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## GMAT

### Course: GMAT > Unit 1

Lesson 2: Data sufficiency- GMAT: Data sufficiency 1
- GMAT: Data sufficiency 2
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- GMAT: Data sufficiency 21 (correction)
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# GMAT: Data sufficiency 20

87-90, pg. 285. Created by Sal Khan.

## Want to join the conversation?

- 89. couldnt part a represent division?(2 votes)
- It doesn't show division in the circle.(3 votes)

## Video transcript

We're on problem 87. It says an employee is paid 1.5
times the regular hourly rate for each hour worked in
excess of 40 hours per week. OK. So after 40, they get overtime. 1.5 times. Excluding sunday. And 2 times the regular
hourly rate for each hour worked on sunday. So each hour worked on Sunday,
regardless of whether or not they're above 40 hours. How much was the employee
paid last week? OK. So let's see. Statement one tells us the
employee's regular hourly rate is $10. $10 per hour is normal. Now based on that, we know
what their overtime is. Overtime is 1.5 times,
so it's $15 an hour. And it tells us that sunday is
double that. $20 an hour. All of that was said in the
problem description, I guess you could call it. But we still don't know how much
they were paid because we don't know how many hours they
worked and when those hours happened to be. So it's still not enough
information. Statement number two. It says last week the employee
worked a total of 54 hours but did not work more than
8 hours on any day. OK. So let's think about that. If you worked no more than 8
hours in a day, how many days would you have to work? Well you would have to work-- I
guess at minimum, you'd have to work 6 days for 8 hours. And 1 day you would
work for 6 hours. Right? Or there's other ways
you could say it. You could have all 7 days you
could be working-- for how many times does 7 go into--
you could be working 7 6/7 hours a day. Now neither of these help us
because we don't know where the hours were allocated. We don't know how many of these hours ended up on sunday. Because that's a critical
question. And we know that there
was some overtime in some form, right? But we don't know if that was
sunday overtime or if that was regular overtime. Imagine working 7 6/7
hours every day. Then you would have 7 6/7
hours for monday through friday, then you get some
overtime for saturday as soon as you got above 40 hours. And then on sunday you would
get paid double. But then you have
this situation. Maybe sunday is a day
you worked 6 hours. Or maybe sunday is one of the
days you worked 8 hours. So we don't know. So, this problem, there's not
enough information to solve this problem. 88. What was the revenue that a
theater received from the sale of 400 tickets, some of which
were sold at the full price, and the remainder which were
sold at reduced price? OK, fair enough. The number of tickets sold at
full price-- so this is statement number one-- so
immediately we know that there were 400 tickets sold. And that is the number of
full-priced tickets plus reduced priced tickets. It's equal to 400, right? Wait. Some of which were sold at full
price and the remainder of which-- oh, they want
to know the revenue. OK. They want to know the revenue. So we have to know how much we
got for each of these tickets in order be able to
figure it out. So number one. The number of tickets sold at
full price were 1/4 of the total number of tickets sold. So 1/4 times-- what was the
total number of tickets sold? Well they already told us that. 400. So it equals 100. And then we could just look at
that and that tells us that the reduced price were equal
to 300 tickets were sold at the reduced price. But that still doesn't tell us
the total revenue because we don't know how much full
price was or how much reduced price was. So that's not enough information
just yet. Problem two says the full price
of a ticket was $25. But we still don't know what
the reduced price is. We know the 25 100, or $2,500
were generated from the sale of the full-price ticket. But the reduced price, they
don't tell us that. How much did they reduce
the price, right? Some of which were sold at full
price and the remainder of which were sold at
a reduced price. We don't know what that is. It was 25% off? 50% off? We don't know. So unless we know the price of
the reduced price ticket, we can't figure this out. So once again, not enough
information to solve the problem. Problem 89. What is that, a circle? The circle represents one
of the operations plus, minus and times. OK. This is interesting. So they say a circle represents
one of the operations plus minus and times
is k circle l plus m equal to k circle l plus
