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Peter works as a teaching assistant and gets paid on a weekly basis.

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Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 18:16
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A
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E

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Question Stats:

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Peter works as a teaching assistant and gets paid on a weekly basis. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours. What is the value of D?

(1) Last week Peter worked for 32 hours.
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.

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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 18:51
Suppose, peter’s wage for first 30 hours = $D per hour
Number of hours that Peter worked in excess of 30 hours = x
Peter’s wage for the extra hours = x (D+10)
Peters total wage if he works over 30 hours = 30D + x (D+10)
(1) Last week Peter worked for 32 hours.
No: of hours Peter worked in excess = x = 32- 30 =2
But this does not help us in finding value of D
So, insufficient.
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours
If Peter worked for 32 hours, x = 2
Peter’s pay = 30D + 2 (D+10)
If Peter worked for 40 hours, x = 10
Peter’s pay = 30D + 10 (D+10)
As we can see that difference is = 30D + 10(D+10) -30D – 2(D+ 10) = 8D + 100
So no new info and insufficient
1) + 2)
Even after combining both the statement, we cannot find the value of D.
Imo. E
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 19:24
Answer:E
D=?
State:1 not sufficient
Total payment of 32 hour= 30xD+(D+10)x(32-30)=32D+20
No information given about total payment
State :2 not sufficient
Given 8X(D+10)=payment for 40 hours- payment for 32 hours=[30D+(D+10)(40-30)]-[32D+20]
8(D+10)=8(D+10) NOT SUFFICEINT
Combining 1 &2,no new information,hence not sufficient
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 19:45
Let T be the total number of hours Peter worked.
For the first 30 hours, peter gets paid D dollars per hour which means 30D.
For every hour in excess of 30, he gets paid (D+10) per hour which means he earns (T-30)(D+10).
Total amount earned= 30D+ (T-30)(D+10)

1) We don't know how much he earned by working for 32 hours. Not sufficient to find D.
2) We can get a linear equation in D. Sufficient.

Answer: B
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 20:15
IMO E

Statement 1: Peter worked for 32 hours.
His income = 30D+(D+10)+(D+10) for 32 hours, D till 30 and D+10 for each extra hour.
Total income for 32 hours = 30D+2D+20 = 32D+20
No constraint to drive D value.
(Insufficient)

Statement 2: if Peter had worked for 40 hours instead of 32hours. he had earned 8(D+10)$ more
Peter earning for 40 hours - earning for 32 hours = 8(D+10)
30D+10D+100-30D-2D-20 = 8(D+10)
8D+80 = 8(D+10)
O=0
No constraint to drive D value.
(Insufficient)

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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 20:59
Peter weekly salary ;
paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours
D*30+(D+10)*(X-30) WHERE X >30 HOURS
#1
Last week Peter worked for 32 hours.
30D+(D+10)*2
32D+20
VALUE OF D IS NOT KNOW INSUFFICIENT
#2
Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.
SALARY OF 40 HOURS - SALARY OF 32 HOURS = $8(D+10)
(30D+10D+100)-(32D+20) = 8D+80
40D+100-32D-20=8D+80
8D+80=8D+80
VALUE OF D CAN BE 1,2,3... UNKNOW INSUFFICIENT
FROM 1&2 NOTHING CAN BE DETERMINED
OPTION E


Peter works as a teaching assistant and gets paid on a weekly basis. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours. What is the value of D?
(1) Last week Peter worked for 32 hours.
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 20:59
E.
Neither statement is enough

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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 21:48
Peter works as a teaching assistant and gets paid on a weekly basis. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours. What is the value of D?
(1) Last week Peter worked for 32 hours.
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.

Solution:

1. For 32 hours, he will get 30D + (D+10)*2 = 32D +20 dollars. However, nothing else is given hence D cannot be determined. Insufficient.

2. For 40 hours, he will get 30D + (D+10)*10 = $8(D+10) more than 32D +20 dollars. However, nothing else is given hence D cannot be determined. Insufficient

Combining them is also no good.

So, 1 and 2 together are not sufficient, Hence Option E is correct
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 06 Jun 2020, 22:18
statement 1 and 2 both are insufficient as
1. 32 hours worked provides no value for D
2. 8 (d+10) also gives no value of d
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 07 Jun 2020, 00:02
Given:
1. Peter works as a teaching assistant and gets paid on a weekly basis.
2. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours.

Asked: What is the value of D?

(1) Last week Peter worked for 32 hours.
Peter gets paid = 30D + 2(D+10) = $(32D + 20)
Value of D can not be derived.
NOT SUFFICIENT

(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.
Peter gets paid for 32 hours = 30D + 2(D+10) = $ (32D + 20)
Peter gets paid for 40 hours = 30D + 10(D+10) = $ (40D + 100)
Difference = 8D + 80 = $8(D+10)
The statement does not provide any additional information, value of D can not be derived.
NOT SUFFICIENT

(1) + (2)
(1) Last week Peter worked for 32 hours.
Peter gets paid = 30D + 2(D+10) = $(32D + 20)
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.
Peter gets paid for 32 hours = 30D + 2(D+10) = $ (32D + 20)
Peter gets paid for 40 hours = 30D + 10(D+10) = $ (40D + 100)
Difference = 8D + 80 = $8(D+10)
Since both statements do not provide any information about D.
NOT SUFFICIENT

IMO E
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 07 Jun 2020, 00:09
Quote:
Peter works as a teaching assistant and gets paid on a weekly basis. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours. What is the value of D?
(1) Last week Peter worked for 32 hours.
(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.


E , imo

Peter works as a teaching assistant and gets paid on a weekly basis. He gets paid D dollars per hour for the first 30 hours and (D+ 10) dollars per hour for the hours worked in excess of 30 hours. What is the value of D?

If n is the total hours worked by peter .
total payment = 30D + (n-30) (D+10)
(1) Last week Peter worked for 32 hours.
Total payment = 30D + 2(D +10) -- no info about total payment . so Cannt get D . insufficient

(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.
If T is the total payment
T + 8(D+10 )= 30D + 10 (D+10 )
T = 30 + 2 (D+10 )..
still we cannot say about D . so Insufficient .

Combining both we cannot get the ans as well.

Hence E .
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.  [#permalink]

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New post 07 Jun 2020, 02:08
Lets first form a general equation for the question stem.
Let T be the total hours worked by Peter... (Lucky if he works and gets paid during the Lockdown)
Let A be the total amount earned by him.

\(\therefore A = 30*D + (T-30)*(D+10)\)
D=?

(1) Last week Peter worked for 32 hours.
T=32

So \(A = 30D + 2*(D+10)\)

If information about A is given, we can find D. But A isn't given......(maybe coz he dint get paid?)
Thus, (A) is insufficient.


(2) Peter got paid $8(D+10) more if worked for 40 hours instead of 32 hours.

Amount he gets for 40 hours, then \(T1 = 30*D + 10(D+10)\)
Amount he gets for 32 hours, then \(T2 = 30*D + 2(D+10)\)

The statment gives us the value of the difference between T1-T2=8(D+10)
30*D + 10(D+10) - {30D + 2(D+10)} = 8(D+10)
8(D+10)=8(D+10).

All the values will cancel out.
Thus, (B) is insufficient... (Had the difference been given only as Dollars, We could find the value of D. But he dint get paid, did he?)

Combining A & B, we dont have any new information that we'd use, thus answer is (E) Both statements are insufficient.
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Re: Peter works as a teaching assistant and gets paid on a weekly basis.   [#permalink] 07 Jun 2020, 02:08

Peter works as a teaching assistant and gets paid on a weekly basis.

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