What is the value of \(x?\)
(1) \(2x + 3y = 12\)
(2) \(5x + 7y = 29\)
Answer: C
Source: GMAT Paper Tests
What is the value of \(x?\)
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Statement 1 => 2x + 3y = 12
There are 2 unknown variables in this equation so the value of x cannot be evaluated. Therefore, statement 1 is NOT SUFFICIENT
Statement 2 => 5x + 7y = 29
There are 2 unknown variables and the target question cannot be answered. Statement 2 is NOT SUFFICIENT
Combining both statements together =>
2x + 3y = 12 .....eqn 1
5x + 7y = 29 .....eqn 2
multiply eqn 1 by 5 and eqn 2 by 2
2x * 5 + 3y * 5 = 12 * 5
5x * 2 + 7y * 2 = 29 * 2
10x + 15y = 60 - 10x + 14y = 58
y = 2
Therefore, 2x + 3(2) = 12
2x + 6 = 12
2x/2 = 12 - 6 = 6 / 2
=> x = 3
Both statements combined together are SUFFICIENT
Answer =C
There are 2 unknown variables in this equation so the value of x cannot be evaluated. Therefore, statement 1 is NOT SUFFICIENT
Statement 2 => 5x + 7y = 29
There are 2 unknown variables and the target question cannot be answered. Statement 2 is NOT SUFFICIENT
Combining both statements together =>
2x + 3y = 12 .....eqn 1
5x + 7y = 29 .....eqn 2
multiply eqn 1 by 5 and eqn 2 by 2
2x * 5 + 3y * 5 = 12 * 5
5x * 2 + 7y * 2 = 29 * 2
10x + 15y = 60 - 10x + 14y = 58
y = 2
Therefore, 2x + 3(2) = 12
2x + 6 = 12
2x/2 = 12 - 6 = 6 / 2
=> x = 3
Both statements combined together are SUFFICIENT
Answer =C