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# GMAT: Data sufficiency 22

Video transcript

We're on question 95. A certain sales person's weekly
salary is equal to a fixed base salary plus a
commission that is directly proportional to the number of
items sold during the week. So let me write this. 95. So the salary is equal to some
base plus a commission that is directly proportional to
the number of items sold during the week. So let's say the number
of items sold is x. x items times the commission
per item. So, I'll call that
lowercase c. And this is the total
commission. Fair enough. If 50 items are sold this week,
what will be the sales person's salary for this week? OK, so they actually told
us that there's 50 items. Fair enough. What will be the sales person's
salary this week? So statement number 1
tells us, last week 45 items were sold. So 45 in last week. That alone doesn't
tell me much. Because I don't know how
much he made last week. Statement 2. Last week's salary was $405. Well, does this help me still? Last week. Because in order to figure out--
we need to figure out-- right now we need to know how
much of his salary in any given week is base, and
how much commission does he get per unit. And the only way we can figure
that out is if you tell us that last week we know that
he sold 45 items. So, for example, last week
he made $405. If I use both statements, let me
see if I can get anywhere. He made $405 last week, which
is equal to his base plus 45 units sold times his commission
per unit. So that's all this information
gives me. Actually if I use both
statements, that's all it gives me. That 405 is equal to
b plus 45 times c. And we need to figure out s
is equal to b plus 50c. What is s equal when
you sell 50 units. And so we have two
linear equations. But we have how many unknowns? We have one unknown, two
unknown, three unknowns. Sorry. One unknown, two unknown,
three unknowns. b and c was already there. So we have 3 unknowns, but only
two linear equations. So we don't have enough
information to solve it. So the answer is E. All of these statements still
do not give us enough information. 96. If Juan had a doctor's
appointment on a certain day, was the appointment
on a Wednesday? So we want to know, was
it on a Wednesday? 1, exactly 60 hours before the
appointment it was Monday. 60 hours before the appointment
it was Monday. This is interesting. OK, so how many days? 60 hours is 2 days. 2 days is 48 hours. It's exactly 2 and 1/2 days. 48 and then another 12. So this is equal to
2 and 1/2 days. So this is interesting. If we said that 2 days before,
it was a Monday, then his appointment had to have been
on a Wednesday, right? Because if you pick any hour
in Wednesday and you go exactly 48 hours ago, it
would be that same exact hour on Monday. So if you said 48 hours ago it
was Monday then this would be enough information. This is 2 and 1/2 days ago. So for example, if his
appointment-- and you know it might sound weird-- but
if his appointment was at Thursday 1 a.m. and you go 2 and 1/2 days
before-- let's see if you go 2 days before you to Wednesday 1
a.m., Tuesday 1 a.m., and then you go 12 hours before. You would end up at
Monday at 1 p.m. So, I've given a case that meets
condition 1, where his appointment wasn't
on Wednesday. It was on Thursday. But of course, I can give
a condition where his appointment was on Wednesday. His appointment was on
Wednesday at 10 p.m. Then if you go 1 day back you're
at Tuesday 10 p.m. I'm sure you can't read that. Then you go another day. You're at Monday 10 p.m. And then you go a half a day. You're at Monday 10 a.m. So, statement 1 does not give
us enough information. That's because of this
pesky half day. Now let's see what statement
2 gets us. Statement 2. The appointment was
between 1 p.m. and 9 p.m. Now, this by itself, obviously,
is useless. I mean, you could have
an appointment any day between 1 p.m. and 9 p.m. But used in conjunction with
each other, it seems like I have enough information. Because let's say the
appointment was at 9 p.m. and 2 and 1/2 days ago
it was a Wednesday. So let me see, sorry, 2 days
ago it was a Monday. So if I have it at Wednesday 9
p.m., if I go back 1 day, I'm at Tuesday 9 p.m. Sorry. 1 day back I'm at
Tuesday 9 p.m. 2 days back I would be
at Monday 9 p.m. And then if I go 1/2 a day more,
I'm at Monday 9 a.m. And if I take the lower bound. Wednesday at 1 p.m. Do the same logic and
you're going to end up at Monday 1 a.m. So at either end of this range,
if I know that if you go 2 days ago, you end up at
Monday, the only day that works is Wednesday. You could try this with
Thursday or Tuesday. You won't end up on Monday if
you go 2 and 1/2 days back. So for this problem, both
statements are necessary in order to know whether his
appointment was on Wednesday. Next problem. 97. What is the value of 5x squared
plus 4x minus 1. First they tell us, x times
x plus 2 is equal to 0. Well let's see, can
we use this alone? Let's just multiply it out. We get x squared plus
4 x is equal to 0. And that tells us that x squared
is equal to minus 4x. Well maybe we could substitute
this in for 4x, or for x squared. So we get 5 times x squared. Well we know that x squared
is minus 4x. Minus 4x plus 4x minus 1. That's minus 20x plus
4x minus 1. No it doesn't get us anywhere,
even playing around with the algebra. So we get minus 16x minus 1. So statement 1 by itself, at
least as far as I can figure out, does not help us
solve this problem. Statement number 2. x is equal to 0. Well that's all we need. x is equal to 0,
then this is 0. This is 0. And we're just left
with negative 1. So this is the only piece of
information we need to solve this problem. And statement 1 doesn't
really help us much. So only statement
2 is necessary. What is that, B? Next problem. 98. At Larry's Auto Supply Store,
brand x antifreeze is sold by the gallon. So x by gallon. And brand y is sold
by the quart. Excluding sales tax, what is the
total cost for 1 gallon of brand x antifreeze-- so 1 of
x-- and 1 quart of brand y? OK, so we want to know the cost.
Equals how much dollars? So let x be the number of
gallons of x and y be the number of quarts of y. So we'd have to know their
prices in order to figure out how much the combination
costs. So let's see, at
least I think. Statement 1. Excluding sales tax, the cost
for 6 gallons of brand x antifreeze and 10 quarts
of y-- so plus 10 of y-- is equal to $58. Well this, once again, by itself
does not help me much. I have two unknowns with
one linear equation. So I can't solve for what
x plus y is equal to. If I could have factored out--
if this was 10x plus 10y I could have factored out a 10,
and I would have had x plus y sitting there. So actually I probably
could have solved, if it was that way. But this isn't quite as easy. So statement number 2. Excluding sales tax, the total
cost for 4 gallons of brand x plus 12 quarts of brand y-- so
it's 12 quarts of brand y-- is equal to $44. And actually, just
to be exact, I realize I misspoke something. Let x be the cost of x
antifreeze per gallon. And y is equal to the cost of
y antifreeze per gallon. And so we are still trying to
figure out x plus y, but I just wanted to be exact. Because we've got 6 gallons. So the cost would be 6 times
x plus 10 quarts of y. So this would be 10
times y to get 58. Et cetera, et cetera. But now we have two equations
with two unknowns. So it's trivial now to
solve for x and y. This is your algebra
1 problem. So, both equations combined are
enough to solve for it. But each independently
are not enough. Because you can't just factor
out a number and just be left with x plus y here. That could have been a trick, if
this was a tricky problem. But it's not. Anyway, see you in
the next video.