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# If a + 2b = 6 and ab = 4 what is 2/a + 1/b?

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Math Expert
Joined: 02 Sep 2009
Posts: 45251
If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 10:15
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Question Stats:

97% (01:27) correct 3% (00:00) wrong based on 63 sessions

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If a + 2b = 6 and ab = 4 what is 2/a + 1/b?

(A) 1/2
(B) 1
(C) 3/2
(D) 2
(E) 5/2

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Senior Manager
Joined: 09 Mar 2017
Posts: 420
Location: India
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Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 11:10
Bunuel wrote:
If a + 2b = 6 and ab = 4 what is 2/a + 1/b?

(A) 1/2
(B) 1
(C) 3/2
(D) 2
(E) 5/2

2/a + 1/b = (2b + a) /ab
6/4 = 3/2

IMO C
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Intern
Joined: 31 Oct 2017
Posts: 2
Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 11:36
Looking at the second part only, ab=4
means 2x2 is 4

So now we now that a is 2 and b is 2 we can solve it

2/a + 1/b

=2/2 + 1/2

= 1 + 0.5 = 1.5
Which means 3/2
Or
Same denominator, just add the nominator = 3/2

So the answer is (C) 3/2

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Intern
Joined: 15 May 2017
Posts: 33
GMAT 1: 770 Q51 V45
Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 16:59
Bunuel wrote:
If a + 2b = 6 and ab = 4 what is 2/a + 1/b?

(A) 1/2
(B) 1
(C) 3/2
(D) 2
(E) 5/2

First recognize that if you are provided with equations and seemingly specific values to seek, that there is probably a shortcut to the manipulation. In this case add the fractions (2/a + 1/b) to find that the fractions can be combined as (2b + a) / ab. Now simply insert the given values of 6 and 4 to find that 6/4 = 3/2 or answer choice C.
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Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 17:51
1
KUDOS
no need to find the value of a & b
just see to find the value of 2/a +1/b = (2b+a)/ab, we require value of 2b+a and ab which i given
Senior Manager
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Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b? [#permalink]

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31 Oct 2017, 19:12
$$\frac{2}{a}$$+$$\frac{1}{b}$$=$$\frac{(2b+a)}{ab}$$= $$\frac{6}{4}$$= $$\frac{3}{2}$$

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Re: If a + 2b = 6 and ab = 4 what is 2/a + 1/b?   [#permalink] 31 Oct 2017, 19:12
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