tmua.fyi Paper 2 Challenge 2 · Question 6

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tmua.fyi Paper 2 Challenge 2 · Q6

Paper 2Algebra

The following argument is offered, where $a$ and $b$ are non-zero real numbers.

\begin{aligned} (1)\quad&a=b\\ (2)\quad&a^2=ab\\ (3)\quad&a^2-b^2=ab-b^2\\ (4)\quad&(a-b)(a+b)=b(a-b)\\ (5)\quad&a+b=b\\ (6)\quad&2b=b,\text{ so }2=1 \end{aligned}

At which step does the argument first fail?

Astep (2)

Bstep (3)

Cstep (4)

Dstep (5)

Estep (6)

Fstep (1)

Gmore than one step fails

Hit does not fail

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