In a certain game, a player can accumulate points only by scoring eith

Question

In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points. If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

A. Four
B. Five
C. Six
D. Seven
E. Eight

PS20410

A. Four
B. Five
C. Six
D. Seven
E. Eight

PS20410

nick1816 · Answer

3x+2y=24

3x = 24 - 2y = 2(12-y)

Since 3x is a multiple of 3, '12-y' or 'y' must be a multiple of 3.

y can take 5 values (0, 3, 6, 9 , 12) and so does x.

B

Enchanting · Answer

Let y be the number of Y score i.e., 2 point
  3t + 2y = 28
 3t = 28 – 2y
  28- 2y is an even number.
 3t must be an even number.
 t must be an even number such that 3t ≤ 28 
t can be 0, 2, 4, 6, and 8
  There are 5 different possible values of t.  
Answer:  Option B.

Archit3110 · Answer

given
3x+2y =24
x = 24-2y/3
x= 2 * ( 12-y)/3
so x can be 0 with y = 12
and value of y =0, 3,6,9,
total 5 values OPTION B

NitishJain · Answer

Say 3x: points by X
2y: Points by Y

3x + 2y =24

x = (24-2y)/3
for x to be integer: y can take values: 12, 9, 6, 3, 0

x can take 5 values.

x = 2(12-y)/3

only values for x: 0,

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • In a certain game, 
 o A player can accumulate points only by scoring either an X, which counts 3 points, or 
o A Y, which counts 2 points

To find  
We need to determine
 • If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have

Approach and Working out  
 • Total points should be of the form 3X + 2Y
• Thus, 3X + 2Y = 24, where X and Y must be ≥ 0
• Possibilities are (X, Y) = (0, 12) or (2, 9) or (4, 6) or (6, 3) or (8, 0)

Thus, option B is the correct answer.

Correct Answer: Option B

Kinshook · Answer

Given: In a certain game, a player can accumulate points only by scoring either an X, which counts 3 points, or a Y, which counts 2 points.

Asked: If a player scored 24 points in the game and t points were made by scoring X's, how many different values could t have?

Let x be the times X was scored and y be the times Y was scored

t = 3x

3x + 2y = 24

(x,y) = {(0,12),(2,9),(4,6),(6,3),(8,0)}: 5 set of values

t will have 5 different values.

IMO B

BrentGMATPrepNow · Answer

So, if X's are worth 3 points and Y's are worth 2 points, then the  TOTAL points = 3X + 2 Y (where X and Y represent the number of X's and Y's scored, respectively)
So, we want to determine the number of different   integer   solutions to  3X + 2Y = 24 
Let's list them in the form (X, Y): 
(0, 12)
(2, 9)
(4, 6)
(6, 3)
(8, 0)

So, X can equal 0, 2, 4, 6, or 8, then t can equal 0, 6, 12, 18 or 24

Answer: B

yazlal25 · Answer

Given 3X + 2Y = 24; 3X = t, How many values can this 't' take is asked. The number of values t can take is the same as the number of values X can take.

Now, we should understand here that X and Y both are integers.

Simplifyling equation

3X = 24 - 2Y
X = 8 - 2Y/3

for X to be an integer Y can be 0 or any multiple of 3.

Y can go from 0, 3, 6, 9, 12 and corresponding value of X would be 8, 6, 4, 2 ,0 (which are 5 distinct values)
 
Hence t can also take 5 values... Option B.

In a certain game, a player can accumulate points only by scoring eith

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a certain game, a player can accumulate points only by scoring eith

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards