sanju09 wrote:If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
I. The value of q is equal to the sum of p and r.
II. p + 3 q - 2 r = 23.
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To combine ratios with a common element, the common element must be represented by the same value in each ratio.
p:q = (3/7) : 2 = 3:14.
q:r = 7 : (11/2) = 14:11.
Combining the ratios:
p:q:r = 3:14:11.
Statement 1: q = p+r.
No new information here.
In p:q:r = 3:14:11, p+r = 3+11 = 14, which is the value of q.
Thus, given ANY combination that satisfies p:q:r = 3:14:11, q=p+r.
If the values in the ratio are doubled so that p=6, q=28, and r=22, q=p+r.
If the values in the ratio are tripled so that p=9, q=42 and r=33, q=p+r.
Since an infinite number of combinations are possible, no way to determine p+q+r.
INSUFFICIENT.
Statement 2: p + 3q - 2r = 23.
This equation is satisfied by the values in the ratio.
If p=3, q=14, and r=11, then p + 3q - 2r3 + 3(14) - 2(11) = 23.
Thus, this is the ONLY combination that will work here.
Any MULTIPLE of 3:11:14 will yield a MULTIPLE of 23.
Thus, p+q+r = 3+14+11 = 28.
SUFFICIENT.
The correct answer is
B.
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