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AnkurGMAT20
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 13 Jan 2024, 06:13
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x of these hours and at a rate of $12 per hour for the remaining y hours. If x and y are integers, which of the following could be Kim's total pay for the 30 hours worked last week?

A. 200
B. 280
C. 325
D. 350
E. 400
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B
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 13 Jan 2024, 10:59
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AnkurGMAT20
Last week Kim worked 30 hours and paid at a rate of $8 per hour for x of these hours and at a rate of $12 per hour for the remaining y hours. If x and y are integers, which of the following could be Kim's total pay for the 30 hours worked last week?

a) 200
b) 280
c) 325
d) 350
e) 400
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Total 30 hour, the easiest way is to think y = 30-x as x+y = 30

Total pay = 8*X + 12(30-X) = 360-4x

Now in total pay put the option and check number is exactly divisible by 4, if divisible by 4 then we will check further else discard.

Option E will directly eliminate as X cant be negative.

Option D will also eliminate as X can't be fraction, Option C can be eliminated as X cant be decimal.

Now we have A and B which is divisible by 4.

If you put Total pay = 200

Then 200 = 360-4X => X = 40 which can't possible as X+Y =30, Option A eliminated.

Remaining Option B is the ans as X = 20 AND Y = 10
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 04 Jul 2024, 05:41
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AnkurGMAT20
Last week Kim worked 30 hours and paid at a rate of $8 per hour for x of these hours and at a rate of $12 per hour for the remaining y hours. If x and y are integers, which of the following could be Kim's total pay for the 30 hours worked last week?

A. 200
B. 280
C. 325
D. 350
E. 400
Show more
­
Think about it this way: If all 30 hrs are paid at the rate of $8 per hour, she would have got 30*8 = $240

For every hour for which $8 is replaced by $12, the overall earning will increase by $4 from $240. Hence $280 is possible by replacing 10 of the $8 hrs by $12 hrs.

Answer (B)
 
Note that if all 30 hrs are replaced, the earning will increase by 30*4 = $120 and will become $360 which is obviously 12*30 = $360

 
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 13 Jan 2024, 07:31
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AnkurGMAT20
Last week Kim worked 30 hours and paid at a rate of $8 per hour for x of these hours and at a rate of $12 per hour for the remaining y hours. If x and y are integers, which of the following could be Kim's total pay for the 30 hours worked last week?

a) 200
b) 280
c) 325
d) 350
e) 400
Show more

Attachment:
Screenshot 2024-01-13 234105.png
Screenshot 2024-01-13 234105.png [ 38.33 KiB | Viewed 11884 times ]

From the information given in the question we can infer that

  • \(x + y = 30 \) -- Equation (1)
  • Total Pay = \(8x + 12y = 4(2x + 3y)\)
    Inference:The total amount paid is a multiple of 4 (because \(x\) and \(y\) are integers)

Answer Choice Elimination

As the total amount paid must be a multiple of 4, we can eliminate Option C and Option D, as both options are not multiples of 4.

A.

4(2x + 3y) = 200

2x + 3y = 30 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = -30 \)

This is not possible. Eliminate A

B.

4(2x + 3y) = 280

2x + 3y = 70 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = 10 \)

The equations provide an acceptable value. Keep B

C.

4(2x + 3y) = 400

2x + 3y = 100 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = 40 \)

This is not possible. Eliminate C

Option B
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 19 Feb 2024, 09:43
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Given->
W1=8x
W2=12y
x+y=30

Q> Total Payment=8x+12y?
if we substitute x as 20 & y=30-20=10
Then Total= 8*20+12*10=160+120=280

Ans = B
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 28 Sep 2024, 04:08
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Instead of checking the options, can we take 8x +12y = p and derive the value of p by solving through equation x + y = 30?
gmatophobia
AnkurGMAT20
Last week Kim worked 30 hours and paid at a rate of $8 per hour for x of these hours and at a rate of $12 per hour for the remaining y hours. If x and y are integers, which of the following could be Kim's total pay for the 30 hours worked last week?

a) 200
b) 280
c) 325
d) 350
e) 400

Attachment:
Screenshot 2024-01-13 234105.png

From the information given in the question we can infer that

  • \(x + y = 30 \) -- Equation (1)
  • Total Pay = \(8x + 12y = 4(2x + 3y)\)
    Inference:The total amount paid is a multiple of 4 (because \(x\) and \(y\) are integers)

Answer Choice Elimination

As the total amount paid must be a multiple of 4, we can eliminate Option C and Option D, as both options are not multiples of 4.

A.

4(2x + 3y) = 200

2x + 3y = 30 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = -30 \)

This is not possible. Eliminate A

B.

4(2x + 3y) = 280

2x + 3y = 70 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = 10 \)

The equations provide an acceptable value. Keep B

C.

4(2x + 3y) = 400

2x + 3y = 100 -- Equation (2)

From Equation (1) we know that \(x + y = 30\), therefore \(2x + 2y = 60\)

Equation(2) - 2*Equation (1) ⇒ \(y = 40 \)

This is not possible. Eliminate C

Option B
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Last week Kim worked 30 hours and paid at a rate of $8 per hour for x 12 Nov 2025, 08:52
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