If Ann saves x dollars each week and Beth saves y dollars ea

SOLUTION

If Ann saves x dollars each week and Beth saves y dollars each week, what is the total amount that they save per week?

We need to find the value of x+y.

(1) Beth saves $5 more per week than Ann saves per week --> y=x+5. Not sufficient.

(2) It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks --> 6x=5y. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, thus we can solve for both and get the value of x+y. Sufficient.

Answer: C.
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If Ann saves x dollars each week and Beth saves y dollars each week, what is the total amount that they save per week?

(1) Beth saves $5 more per week than Ann saves per week.
(2) It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks.

Ann : x / week
Beth: y / week

To find: x + y

Statement 1:
y = 5 + x
Or, x + y = 5 + 2x
x + y has many values for different x.
Not sufficient.

Statement 2:
6x = 5y
Or, x = (5/6)y
x has different value for different y.
Not sufficient.

Combining statements (1) and (2)
y = 5 + x
Or, y = 5 + (5/6)y
Or, (1/6)y = 5
Or, y = 30
So, x = (5/6)*30
Or, x = 25
Or, x + y = 25 + 30 = 55
Sufficient.

Hence, answer is (C).

If Ann saves x dollars each week and Beth saves y dollars each week, what is the total amount that they save per week?

(1) Beth saves $5 more per week than Ann saves per week.
(2) It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks.

Sol:

So we need to find the x+y =??

From St 1, we have y=x+5 or Total savings ie. x+y= 2x+5----> Clearly not sufficient as x can have any value. So A and D ruled out
From St 2, we have 6 weeks of Ann savings equals Beth's savings of 5 weeks so we have 6x= 5y. So St 2 is not sufficient so B ruled out

Combining we get that 6x= 5y and y= x+5....On Solving we get 6x/5= x+5 or 6x= 5x+25 or x=25 and y =30.

so x+y = $55.
Ans C
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stmt1 : Beth saves $5 more per week than Ann saves per week.
Ann = X; Beth =Y=>X+5;
Not Sufficient.

STMT2 : It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks.
6x =5y
Not Sufficient.

Combining i & ii we get ,
6X= 5(x+5) => x=25;
y=30;
They together save 30+25 = 55$;

Solution:

Question Stem Analysis:

We need to determine the total amount Ann and Beth save each week, given that Ann saves x dollars each week and Beth saves y dollars each week. That is, we need to determine the value of x + y.

Statement One Alone:

This tells us that y = x + 5. However, without knowing the value of either x or y, we can’t determine the value of x + y. Statement one alone is not sufficient.

Statement Two Alone:

We see that 6x = 5y. However, without knowing the value of either x or y, we can’t determine the value of x + y. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we have two linear equations and two variables. Note that neither equation is dependent on the other, which means that one equation is not a linear multiple of the other. Thus, we can determine the values of x and y and hence the value of x + y. Both statements together are sufficient.

Answer: C
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Given: Ann saves x dollars each week and Beth saves y dollars each week

Statement 1: Beth saves $5 more per week than Ann saves per week
We can write: y = x + 5
Since this equation does not provide it sufficient information to find the value of x + y, statement 1 is NOT SUFFICIENT

Statement 2: It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks.
We can write: 6x = 5y
Since this equation does not provide it sufficient information to find the value of x + y, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements we get to the following system of equations:
y = x + 5
6x = 5y
Since we have two different linear equations with two variables, we COULD solve the system for x and y, which means we COULD answer the target question with certainty (although we would never waste precious time on test day actually calculating the value of x + y)

Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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