GMAT Math

Is the hunderdths of the decimal D greater than 5 ?
1.The tenths digit of 10D is 7 ?
2.The thousandths digit of D/10 is 7



 A grocer buys apples for 63$ per pound.if 10%of the apples go bad and he still wants to make a 20%profit over his purchase price ,what should be the sales price ?
A) 66
B) 70
C) 75
D) 77
E) 84
these questions from the gmat avengers guide

Hi,

Question #1 Solution:

You can translate the question to D = a.bcdefg so on so forth, with "b" being the tenth, "c" being the hundredth, and "d" being the thousandth. The questions asks whether c > 5.

With Statement #1, by multiplying D by 10 you increase the number ten-fold, which gives you 10D = ab.cdefg
"c" is now the tenth digit of 10D, and is equal to 7 base on the statement, which is certainly greater than 5. SUFFICIENT

With statement #2, by dividing D by 10 you decrease the number ten-fold, which gives you D/10 = .abcdefg
"c" is now the thousands digit of D/10, and is equal to 7 base on the statement, which is certainly greater than 5. SUFFICIENT.

Answer is D.
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Question #2 Solution:

This is a good one to apply smart number.

Let's say the grocer bought 100 lbs of apple. He then have spent 63 dollars. he wants to make 20% profit, he will need to make 63*(120%) = 63*(1.2) = 75.6 dollars.

since 10% of the apple went bad. he only has 100*(90%) = 90 pounds of apply left to sell.

Total sales/total pounds = 75.6/90 = .84

Answer is E.

Here is short soln:
The final percentage the seller will make of original spend will be 120%.

Applying formula :
final % = final price / original price

Original Price = 63/90*100

120/100 = fp / (63/90*100)
fp = 84