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akhilvarma8
GMAT 2: 660 Q45 V35
Posts: 19
16 Jun 2019, 23:05
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A
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42%
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What is the remainder when positive integer x is divided by 3?
(1) When 75 – x is divided by 3, the remainder is 1.
(2) When x^2 is divided by 3, the remainder is 1.
Looking for a good solution as I am unable to get how the answer is different from mine.
(1) When 75 – x is divided by 3, the remainder is 1.
(2) When x^2 is divided by 3, the remainder is 1.
Looking for a good solution as I am unable to get how the answer is different from mine.
17 Jun 2019, 03:21
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Statement (1): \(75-x = 3a + 1\)
\(x = 74 - 3a\)
by substituting \(a\) with values (0,1,2,..), \(x\) will be (74,71,68,...) --> when divided by 3, \(r\) is the same (2) -->Sufficient
Statement (2): \(x^2 = 3b + 1\)
by substituting \(b\) with values (0,1,2,3,4,5,...), \(x^2\) will be (1,4,7,10,13,16,...)
As \(x\) is (+ve) Integer, \(x^2\) can be (1,4,16,..) & \(x\) can be (1,2,4,..) --> when divided by 3, \(r\) is different (1,2,1,..) --> Insufficient
\(x = 74 - 3a\)
by substituting \(a\) with values (0,1,2,..), \(x\) will be (74,71,68,...) --> when divided by 3, \(r\) is the same (2) -->Sufficient
Statement (2): \(x^2 = 3b + 1\)
by substituting \(b\) with values (0,1,2,3,4,5,...), \(x^2\) will be (1,4,7,10,13,16,...)
As \(x\) is (+ve) Integer, \(x^2\) can be (1,4,16,..) & \(x\) can be (1,2,4,..) --> when divided by 3, \(r\) is different (1,2,1,..) --> Insufficient
17 Jun 2019, 09:05
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Hi Akhil,
Remainder questions can be quite tricky if you adopt a very rigid approach of working and use the remainder formula, Dividend = (divisor * quotient) + remainder.
Remember the GMAT quant section is foremost a test of reasoning with math involved. Remainder questions are unique as they test you on your number sense as well as reasoning.
While solving remainder DS questions, the best process is to always make a list of values. For example, if we have a statement which says that when x is divided by 3, the remainder is 5, rather than use the reminder equation, we can just think of numbers and create a quick list. The first number when divided by 5 that will give a remainder 3 will be 3 itself. The next number can be easily obtained by adding the divisor to the first number, in this case 3 + 5, so the second number will be 8. Now the third number will be 8 + 5 = 13 and so on.....
The question here gives us x to be a positive integer and asks us for the remainder when x is divided by 3.
Statement 1 : When 75 – x is divided by 3, the remainder is 1
75 is perfectly divisible by 3, so we know that 73 when divided by 3 will give us a remainder 1. Now making a list of values for x,
x = (2, 5, 8, 11, 14, 17, 20.......). In all these cases the remainder when x is divided by 3 will always be 2. Sufficient.
Statement 2 : When x^2 is divided by 3, the remainder is 1
x^2 = (1, 4, 7, 10, 13, 16, 19, 22, 25.....)
Since x has to be a positive integer, the only values of x we can consider will be x = (1, 2, 4, 5......).
Here when x is divided by 3, the remainder can be 1 or 2. Insufficient.
Answer : A
Takeaway : The list of values will also help if you have to combine two statements. Rather than creating equations and working with them algebraically, we can just create a list of values for both statements and take the overlapping values when we combine the two statements.
Hope this helps!
Aditya
CrackVerbal Quant Expert
Remainder questions can be quite tricky if you adopt a very rigid approach of working and use the remainder formula, Dividend = (divisor * quotient) + remainder.
Remember the GMAT quant section is foremost a test of reasoning with math involved. Remainder questions are unique as they test you on your number sense as well as reasoning.
While solving remainder DS questions, the best process is to always make a list of values. For example, if we have a statement which says that when x is divided by 3, the remainder is 5, rather than use the reminder equation, we can just think of numbers and create a quick list. The first number when divided by 5 that will give a remainder 3 will be 3 itself. The next number can be easily obtained by adding the divisor to the first number, in this case 3 + 5, so the second number will be 8. Now the third number will be 8 + 5 = 13 and so on.....
The question here gives us x to be a positive integer and asks us for the remainder when x is divided by 3.
Statement 1 : When 75 – x is divided by 3, the remainder is 1
75 is perfectly divisible by 3, so we know that 73 when divided by 3 will give us a remainder 1. Now making a list of values for x,
x = (2, 5, 8, 11, 14, 17, 20.......). In all these cases the remainder when x is divided by 3 will always be 2. Sufficient.
Statement 2 : When x^2 is divided by 3, the remainder is 1
x^2 = (1, 4, 7, 10, 13, 16, 19, 22, 25.....)
Since x has to be a positive integer, the only values of x we can consider will be x = (1, 2, 4, 5......).
Here when x is divided by 3, the remainder can be 1 or 2. Insufficient.
Answer : A
Takeaway : The list of values will also help if you have to combine two statements. Rather than creating equations and working with them algebraically, we can just create a list of values for both statements and take the overlapping values when we combine the two statements.
Hope this helps!
Aditya
CrackVerbal Quant Expert
