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Let <x, y, z> denote 2x + yz. Moreover, let x + y = 2p

Expert replies
by Max@Math Revolution » Fri Nov 22, 2019 12:19 am
[GMAT math practice question]1

Let <x, y, z> denote 2x + yz. Moreover, let x + y = 2p, y + z = 2q, z + x = 2r, xy = a, yz = b and zx = c.
How can < x, 3y, z > + < y, 3z, x > + < z. 3x, y > be written in terms of a, b, c, p, q and r?

A. p+q+r+a+b+c
B. 2(p+q+r+a+b+c)
C. 2(p+q+r+a+b+c)
D. 2(p+q+r)+3(a+b+c)
E. 3(p+q+r)+2(a+b+c)
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Source: — Problem Solving |

by Max@Math Revolution » Sun Nov 24, 2019 5:57 pm
=>

When we add x + y = 2p, y + z = 2q, and z + x = 2r, we have x + y + y + z + z + x = 2p + 2q + 2r, 2(x + y + z) = 2(p + q + r) or x + y + z = p + q + r.
When we add xy = a, yz = b and zx = c, we have xy + yz + zx = a + b + c.
< x, 3y, z > = 2x + 3yz, < y, 3z, x > = 2y + 3zx, < z, 3x, y > = 2z + 3xy.
Then < x, 3y, z > + < y, 3z, x > + < z, 3x, y > = 2x + 3yz + 2y + 3zx + 2z + 3xy = 2(x +y + z) + 3(xy + yz + zx) = 2(p + q + r) + 3(a + b + c).

Therefore, the answer is D.
Answer: D
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