A clothing store's revenue last May was 6 percent less than

Lemme try and help you on this one.

The easiest way out is to put the alphabetical statements in the form of equations in as minimum variables as possible.

Let us assume the revenue for April = R
Revenue for May therefore is = 0.94 R

Let the expense for April = EA
Let the expense for May = EM

We are not given any relationship between EA and EM

But we also know that R > EA

Now what we are asked is:

R- EA > 0.94 R - EM

or

0.06 R > EA - EM

1) The stores revenue last May was $2,400 less than its revenue last April. This statement does not tell us any relationship between EA and EM which is required to solve the inequality. Hence, it is not sufficient.

2) The stores expenses last May were 4 percent less than its expenses last April.
It says EM = 0.96 EA

Therefore, we get EA - EM = 0.04 EA

Hence, out inequality can be reduced to

0.06 R > 0.04 EA
or

R> 2/3 EA

Since we already know R> EA, it has to be greater than 2/3 EA. Hence, this statement is sufficient to answer the question.

Therefore B as an answer.
Hope it helps!!!

Kudos if you find it useful!!!!!

Solution :
Statement (1) is not sufficient.

Statement (2) is sufficient, refer following figure.

Gross Profit = Revenue - Expense
Revenue > Expense as given for both months.

Revenue Expense
April R E
May .94R .96E

Is R - E > .94R - .96E

Yes.

OA B.

Given:
a) \(R_m=0.94*R_a\)
b) \(R_m>E_m\)
c) \(R_a>E_a\)
Legend: m = March, a = April

Question:
Is \(P_m<P_a\)?
OR is \(R_m-E_m<R_a-E_a\)? (Since, Profits = Revenues - Expenses)
OR is \(E_a-E_m<0.06*R_a\)? (Re-arranging and using info from a) above)....Lets call this as (d)


Statement 1) \(R_m = R_a- $2400\)
Substituting this value in a), we get:
\(R_a - $2400 = 0.94 * R_a\)
\(0.06*R_a = $2400\)
\(R_a = $40,000\)

Substituting this in Question inequality of (d), the question becomes:
Is \(E_a-E_m < 0.06*40000\)?
Or is \(E_a-E_m<2400\)
But we don't know the value of\(E_a\) OR \(E_m\) to say this for sure. INSUFFICIENT.

Statement 2) \(E_m=0.96*E_a\)
Then Question inequality of (d) becomes:
Is \(0.04*E_a < 0.06 * R_a\)?
OR is \(E_a < 1.5*R_a\)?

Now from (c) we know that \(E_a < R_a\)
So \(E_a < 1.5*R_a\) definitely. SUFFICIENT.

Answer B

Thought about it a bit more.

Simplifying algebraically:

.94R-.96E = .94R-.94E-.02E = .94(R-E)-.02E
Since we are subtracting, we assume E is positive (-E is negative). R-E > .94 (R-E) ALWAYS (given R-E is positive). Thus, R-E > 0.94 (R-E) – 0.02E

Stmt 1 - Insuff clearly

Stmt 2 -
April May
Revenue------------ R 0.94R
Expense------------ E 0.96E

Given - R>E
Question - is Profit in May < Profit in April ( i.e 0.94R-0.96E < R-E ?)
Simplifying the above , we get is 4E>6R ? Ans is NO since R>E . Sufficient

I think this one is pretty difficult. My math isn't that good, so I had to use a plug-n-chug method.

Given the below equations:

Assume some extreme cases:
Case 1: R=1000 | E=999.99
R-E = 0.01 | .94R-.96E = -19.99 | April > May
Case 2: R=1000 | E=0
R-E = 1000 | .94R-.96E = 940 | April > May

So no matter what, April always greater than may.

Let x be the revenue for April. Therefore revenue for May is 0.94x.
Let y be the cost for April.

We are asked whether GP for May is less that GP for April?

Gross Profit = Revenue - Cost
GP for April = (x-y)

Change in revenue and change in cost will impact GP. In comparison to April, May has seen reduction in both cost and revenue.
In order for GP of May to be less than that of April, reduction in revenue has to be greater than reduction in cost.
so we can rephrase the question as
is reduction in revenue > reduction in cost ?

statement 1 :- The stores revenue last May was $2,400 less than its revenue last April.
No information about cost is given. statement in insufficient.

statement 2 :- The stores expenses last May were 4 percent less than its expenses last April.
Therefore cost for May is 0.96y.
We want to find whether
is reduction in revenue > reduction in cost ?
is 0.6x(reduction in revenue)>0.4y(reduction in cost)
x/y>0.4/0.6
x/y>2/3 ....... ?

In the question it is given that the store's revenue last April was greater than its expenses last April.
so x/y has to be greater that 1.
Therefore x/y is greater that 2/3 and hence GP for May is less than that for April.
Statement is sufficient.

