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If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =

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GMAT Club team member
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Status: GMAT Club Team Member
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Joined: 02 Nov 2016
Posts: 5905
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If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =  [#permalink]

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New post 20 Mar 2020, 23:42
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (02:03) correct 31% (02:20) wrong based on 16 sessions

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If \(\frac{2}{5} p + q = 3q - 10,\) and if \(q = 10 - p,\) then \(\frac{p}{q} =\)

(A) 5/7

(B) 3/2

(C) 5/3

(D) 25/6

(E) 6

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Re: If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =  [#permalink]

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New post 21 Mar 2020, 07:17
1

Solution



Given
In this question, we are given that
    • Two equations of p and q: (2/5)p + q = 3q – 10 and q = 10 – p

To find
We need to determine
    • The value of p/q

Approach and Working out
Substituting the value of q in the first equation, we get
    • (2/5)p + 10 – p = 3(10 – p) – 10
    Or, 2p/5 + 10 – p = 30 – 3p – 10
    Or, 2p + 50 – 5p = 150 – 15p – 50
    Or, 2p – 5p + 15p = 150 – 50 – 50
    Or, 12p = 50
    Or, p = 50/12

Hence, q = 10 – p = 10 – 50/12 = 70/12
Therefore, p/q = 50/12: 70/12 = 5/7

Thus, option A is the correct answer.

Correct Answer: Option A
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Re: If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =   [#permalink] 21 Mar 2020, 07:17

If 2/5 p + q = 3q - 10, and if q = 10 - p, then p/q =

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