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# GMAT: Data sufficiency 22

## Video transcript

we're on question 95 a certain salesperson weekly salaries equal to a fixed base salary plus a commission that is directly proportional to the number of items sold during the week I mean right there 95 so the salary is equal to some base plus plus a commission that is directly proportional to the number of items sold during the week so let's say the items number of items sold is X X items x I don't know the Commission per item so I'll call that lower case C and this is a total Commission fair enough Commission hey if 50 items are sold this week what will be the sales salesperson salary for this week okay so they actually told us that there's 50 items fair enough what will be the salesperson salary this week so statement number one tells us last week 45 items were sold so 45 in last week that alone doesn't tell me much right because I don't know how much he made last week statement to last week's salary was four hundred five dollars four hundred and five dollars well does this help me still last week because in order to figure out what 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 right and the only way we could figure that out is if you tell us the last week we know that he sold 45 items so for example last week he made four hundred five dollars if I use both statements let me see if I can get any where he made four hundred five dollars last week which is equal to his base plus forty five units sold times his Commission per unit so that's all this information gives me if actually if I use both statements that's all it gives me right the 405 is equal to B plus 45 times C and we need to figure out s is equal to B plus 50 C right what is s equal when when 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 right B and C was already there so we have three unknowns but only two linear equations so we don't have enough information to solve it so the answer is what is that e we all ball of these statements still do not give us enough information 96 96 if one 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 one exactly 60 hours before the appointment it was Monday 60 hours before the appointment it was Monday 60 hours before it was Monday this is interesting okay so how many at 60 hours is two days two days is 48 hours two days it's exactly two and a half days right 48 and then another 12 so this is equal to two and a half days two and a half days before so this is interesting if we said if you said that two days before it was a Monday then his appointment had to have been on a Wednesday right because if you pick if you pick any hour and Wednesday and you go exactly 48 hours ago it would be that same exact hour on Monday right so if you said 48 hours ago it was Monday then you then this would be enough information this is two and a half days ago so for example if his appointment and you know it might sound weird but if his appointment was at let's say Thursday Thursday 1:00 a.m. and you got two and a half days before let's see if you go two days ago before you go to Wednesday 1 a.m. Tuesday 1 a.m. and then you go 12 hours before you would end up at Monday at 1:00 p.m. Monday at 1:00 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 if his point was on Wednesday at 10:00 p.m. then if you go one day back you at Tuesday 10 p.m. I don't know I'm sure you can't read that then you go another day you're at Monday 10 p.m. and then you go half a day you're at Monday 10 a.m. so statement 1 does not give us enough information it's because of this pesky half day now let's see what statement to get us for us statement 2 the appointment was between 1:00 p.m. and 9:00 p.m. 1:00 p.m. to 9:00 p.m. now this by itself obviously is useless I mean you could have an appointment any day between 1:00 p.m. and 9:00 p.m. but used in conjunction with each other it seems like I have enough information because let's say the appointment was at 9:00 p.m. and 2 days two and a half days ago it was a Wednesday so let me see you 9:00 p.m. sorry two days ago it was a Monday so if I have it at Wednesday 9:00 p.m. if I go back one day I'm at Tuesday 9:00 p.m. Tuesday I met sorry one day back I'm at Tuesday 9:00 p.m. two days back I'm at Monday 9:00 p.m. and then if I go half a day more I'm at Monday 9:00 a.m. right and if I take the lower bound Wednesday at 1:00 p.m. do the same logic and you're going to end up at Monday 1:00 a.m. so at either end of this range if I know that if you go two days ago you end up with Monday the only day that works is Wednesday you could try this with Thursday or Tuesday you won't end up Monday if you go two and a half 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 multiply it out we get x squared plus 4x 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 so or 4x 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 that's minus 20x plus 4x minus 1 oh doesn't get us anywhere even playing around with the algebra so we get minus 16x minus 1 so a statement by statement 1 by itself at least as far as I can figure out does not help us solve this problem statement number two statement number two X is equal to zero 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 99 98 98 at Larry's auto supply store Brand X antifreeze is sold by the gallon so X by gallon and brand Y sold by the court Y by the quart excluding sales tax what is the total cost for one gallon of Brand X antifreeze so 1 of X 1 of X and one quart of blant Brent brand y okay 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 we'd have to know their prices in order to figure out how much does the combination cost so let's see at least I think statement 1 excluding sales tax the cost for 6 gallons of Brand X antifreeze so 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 to eat 2 unknowns with one linear equation so I can't solve for what X plus y is equal to I mean there's if I could have factored out if this was 10 X + 10 Y I could have factored out of 10 and I would have had X plus y right sitting there so I should I probably could have solved if it was that way but this isn't quite as easy so statement number two excluding sales tax the total cost for 4 gallons of Brand X for gallons of Brand X plus 12 quarts of Brand y plus 12 quarts of brand y is equal to \$44 and actually just to be exact I've I realize I misspoke something let X let X be the cost X equals the cost of X antifreeze per gallon and Y is equal to the cost of y antifreeze for gallon and so we want one so we are still trying to figure out X plus y but I just wanted to be exact because we got 6 gallons so the cost would be 6 times X plus 10 quarts of y so it would be 10 times y to get 58 etc etc but now we have two equations with 2 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