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.

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

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.

I did the same, but selecting values for this question made me feel vulnerable to a yes/no outcome, so I was looking for an algebraic explanation. Also, the question indicates that revenue is greater than expense for both months, so I don't think you can end up a with a negative value for May.

These numbers work a bit better for your first example.

May: Revenue = 1000 Exp = 200
April: Revenue= 940 Exp= 192

Now that I think about it, I may have just answered my own question!

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

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

Isn't the answer to the question yes, it is less.

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

Ans B

R>E for both months

Profit in April, Pa = Ra-Ea

Profit in May, Pm = Rm-Em

comparing....Revenue decreased by 6% and expenses by 4%

Profit comparision....( bigger no. decreased by more) - (a smaller no. decreased by less) =>overall profit decreased more=> B is sufficient

A

doesnt even connect hw expenses vary...so not sufficient

here is another way to look at statement 2. Already explained but will simplify through algebra...

Let ---------------- --Apr---------------May
Revenue---------- ----X--------------- 0.94X ( given in stem that revenue is 6% less in May)
Expense ---------- ----Y ---------- ----0.96Y ( Given in statement 2 that expense in May is 4% less)

We have to prove is : 0.94X - 0.96 Y > X- Y
(Profit of May is greater than Apr)

We are told that in both months Profit is +ve or greater than zero. Means that X>Y --> X/Y > 1.

now reducing the above equation 0.94X - 0.96 Y > X- Y
we get X/Y < 2/3

Now for (0.94X - 0.96 Y > X- Y) equation to be true, X/Y < 2/3 has to be true.

But we are told X/Y>1 therefore the above equation doesn't hold true.

Hence 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

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.

Answer is yes, isn't it?! Profit for May is less than April...

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.