Algebra for 11+

I would start by rewriting the division as a multiplication: Q * 5D = ABC. Then try narrowing down what some of the digits can be, using the restriction on other digits.

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It may help to give an example of what Dr. Peterson means by "narrowing down what some of the digits can be, using the restrictions on the other digits."

Can Q equal 1? No, because 1 times (50 + D) is less than 60 and so cannot be a three-digit number.

Can D equal 1? No, because Q times 50 + 1 = 50Q + Q. But in that case C = Q, and we know that the numbers are all different. (How do we know that for certain?)

Keep on eliminating possibilities.
 
What could be the largest possible value of A?
 
Subhotosh Khan said:
What could be the largest possible value of A?
Click to expand...
Q*D '=' C (there may be a carry over)
1*2 = 2 X (can't repeat digits)
1*3 = 3 X (can't repeat digits)
1*4 = 4 X (can't repeat digits)
1*6 = 6 X (can't repeat digits)
2*3 = 6 possible (so C can be 6)
2*4 = 8 X (no 8)
2*6 '='2 X (can't repeat digits)
3*4 '='2 X possible so C can be 2
3*6 '='8 X (no 8)
4*6 '='4 X (can't repeat digits)

So C can be 2 or 6.
When C=2, then Q=3, D=4 OR Q=4, D=3
When C=6, then Q=2, D=3 OR Q=3, D=2

Combine this with what Subotosh Khan posted above.
 
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