TutorMe homepage
Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Hương T.
Tutor for 2 years, 50 Quantitative GMAT, former social media researcher, marketing manager
Tutor Satisfaction Guarantee
Geometry
TutorMe
Question:

ImageImage http://gmatclub.com/forum/download/file.php?id=26518 A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown? A) 72 B) 78 C) 84 D) 96 E) 108

Hương T.
Answer:

Area of the shape is Area of triangle ACF = 1/2*(ABxAF) AB = 12 (height of the paper) Problem turns into find AF Suppose EF =x. Also, points A and D coincide after the paper is folded, so CD = CA = AF = 18-x, BC = EF = x (ACDF is a parallelogram). Noticing that line AC is the hypotenuse of triangle ABC, we can calculate it with the information we have. 12^2+x^2=(18-x)^2 144+x^2=324-36x+x^2 36x=180 x=5 Thus, the base, AF = AC = 18-5=13 And the area of the triangle is 1/2*13*12=78 Answer is B

Numerical Analysis
TutorMe
Question:

The last digit of 12^12+13^13–14^14×15^15 A. 0 B. 1 C. 5 D. 8 E. 9

Hương T.
Answer:

Note A: Last digit of power of number has the last number is 2: Form of power: (4n) : last digit: 6 Form of power: (4n+1) : last digit: 2 Form of power: (4n+2) : last digit:4 Form of power: (4n+3) : last digit:8 => last digit of 12^12 is 6 Note B: Last digit of power of number has the last number is 3 Form of power: (4n) : last digit: 1 Form of power: (4n+1) : last digit: 3 Form of power: (4n+2) : last digit:9 Form of power: (4n+3) : last digit:7 => last digit of 13^13 is 3 Note C: Last digit of power of number has the last number is 4 Odd power: 2n+1: last digit 4 Even power: 2n: last digit 6 => last digit of 14^14 is 6 Note D: The last digit of power of number has the last number is 5 always is 5 => last digit of 15^15 is 5 Normally: we will create conclusion about this kind of question like: 6+3 - (last digit of 6*5) = 9 (wrong answer) However, because 14^14x15^15 much greater than (12^12+13^13) so the result must be negative and the last digit is (last digit of 6x5) - (6+3) = 1 The Answer is: B (1)

Algebra
TutorMe
Question:

How many integrals value of x satisfy the inequality (1−x^2)(4−x^2)(9−x^2)>0 ? A 0 B 1 C 3 D 5 E Greater than 5

Hương T.
Answer:

Solution 1: X is an integer so 9-x^2 > 4-x^2 > 1-x^2 (1−x^2)(4−x^2)(9−x^2)>0 ? <=> x^2<1 or 4<x^2<9 <=> x^2 = 0 <=> x = 0 Only 1 value : B Solution 2: Try: X = 0: Result is 36>0 Try: X = 1,2,3 : Result is 0 Try: X = 4 and above: Result is negative Only 1 value: B

Send a message explaining your
needs and Hương will reply soon.
Contact Hương
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.