Let x and y be positive intergers such that 3x + 7y isdivisible by 11. Which of
ID: 2938854 • Letter: L
Question
Let x and y be positive intergers such that 3x + 7y isdivisible by 11. Which of the following must also bedivisible by 11? (a) 4x + 6y (b) x + y +5 (c) 9x + 4y (d) 4x -9y (e) x + y -1 Please explain, I'm studying for GRE and need to checkunderstanding. Thanks Let x and y be positive intergers such that 3x + 7y isdivisible by 11. Which of the following must also bedivisible by 11? (a) 4x + 6y (b) x + y +5 (c) 9x + 4y (d) 4x -9y (e) x + y -1 Please explain, I'm studying for GRE and need to checkunderstanding. ThanksExplanation / Answer
QuestionDetails: Let x and y be positive intergers such that 3x + 7y isdivisible by 11. Which of the following must also bedivisible by 11? (a) 4x + 6y (b) x + y +5 (c) 9x + 4y (d) 4x -9y (e) x + y -1 Please explain, I'm studying for GRE and need to checkunderstanding. ThanksOK...THERE ARE THEORIES TO DO THIS.
BUT SINCE YOU SAY THIS IS FOR AN OBJECTIVE TEST LIKE GRE ,I SUGGESTTHE FOLLOWING PRACTICAL WAY .
3X+7Y=11 IMPLIES ......GCD[X,Y]=11.......SEE BELOW FOR REASON
SO TAKE X=11 AND Y=22 SAY ..NOW CHECK THE 5 ALTERNATIVES FORDIVISIBILITY BY 11.
(a) 4x + 6y =4*11+6*22........OK DIVISIBLE BY 11
(b) x + y +5 = 11+22+5=38..............NO ...NOTDIVISIBLE BY 11
(c) 9x + 4y =....OK
(d) 4x -9y =.....OK
(e) x + y -1=.....NO ...NOT DIVISIBLE BY 11
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GIVEN THAT
3X+7Y=11K......................................1
WHERE K IS AN INTEGER.
THIS IS POSSIBLE ONLY WHEN
GCD OF ONE OF THE NUMBERS IN [3 , X] ...AND ONE OF THENUMBERS [7 , Y] IS 11
OBVIOUSLY WE CAN RULE OUT THE COMBINATIONS OF 3 & 7......3&Y..........X&7
SO THAT LEAVES US WITH THE ONLY POSSIBILITY OF X AND Y .
SO
GCD (X,Y)=11.........................2
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