From Leland's gross pay of p dollars last week, t percent

Question

From Leland's gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings. What amount of Leland's gross pay last week remained after these two deductions?

(1) p - s = 244
(2) pt = 7,552

(1) p - s = 244 
(2) pt = 7,552

Bunuel · Accepted Answer

From Leland's gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings. What amount of Leland's gross pay last week remained after these two deductions?

(1) p - s = 244
(2) pt = 7,552

We need to find the value of  p-\frac{pt}{100}-s .

(1) p - s = 244 --> we need to find the value of  244-\frac{pt}{100} . Not sufficient.

(2) pt = 7,552 --> we need to find the value of  p-\frac{7,552}{100}-s . Not sufficient.

(1)+(2)  p-\frac{pt}{100}-s=244-75.52=168.48 . Sufficient.

Answer: C.

Hope it's clear.

prude_sb · Answer

My interpretation of the question is that we need to find the value of p-t-s in dollars
so my answer would be 

stat1 alone: insufficient since t is unknown
stat2 alone: insufficient since s is unknown nor is the value of p or t or p-t

stat2 & stat1: insufficient since massaging these eqs to get p-t-s does'nt seem to be possible

I would pick E

ricokevin · Answer

That's what I thought. E.

But the correct answer is C...

(maybe the correct answer is wrong...)

prude_sb · Answer

ooops... just realized that it is t percent not t dollars so what we need to find is p - pt/100 - s

which can be found if we use info from both the statements so ans is C!

lwwlwwlww · Answer

From Leland's gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings. What amount of Leland's gross pay last week remained after these two deductions?

(1) p - s = 244
(2) pt = 7,552

(1) p - s = 244
(2) pt = 7,552

the amount after two deductions is p- (t%)p-s
we get p-s from (1) but we don't know p(t%) , so it is insufficient
we get pt from (2) ,it means p(t%)=7552/100 . But we don't know p-s, it is insufficient.

combining the two data, we can get p- (t%)p-s. Therefore, the ans is C

bulletpoint · Answer

So what would the actual answer be if we had to calculate it? And if the question says t%, isnt the equation just p - pt - s, and not p -pt% - s?

From what I gather, if we plug in the numbers we get: 244- 7552= -7308?? Does that mean Leland is losing money?

Fabino26 · Answer

I am happy I'm not the only one making careless mistakes. 244-75.52=168.52

Bunuel · Answer

Thank you.

Actually it's 168.48.

TooLong150 · Answer

Need p - pt/100 - s. Only C can give the required elements.

JackSparr0w · Answer

after Bunuel's explanation, I think thats a wrap on this one. Very concise.

jgcanada · Answer

The question is using both percent and fixed value in the stem.

P - tP - S = ?

P is fixed weekly income
t is percent to be multiplied by P to know the amount for tax
S is fixed savings amount

ryuken101 · Answer

I don't understand...How is pt/100 considered a dollar amount?

I get 244 - 7552????...

I understand now... pt= 7552 is just the numerator... I assumed pt=7552 is the same pt/100=7552

ghancock · Answer

I am confused on how we would know from the stem that t percent is does not already assume that it would be divided by 100?

If it were 4%, I would already make the assumption that is equal to 4/100 or .04.

It feels misleading of the prompt to force the test taker to make the assumption that has not already been completed by multiplying  pt .

I wound up in the same boat as the poster who got to a negative number when combining both statements. At that point I decided not to sit and scratch my head and went for E in order to move on.

Bunuel · Answer

4% = 4/100, similarly t% = t/100.

KrishnakumarKA1 · Answer

Prompt analysis
Gross pay will be p(1-0.01*t) - s = p-s - 0.01pt

Superset
The value will be any positive real number

Translation
To find the gross pay, we need
1#Exact value of p, t, s
2# the value of p-s and pt
3# any other relation so that we can come up to the exact figure

Statement analysis
St 1: p-s = 244. We don't know the value of pt. INSUFFICIENT
St 2: pt = 7.552. We don't the value of p-s. INSUFFICIENT
St 1 & St 2: we know p-s and pt. SUFFICIENT

Option C

ScottTargetTestPrep · Answer

We are given that from p dollars, t percent was deducted for taxes and then s dollars was deducted for savings. Thus, what remained was:

p(1 - t/100) - s = p - pt/100 - s = p - s - pt/100

So we need to determine a value of p - s - pt/100.

Statement One Alone:

p - s = 244

Statement one alone is not sufficient to answer the question. Although we know the value of p - s, we still need the value of pt.

Statement Two Alone:

pt = 7,552

Statement two alone is not sufficient to answer the question. Although we know the value of pt, we still need the value of p - s.

Statements One and Two Together:

Since we know that p - s = 244 and that pt = 7,552, we see that p - s - pt/100 = 244 - 7,552/100.

Answer: C

Hungryman1 · Answer

I thought you weren't allowed to reorder subtraction. That is, it does not have the communicative property.

ScottTargetTestPrep · Answer

Notice the following:

5 - 3 - 4 = 5 - 7 = -2

just as

5 - 4 - 3 = 5 - 7 = -2

We are able to do what we did because we left the first term as it was. We just reordered the last two terms just as I did in the example above. So, what we did is totally fine.

egmat · Answer

You're right that  subtraction is NOT commutative  — meaning  a - b ≠ b - a .

However,  we're not swapping the order of subtraction here . Let me clarify what's actually happening.

The Key Principle: 
 Subtracting a number is the same as adding its negative.

So when we have:
 Remaining = p - (pt/100) - s

We can rewrite this as:
 p + (-pt/100) + (-s)

Now,  addition IS commutative and associative , so we can rearrange:
 = p + (-s) + (-pt/100) 
 = (p - s) - pt/100

Quick Numeric Check:

Let's verify with simple numbers:  10 - 3 - 2

Method 1:  Left to right → 10 - 3 - 2 = 7 - 2 =  5 
 Method 2:  Regroup → (10 - 2) - 3 = 8 - 3 =  5  ✓

Same answer! We're not breaking any rules.

Applying This to the Problem:

We need:  p - (pt/100) - s

Rewriting:  (p - s) - (pt/100)

From Statement 1:  p - s = 244 
From Statement 2:  pt = 7552 , so  pt/100 = 75.52

Together:  244 - 75.52 = 168.48  ✓

Answer: C

From Leland's gross pay of p dollars last week, t percent

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From Leland's gross pay of p dollars last week, t percent

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