k circle m for all numbers k, l, and m? Well essentially, what
are they doing? They're doing the distributive
property, right? They're saying that k-- whatever
this operation times l plus n-- is the same thing
as k times whatever this operation is with l, plus
k whatever this operation is with m. And the only places where the
distributive property works is either with multiplication
or division. And division isn't one
of these properties. So essentially this doesn't
work with addition or subtraction. So if essentially we're able
to prove or disprove that multiplication is this operator,
then we have enough information. This question could be rephrased
as: is circle equal to multiplication? So if we can answer this with
the statements, then we can answer this top one. Because only multiplication
works with this. Or division, but division isn't
one of the options. Statement one says k circle 1 is
not equal to 1 circle k for some numbers k. Well this immediately tells
me that this is not multiplication, right? In fact, this tells me that
this is subtraction. Right? Because the only time where k
minus 1 is different than 1 minus k, with addition, they'd
always be equal to each other. With multiplication they'd
always equal each other. So this has to be if you believe
statement one, then circle is subtraction. Which tells you that this
statement up here is not true. So statement one alone is
sufficient to determine whether this statement
is true. Or another way to phrase
problem, whether circle is equal to multiplication. So statement one
is sufficient. Statement one actually tells
us that the circle is subtraction. Statement number two. Circle represents subtraction. OK well they just told
it outright there. Well so this and this are
equivalent information and so they're enough to determine that
this up here is not true. Remember, they're not saying,
is the statement true? They're just saying, do you
have enough information to figure it out? And we know that this isn't
true because circle is subtraction. And this statement only holds
true if the circle is equal to multiplication. So each statement alone
is sufficient to solve that problem. Problem 90. How many of the 60 cars sold
last month by a certain dealer had neither power windows
nor a stereo? OK. So it tells us 60 sold. And we want to know how
many had neither power windows nor a stereo. Statement one tells of the 60
cars sold, 20 had a stereo but not power windows. Fair enough. But that still doesn't tell
us how many had neither. So let me draw a little circle
Venn Diagram here. OK. So that's all 60 cars
that were sold. That pool right there,
that set. 20 had stereos with
no power windows. So let me draw some Venn
Diagrams. [SNEEZES] Excuse me. All right. That sneeze that I was talking
about a couple of videos ago finally happened and
I feel-- [SNEEZES] excuse me. All right. Back to the problem. 20 had stereos with
no power windows. So let's say that this is the
pool that had stereos. This is the pool that
had power windows. And what we care, actually, is
what had neither stereo nor power windows. So we care about this outside. Oh, that looks tacky. That's a little garish. But anyway. So if this is stereos, this is
power windows, this would be stereos and power windows. You're saying 20 had stereos
but no power windows. So that's this right here. So I'll do another fill. Yeah. That's not pleasant
to look at. But this is 20 stereo,
no power window. But that alone doesn't tell us
what this green area is. So what's the second
statement? That's too dark. Statement two tells us, of the
60 cars sold, 30 had both power windows and a stereo. So that tells us that this range
right here-- let me do it in another tacky color. That tells us that that's
how many had power windows and stereos. Let me make sure I have
a good color here. So that's 30. I know that you can't
see that. OK. So we could answer a couple
of questions. We can answer, how many cars
sold had stereos in general? Well 50, right? 20 had a stereo, no
power windows. 30 had a stereo with
power windows. So a total of 50 stereos
were sold. We know that. 50 had stereos. But that still doesn't
answer our question. Of the 10 that remained-- 60
were total, and there's 10 left within this space
and this space. We don't know how those
10 fall out. Maybe 5 had neither and
5 had only power windows with no stereo. Or maybe there were no cars with
only power windows and no stereos, and all
10 had neither. So you don't know, even
using both statements. So, at least for this one, they
haven't given us enough information to figure out
how many had neither. They did give us enough
information figure out how many stereos got sold,
or how many cars with stereos got sold. Anyway. See you in the next video.