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Tutor profile: Dheeraj M.

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Dheeraj M.
Math Major ; International Math Olympiad Winner ; Studies at Duke
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Questions

Subject: SAT

TutorMe
Question:

Margaret stays in a hotel that charges $100 per night plus tax for a room. A tax of 6% is applied to the room rate, and an additional onetime untaxed fee of $10.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights?

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Dheeraj M.
Answer:

This Questions asks us for an equation. Base charge : 100 $ per night Tax Rate : 6% per night . One time fee : 10 $ (untaxed) As number of nights is $$x$$, Total fee : $$ 100*x + (6/100)*100*x + 10 : 100x + 6x + 10 : (106x + 10 )$ $$ . So , for 10 nights , Margaret has to pay 106*10 + 10 = 1070 $$ $ $$

Subject: GRE

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Question:

Quantity A Quantity B $$ x^{2} + 2 $$ $$2x - 2$$ Option A: Quantity A is greater. Option B : Quantity B is greater. Option C : The two quantities are equal. Option D : The relationship cannot be determined from the information given.

Inactive
Dheeraj M.
Answer:

Such kind of questions in GRE Math are called Quantitative Comparison Questions . We get around 8 of such kind in the real GRE , per section. Strategy 1 : Use substitution. Try to plug in different value in place of $$x$$. Strategy 2 : Try to prove 2 options among 1,2,3 to be right , if yes , Option 4 is the right answer. Plug-in 1 : $$x = 0 $$ Then Option-1 would become : $$ 0^{2} + 2 = 2 $$ Option-2 would become : $$ 2*0 - 2 = -2 $$ This says Option 1 > Option 2 ( 2>-2) Plug-in 2 : $$x = 3 $$ Option-1 Value : $$ 3^{2} + 2 = 11 $$ Option--2 Value : $$ 2*3 - 2 = 4 $$ Again , Option-1 > Option-2 . Considering negative values of x , i.e -1,-2 , we get Option 1 to be positive and Option-2 to be negative . Hence , we can say that Option-1 is always Greater than Option-2 A is the Correct Answer.

Subject: Basic Math

TutorMe
Question:

We have 14 apples and 10 oranges in a basket . What is the percentage of Oranges and Apples ( Individual) in the basket.

Inactive
Dheeraj M.
Answer:

As there are 14 Apples and 11 Oranges in the Basket , on total , we have 25 ( 14 + 11 ) Fruits in the basket. To Calculate the percentage of each fruit : Percentage of $$X$$ in total of $$Z$$ ( $$Z=X+Y$$ ) : {$$(X)/(X+Y)$$} * 100 Percentage of Apples in Basket : (No.of Apples / Total Fruits)*100 = (14 / 25)*100 = 56% Percentage of Oranges in Basket : (No.of Oranges / Total Fruits)*100 = (11 / 25)*100 = 44%

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