A trip coordinator bought a certain number of $47

[BTGmoderatorDC]

A trip coordinator bought a certain number of $47 tickets and a certain number of $25 tickets for a concert. How many $47 tickets did she buy?

(1) The trip coordinator spent a total of $595 on tickets for the concert.
(2) She bought half as many $25 tickets as $47 tickets.

What's the best way to determine whether statement 1 is sufficient?

OA A

[GMATGuruNY]

A trip coordinator bought a certain number of $47 tickets and a certain number of $25 tickets for a concert. How many $47 tickets did she buy?

(1) The trip coordinator spent a total of $595 on tickets for the concert.
(2) She bought half as many $25 tickets as $47 tickets.

What's the best way to determine whether statement 1 is sufficient?

Statement 1:
47x + 25y = 595.
Here, x and y must be POSITIVE INTEGERS.
When an equation with two variables is constrained to positive integers, be careful!
If only ONE COMBINATION of positive integers will satisfy the equation, then the equation is SUFFICIENT to solve for the two variables.

Rephrasing 47x + 25y = 595, we get:
47x = 595 - 25y = (MULTIPLE OF 5) - (MULTIPLE OF 5) = MULTIPLE OF 5.
Since 47x must be a multiple of 5 less than 595, only two cases are possible:
Case 1: x=5, with the result that 47x = 47*5 = 235
Case 2: x=10, with the result that 47x = 47*10 = 470.

Test whether Case 1 yields an integer value for y.
Substituting 47x = 235 into 47x + 25y = 595, we get:
235 + 25y = 595
25y = 360.
y = 360/25.
Since y is not an integer, Case 1 is not viable.

Implication:
Only Case 2 is viable, with the result that x=10.
Thus, the number of $47 tickets = 10.
SUFFICIENT.

Statement 2:
Case 1: One $25 ticket, two $47 tickets
Case 2: Two $25 tickets, four $47 tickets
Since the number of $47 tickets can be different values, INSUFFICIENT.

The correct answer is A.

[[email protected]]

Hi lheiannie07,

We're told that a certain number of $47 tickets and a certain number of $25 tickets were purchased for a concert. We're asked for the number of $47 tickets purchased. This question can be solved with a bit of logic and some 'brute-force' arithmetic.

1) The trip coordinator spent a total of $595 on tickets for the concert.

At first glance, the information in Fact 1 implies that there could be multiple solutions, since we have 2 variables and just one equation: 47X + 25Y = 595. However, there is an important Number Property pattern here that limits the possibilities - the number of $25 tickets will add up to a total that is a MULTIPLE of 25. $595 is NOT a multiple of 25 though, so we will have to find a specific multiple of 47 that completes the equation (and that multiple will have to end in either a 5 or a 0)

(47)(5) = 235... which would leave 595 - 235 = 360 for $25 tickets. That is NOT possible though (360 is NOT a multiple of 25), so this is NOT an option.
(47)(10) = 470... which would leave 595 - 470 = 125 for $25 tickets. That IS possible (125 IS a multiple of 25), so this IS an option.
(47)(15) = 705 .... this is NOT an option (the total is TOO HIGH).
Thus, there's only one solution: 10 $47 tickets and 5 $25 tickets
Fact 1 is SUFFICIENT

2) She bought half as many $25 tickets as $47 tickets.

With Fact 2, we could have....
1 $25 ticket and 2 $47 tickets
2 $25 tickets and 4 $47 tickets
Etc.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[BTGmoderatorDC]

A trip coordinator bought a certain number of $47 tickets and a certain number of $25 tickets for a concert. How many $47 tickets did she buy?

(1) The trip coordinator spent a total of $595 on tickets for the concert.
(2) She bought half as many $25 tickets as $47 tickets.

What's the best way to determine whether statement 1 is sufficient?

Statement 1:
47x + 25y = 595.
Here, x and y must be POSITIVE INTEGERS.
When an equation with two variables is constrained to positive integers, be careful!
If only ONE COMBINATION of positive integers will satisfy the equation, then the equation is SUFFICIENT to solve for the two variables.

Rephrasing 47x + 25y = 595, we get:
47x = 595 - 25y = (MULTIPLE OF 5) - (MULTIPLE OF 5) = MULTIPLE OF 5.
Since 47x must be a multiple of 5 less than 595, only two cases are possible:
Case 1: x=5, with the result that 47x = 47*5 = 235
Case 2: x=10, with the result that 47x = 47*10 = 470.

Test whether Case 1 yields an integer value for y.
Substituting 47x = 235 into 47x + 25y = 595, we get:
235 + 25y = 595
25y = 360.
y = 360/25.
Since y is not an integer, Case 1 is not viable.

Implication:
Only Case 2 is viable, with the result that x=10.
Thus, the number of $47 tickets = 10.
SUFFICIENT.

Statement 2:
Case 1: One $25 ticket, two $47 tickets
Case 2: Two $25 tickets, four $47 tickets
Since the number of $47 tickets can be different values, INSUFFICIENT.

The correct answer is A.

Thanks a lot!

[BTGmoderatorDC]

Hi lheiannie07,

We're told that a certain number of $47 tickets and a certain number of $25 tickets were purchased for a concert. We're asked for the number of $47 tickets purchased. This question can be solved with a bit of logic and some 'brute-force' arithmetic.

1) The trip coordinator spent a total of $595 on tickets for the concert.

At first glance, the information in Fact 1 implies that there could be multiple solutions, since we have 2 variables and just one equation: 47X + 25Y = 595. However, there is an important Number Property pattern here that limits the possibilities - the number of $25 tickets will add up to a total that is a MULTIPLE of 25. $595 is NOT a multiple of 25 though, so we will have to find a specific multiple of 47 that completes the equation (and that multiple will have to end in either a 5 or a 0)

(47)(5) = 235... which would leave 595 - 235 = 360 for $25 tickets. That is NOT possible though (360 is NOT a multiple of 25), so this is NOT an option.
(47)(10) = 470... which would leave 595 - 470 = 125 for $25 tickets. That IS possible (125 IS a multiple of 25), so this IS an option.
(47)(15) = 705 .... this is NOT an option (the total is TOO HIGH).
Thus, there's only one solution: 10 $47 tickets and 5 $25 tickets
Fact 1 is SUFFICIENT

2) She bought half as many $25 tickets as $47 tickets.

With Fact 2, we could have....
1 $25 ticket and 2 $47 tickets
2 $25 tickets and 4 $47 tickets
Etc.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Thanks a lot!