMO E
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Re: If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?  [#permalink]

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10 Mar 2019, 19:53
Bunuel wrote:
If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?

A. 5/12

B. 2/5

C. 12/5

D. 5/7

E. 7/5

Adding 1/a + 1/b, we have:

b/ab + a/ab = (b + a)/ab = 7/5.

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Re: If a + b = 7 and ab = 5, then what is the value of 1/a + 1/b?   [#permalink] 10 Mar 2019, 19:53
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