The expression 2a2 +2b2 can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y 18. Is -y+3- = 3?(1) The difference between a and b can be expressed as an even multiple of 3.(2) b when divided by 3 is an integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

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The expression 2a² +2b² can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y < 18. Is |y+3| = 3?

(1) The difference between a and b can be expressed as an even multiple of 3.

(2) b when divided by 3 is an integer.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'C'. Can you explain this answer?

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Test: Divisibility And Remainders- 1

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The expression 2a2 +2b2 can be written in the form of 18x + y, where a...

Steps 1 & 2: Understand Question and Draw Inferences

a, b, x and y are integers ≥ 0 and y < 18
2a²+2b²=18x+y

- Since both the terms on the left hand side of the above equation are even, their sum will be even as well. So, the left hand side of the equation is even
- Therefore, the right hand side of the equation will be even as well
- So, the sum of even term 18x and of y will be even
- This means, y must be even.

To Find: If |y+3| = 3?

Let’s first understand what are the values of y for which this equation will hold true.
So, let’s first solve for the values of y that satisfy this equation and then, using Statements 1 and 2, we will figure out if y does indeed have those values.
For the equation |y + 3| = 3, two cases are possible:
If y+3 ≥ 0
- Then y+3 = 3, i.e. y = 0
If y +3 < 0
- -y -3 = 3, i.e. y = -6. However as y ≥ 0, this case is not possible.
So, y = 0 is the only possible value of y, under the given constraints, for which |y + 3| = 3
So, the answer to the question will be YES only if y = 0.
Now, when y = 0, then the equation 2a² + 2b² = 18x + y becomes:
Hence, we can write 2a²+2b²=18x

That is, a² + b² = 9x
That is, a² + b² is divisible by 9
So, if we find that a² + b² is divisible by 9, then that will mean that y = 0, which in turn means that the answer to the asked question is YES.

Step 3: Analyze Statement 1 independently

The difference between a and b can be expressed as an even multiple of 3.

a – b = 3*2k, where k is an integer
- Two cases arise
- If (a-b) ≥0, |a-b| = (a-b)
- So, we have ,
  - a = b + 6k
  - Substituting a = b +6k in a²+b², have

(b+6k)²+b²=2b²+36k²+12bk
36k² is divisible by 9, but we do not know if 2b² + 12bk is divisible by 9.
If (a-b) < 0, |a-b| = (b-a)
So, we have
- b = a + 6k
- Substituting b= a +6k in a² + b², we have
- a²+(a+6k)²=2a²+36k²+12ak

- 36k² is divisible by 9, but we do not know if 2a² + 12ak is divisible by 9.

Insufficient to answer.

Step 4: Analyze Statement 2 independently

2. b when divided by 3 is an integer.

b = 3p, where p is an integer > 0
However the statement does not tell us anything about a.

Hence, insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

From statement-1,
1. a²+b²=2b²+36k²+12bk or
2. a²+b²=2a²+36k²+12ak
From statement-2, b = 3p

Substituting (2) in (1. a), we have
- a²+b²=18p²+36k²+36pk
- All the terms 18p²+36k²+36pk are divisible by 9, hence we can say that a2+b2=9x

For (1.b), we know that
- b = a + 6k, i.e. a = b – 6k = 3p – 6k
- Substituting a = 3p – 6k and b = 3p in a² + b², we have
- a²+b²=(3p−6k)²+9p²=18p²+36k²−36pk
- All the terms 18p2+36k2−36pk are divisible by 9, hence we can say that a²+b²=9x
Suffecient to answer.

Answer: C

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The expression 2a2 +2b2 can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y < 18. Is |y+3| = 3?(1) The difference between a and b can be expressed as an even multiple of 3.(2) b when divided by 3 is an integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

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The expression 2a2 +2b2 can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y < 18. Is |y+3| = 3?(1) The difference between a and b can be expressed as an even multiple of 3.(2) b when divided by 3 is an integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The expression 2a2 +2b2 can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y < 18. Is |y+3| = 3?(1) The difference between a and b can be expressed as an even multiple of 3.(2) b when divided by 3 is an integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The expression 2a2 +2b2 can be written in the form of 18x + y, where a, b, x and y are non-negative integers and y < 18. Is |y+3| = 3?(1) The difference between a and b can be expressed as an even multiple of 3.(2) b when divided by 3 is an integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?.

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