Question

5. Let a, b,c,d be real numbers such that la - bl = 2.lb-cla
3. lc - dl = 4. Then the sum of all possible values of la-d
is
(a) 9 (b) 18
(c) 24 (d) 30​

Answer 1

Answer:

I'm reading your third condition as |c−d|=4.

I'm lining up the points on a figure showing the number line with ticks. WLOG we may assume a=0, b=2 and then obtain for c the two possibilities c1=−1, c2=5. This leads to the four possible d-values d11=−5, d12=3, d21=1, d22=9. The sum of the absolute values of these four numbers is 18.

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