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please, i need expert's help

by bek_gmat » Wed Jul 20, 2011 6:14 am

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I've started GMAT prep this week and been studying 'Manual for GMAT' by the princeton review.

There are some problems given in the book and neither the answer nor the explanation is provided. Would be great if some expert can help me out with following problems:

1. Fredrico earns a salary of $350 in a certain week at an appliance store. In addition, he receives a bonus equal to 2/5 of the amount of his total sales that exceed $1500. If he earns $770, what were Fredrico's total sales for the week?

A $1600
B $1750
C $1925
D $2225
E $2550

I know that to get the solution one has to first subtract 350 from 770 which is equal to $420; this is Fredric's bonus. Now according to the problem, some amount's 40% (2/5) should be equal to $420. If calculated this amount is $1,050 which is not given in any answer choice, and moreover it's less than $1,500. So it's not making any sense.

2. Kevin flips a coin four times. What's the probability that he gets heads on at least one of the four flips?

A 1/16
B 1/4
C 3/4
D 13/16
E 15/16

Well, this was very confusing for me since i didn't studied probability at school. I'll appreciate if someone can explain the solution in detail!

Thanks bunch!
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by vineeshp » Wed Jul 20, 2011 7:10 am
1. Fredrico earns a salary of $350 in a certain week at an appliance store. In addition, he receives a bonus equal to 2/5 of the amount of his total sales that exceed $1500. If he earns $770, what were Fredrico's total sales for the week?

A $1600
B $1750
C $1925
D $2225
E $2550

I know that to get the solution one has to first subtract 350 from 770 which is equal to $420; this is Fredric's bonus. Now according to the problem, some amount's 40% (2/5) should be equal to $420. If calculated this amount is $1,050 which is not given in any answer choice, and moreover it's less than $1,500. So it's not making any sense.
Well. 420 is his bonus. But he earned this on the sales exceeding 1500. If his sales is 1500, he earned a bonus of 0. If his sales is 1600, his bonus is only on the 100 (1600 - 1500) . 2/5 of 100 = 40.

His bonus is 420 = 2/5 of amount above 1500. = 2/5 of x
Gives x = 1050. But this is his sales exceeding 1500. So his total sales includes 1500 also. So total sales = 1050 + 1500 = 2550.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by knight247 » Wed Jul 20, 2011 7:16 am
Hope this is detailed enough
1)
Fredrico earns a base salary of $350 in a given week
This is the fixed component of his salary

If his salary is $770 in a week then subtracting $350 from it will given you his sales bonus
770-350= $420 (sales bonus)

Now if his sales exceed $1500 in a week then he gets 2/5th the amt as a sales incentive

2/5*X=420
x=420*5/2=

$1050

But remember, $1050 is his sales amount over and above his montly target of $1500

So total sales is 1050+1500=2550 E

2)

Multiple ways to approach this

When a coin is flipped 4 times the total # of possiblities is 16

HHHH
HHHT HTHH HHTH HHHT
HHTT TTHH HTHT THTH THHT HTTH
HTTT THTT TTHT TTTH
TTTT

Simplest way is

Probability of getting heads on atleast 1 flip + Probability of not getting a single head in 4 flips=1


The only way of not getting heads on a single flip is TTTT and the probability of that is 1/16. i.e.
1/2*1/2*1/2*1/2 or count the total no of possibilities in the pyramid above =16 and there is only one desired outcome i.e. TTTT hence 1/16

So
Probability of gettin heads on atleast 1 flip =1-1/16=15/16 Hence E
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by vineeshp » Wed Jul 20, 2011 7:22 am
2. Kevin flips a coin four times. What's the probability that he gets heads on at least one of the four flips?

A 1/16
B 1/4
C 3/4
D 13/16
E 15/16

Well, this was very confusing for me since i didn't studied probability at school. I'll appreciate if someone can explain the solution in detail!
It is difficult to explain this if you do not know probability at all. You must learn it first before attempting problems. But I will give it a try.
When you flip a coin there are 2 possible outcomes. Heads or tails.
Probability = No. of favourable outcomes / No of total outcomes.
So
probability of getting heads = 1 / 2 (heads is favourable=1. Possibilities = 2 i.e. heads or tails.)
Similarly, probability of getting tails = 1 / 2.
You can also find probability of getting tails as total probability - probability of heads. = 1 - 1/2 = 1/2.

Now when you toss the coin twice. there are 4 possible outcomes. getting 2 heads(HH), getting 2 tails (TT), first heads then tails (HT) and first tails then heads(TH).
No of total outcomes =4.
No of outcomes of getting heads on the first and heads on the second. = HH = 1.
Probability of HH = 1/4.
You can also find this using mutliplication. Probabilty of heads on the first * probability of getting heads on the second. = 1/2 * 1/2 = 1/4.
Similarly probability of getting tails both times = 1/2 * 1/2 = 1/4.

Now to the real problem.. Probability of getting atleast one heads.
So this means all outcomes apart from TTTT are acceptable, right? (HTTT, HHTT,HTHT... and so on)

What is the probability of TTTT = 1/2 * 1/2 * 1/2 *1/2 = 1/16. This is our unfavourable case.
So all other cases are favourable. from the earlier explanation of favourable probability = 1 - unfavourable probability, Probability of atleast one heads = Total Probability (always 1) - (unfavourable Probability) = 1 - 1/16 = 15/16.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by knight247 » Wed Jul 20, 2011 1:32 pm
Hey bek_gmat
Since u've just started studying for the GMAT i would recommend keeping that gmat manual aside for the moment. Refer to Nova GMAT math bible which is an extremely good book if ur starting from scratch. It starts from the extremely basic levels and slowly moves on to harder levels and strengthens ur basics as u go along. Make sure u go thru it absolutely religiously. Basics of Probability and Combinatorix(along with all the other topics) will all be covered once ur done with that. U could also try the gmat math bible by Jeff Sackmann. I haven't tried it but many ppl vouch for that as a basics strengthener. Send me a pm if u don't know where to buy them from.

Cheers
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by Scott@TargetTestPrep » Thu May 09, 2019 5:00 pm
bek_gmat wrote:I'

1. Fredrico earns a salary of $350 in a certain week at an appliance store. In addition, he receives a bonus equal to 2/5 of the amount of his total sales that exceed $1500. If he earns $770, what were Fredrico's total sales for the week?

A $1600
B $1750
C $1925
D $2225
E $2550

Letting T = the total sales for the week, we can create the equation:

770 = 350 + 2/5(T - 1500)

420 = 2/5(T - 1500)

420 = 2/5(T) - 600

1020 = 2/5(T)

T = 1020 x 5/2 = 2550

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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