Yes, I was referring to smart numbers ..Looks like its difficult to solve this using smart numbers?
I would strongly suggest that you should stick to the method of solving which is quite straight forward as shown by yezz above. You may not be able to put your finger on the right numbers for a long time so its a gamble.
Nevertheless, if you do insist on using numbers to figure out, pick numbers smartly (I don't know what you mean by smart numbers except LCM/HCF is some cases and 100 in percentages.)
Let me explain what I mean by 'picking numbers smartly'
I see that the given ratio is 5:3
So actual numbers could be K-10 and A-6. If K gives 10 to A, ratio becomes 0:16. K has less than A but we need K to retain more than A so that the ratio is 7:5.
Actual numbers could be K-50 and A-30. If K gives 10 to A, ratio becomes 40:40 i.e. 1:1. The ratio has increased from before. Both have equal numbers. If the common multiplier chosen is less than 10, K will have less than A. If the common multiplier chosen is more than 10, K will retain more than A. So we need to go higher up.
Actual numbers could be K-100 and A-60. If K gives 10 to A, ratio becomes 9:7. Still less than 7:5. So we need to go further up
Actual numbers could be K-150 and A-90. If K gives 10 to A, ratio becomes 7:5.
There is a logic you are following to reach to the answer. Say, if I had jumped to K-200, A-120 directly, the new ratio would be 19:13 which is greater than 7:5 so I would try and find something in between K-100 and K-200. But using this approach, I am hoping that the multiplier will be an easy round number. Though it is true in most cases for GMAT, I would still not use this approach considering that the alternative standard method is quick and clean.
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