Ans - B

We can start by using the following variables:

a = revenue last April

b = expenses last April

c = revenue last May

d = expenses last May

We are given that a clothing store's revenue last May was 6 percent less than its revenue last April. Thus,

c = 0.94a

We are also given that the store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Thus:

c > d and a > b

We need to determine whether a - b > c - d, or

Is a - b > 0.94a - d ?

Is 0.06a > b - d ?

Statement One Alone:

The store’s revenue last May was $2,400 less than its revenue last April.

We can create the following equation:

c = a - 2,400

Since c = 0.94a, we can substitute 0.94a for c in the above equation and we have:

0.94a = a - 2,400

2,400 = 0.06a

a = 40,000 and c = 37,600

However, we still cannot determine whether 0.06a > b - d. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The store’s expenses last May were 4 percent less than its expenses last April.

Using the information in statement two, we can create the following equation:

d = 0.96b

We can substitute 0.96b for d in the inequality question and we have:

Is 0.06a >b - 0.96b ?

Is 0.06a > 0.04b

Is 6a > 4b ?

Since we are given that a IS GREATER THAN b, then 6a MUST BE GREATER THAN 4b. Statement two alone is sufficient to answer the question.

Answer: B
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Actually found my way of doing it. Follow me ok?
APR MAY
Rev X 0.94X
Exp Z Y
Profits X-Z> 0.94X+Y?

Is 0.06x>Z+Y?

We also know that '0.94x>y' and that 'x>z'
Statement 1

0.06X = 2400

We can find the value of 'x' here but we still don't know if its greater

For instance if y=0.93x and z=0.93x then answer is NO

If y=0.01x and z=0.01x answer is YES

This is even without knowing the value of X since 'X' must be a positive number

Staetment 2

y=0.96z therefore we have that

0.06x>0.04z?

6x>4z ---> 3x>2z?

Well, since both numbers must be positive and since x>z then answer to this is YES

Hence sufficient

Answer: B

Hope this clarifies
Kudos if you like

My little contribution based on the previous explanations above.

a=April
m=May
R=Revenue
E=Expenses

Profit April: Ra-Ea
Profit May: 0.94Ra-Em

1) No info on expenses. Insuff.

2)

Profit April: Ra-Ea
Profit May: 0.94Ra-0.96Ea

For May, the revenue has decreased by a greater percentage than the expenses. Therefore, the profit in April is greater. Suff. B

Agree? Kudos. Better method? Please comment.

we can solve this with logic


6% from something bigger is > 4% from something smaller

Tricky question.


A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?

(1) The stores revenue last May was $2,400 less than its revenue last April.
(2) The stores expenses last May were 4 percent less than its expenses last April.


Let the Revenue in May and April be Rm and Ra respectively. Also, let the expenses in May and April be Em and Ea resp.

Given that Ra-Rm=0.06 and Rm> Em and Ra> Ea.

Profit = Revenue - Expenses

To evaluate: Rm-Em < Ra-Ea?

Ea-Em < Ra- Rm or Ea-Em < 0.06

Statement 1: The stores revenue last May was $2,400 less than its revenue last April.

From this statement, we can deduce about the revenue values but no information is presented about the expenses. As such, we won't be able to determine the condition.

Statement 2: The stores expenses last May were 4 percent less than its expenses last April.

Em=0.96* Ea.

Ea-Em= Ea-0.96*Ea = 0.04 * Ea

Since Ea < Ra (given) , 0.04 Ea < 0.04 Ra < 0.06 Ra

Hence B alone is sufficient.

ThatDudeKnows avigutman please confirm if my understanding is correct here

Given rev> exp:
1. If revenue decreases by more % compared to expenses decrease %, then revised GP will be lesser than older GP
2. If revenue decreases by equal % as expenses %, then revised GP will decrease by same % and will still be lesser than older GP
3. If exp decreases by more % that revenue %, then revised GP will be more than older GP
And does the above hold rtrue regardless of the magnitude of either expense or revenue given revenue > expense? So basically does the above hold true even of revenue or exp take very low or high figures compared to each other given the condition is met

Yes, all true. I advise you to draw a number line and apply some reasoning to test those "rules.", Elite097

 

­Statement 1:
No information about expenses. 
INSUFFICIENT.

Statement 2:
Let the revenue in April = 100, with the result that the revenue in May = 6% less $100 = 94
Let x = the expenses in April, with the result that the expenses in May = 4% less than x = 0.96x
Is May's profit less than April's profit?
Translated into math:
94 - 0.96x < 100 - x ?
0.04x < 6 ?
x < 150 ?
Since the prompt requires that the expenses in April be less than the revenue in April, we know that x < 100.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.



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Bunuel can you chime in. I am struggling to understand the OE.