Trial and error is too long and is not exhaustive enough.
There is a simpler solution.
Now, we know that 23x + 11y = 170
The units digit of 23 and 11 should add up to a 0.
So taking the units digit only ->
23x --> 3, 6, 9, 2, 5, 8, 1, 4, 7, 0
11y --> 1, 2, 3, 4, 5, 6, 7, 8, 9, 0
There are a lot of combinations, but trying the easiest first helps ->
(0,0)
23*10 + 11*10 = 340 !! (Voila) This is exactly double of what we need. Halve it.
So, x and y are 5 each.
(Cross checking with Option 1, we see that x is 5 is given, so we can be sure that this is the only answer)
Takes 45 seconds.
But, to be doubly sure, take some other combination in random, Say, (6, 4)
23*2 + 11*4 = 46 + 44 = 90 (Too low)
A bit higher is (5,5), almost confirmed. Have a leap of faith and mark B.
Bunuel wrote:
Bunuel wrote:
A store sells erasers for 0.23$ per piece and pencil for 0.11$ per piece. How many eraser and pencils did Jessica buy?
(1) She bough 5 erasers. Clearly insufficient.
(2) She spent total of 1.70$ --> \(0.23e+0.11p=1.70\) --> \(23e+11p=170\) --> by trial and error we can find that the only non-negative integer solution for this equation is e=5 and p=5. Sufficient.
Answer: B.
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