Shyam placed red and blue balls in an empty bag. Ramesh removed 10

Question

Shyam placed a total of 20 red and blue balls in an empty bag. Ramesh removed 10 balls without revealing their colors. Despite this, Shyam was able to correctly deduce that at least 3 of them must have been red.

Based on this information, select for  x  the option that  cannot  be the number of Red balls Shyam originally placed in the bag, and select for  y  the maximum number of blue balls he could have placed. Make only two selections, one in each column.

Bunuel · Accepted Answer

Official Solution: Since Shyam correctly states that at least 3 of the 10 removed balls were red, then at most 7 of the removed balls were blue. This, in turn, means there could not have been more than 7 blue balls in the bag either. If there had been more than 7 blue balls in the bag, it would have been possible to remove 10 balls with more than 7 blue, and respectively fewer than 3 red, which contradicts Shyam's statement. Thus, the maximum number of blue balls initially in the bag was 7, meaning the minimum number of red balls was 13. This makes having only 7 red balls impossible. Correct answer: x "7" y "7" GMAT-Club-Forum-3sgirq0q.png

crimson_king · Answer

The question should be altered here from the number of Red balls Shyam placed to the total number of balls Shyam placed. Only then does the answer make true sense

Bunuel · Answer

Please offer your reasoning first, then let's wait for the official explanation!

Suyash1331 · Answer

since there are at least 3 red balls even after removing 10 balls, this means that there are more than 10 balls. hence x = 7

maximum blue balls can be 7 as well because after removing 10 balls he says that at least 3 balls are red, which means that after removing all the blue balls 3 red will remain if 10 are total balls.
if y > 7 then we cannot say that minimum 3 red balls are still there. its a common sense question

AbhiS101 · Answer

Maximum No of blue balls should be 7, even if Ramesh has taken all the blue balls i.e 7 it will guarantee atleast 3 red balls
As per questions at least 3 balls should be red, i believe maximum could be 10 so can't be less than 10

IMO 7 & 7

technie0903 · Answer

Did not get how we deduced the value of x = 7. How were we able to reach this conclusion : "meaning the minimum number of red balls was 13"? GMAT-Club-Forum-zsdd2am7.png

technie0903 · Answer

Did not get how value of x is 7. How we reached this conclusion : meaning the minimum number of red balls was 13? GMAT-Club-Forum-76c2dfm4.png

Bunuel · Answer

The minimum number of red balls was 13 because there could not have been more than 7 blue balls in the bag. If there were more than 7 blue balls, it would have been possible to remove 10 balls with more than 7 blue, leaving fewer than 3 red, which contradicts Shyam’s certainty that at least 3 red balls were removed. GMAT-Club-Forum-0l589u37.png

x	y
		7
		14
		15
		16
		17
		18

Shyam placed red and blue balls in an empty bag. Ramesh removed 10

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Shyam placed red and blue balls in an empty bag. Ramesh removed 10

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