GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the 7-inch square above, another square is inscribed. Wha
[#permalink]
06 Oct 2018, 15:15
06 Oct 2018, 15:15
Expert Reply
2
Bookmarks
00:00
Question Stats:
67% (01:11) correct
32% (01:27) wrong based on 55 sessions
Hide Show timer Statistics
Attachment:
Capture.JPG [ 15.52 KiB | Viewed 6180 times ]
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?
(A) \(\frac{3}{12}\)
(B) \(\frac{24}{49}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{25}{49}\)
(E) \(\frac{7}{12}\)
Re: In the 7-inch square above, another square is inscribed. Wha
[#permalink]
15 Nov 2018, 00:48
15 Nov 2018, 00:48
1
This problem seems more intuitive to me, so I'll do my best to explain it.
The problem starts off by saying that this is a 7-inch square and we need to find the fraction that is shaded. Since this is implying area without saying it, we can multiply both sides to get a total area of 49 for the big square.
To get the smaller square, it is a little harder for me to explain. In the sides, we see that there is a 3 and 4. Because a square is even on all the sides, you can put a 4 at the top bordering the 3 or a 3 on the bottom bordering the 4. From here we realize that both sides are now 3 and 4, which fit into Pythagorean's Theorem of a 3,4,5 area triangle. The hypotenuse of 5, would be a side of the inner triangle. This is important because we can now find the inner square.
If the inner square is 5-inches, it means it covers a total of 25 square inches.
From the original 7-inch square, we see that it is 49 inches. So, 49-25 = 24 inches left unshaded, out of the 49 possible, hence the fraction \frac{24}{49}.
B is your answer.
The problem starts off by saying that this is a 7-inch square and we need to find the fraction that is shaded. Since this is implying area without saying it, we can multiply both sides to get a total area of 49 for the big square.
To get the smaller square, it is a little harder for me to explain. In the sides, we see that there is a 3 and 4. Because a square is even on all the sides, you can put a 4 at the top bordering the 3 or a 3 on the bottom bordering the 4. From here we realize that both sides are now 3 and 4, which fit into Pythagorean's Theorem of a 3,4,5 area triangle. The hypotenuse of 5, would be a side of the inner triangle. This is important because we can now find the inner square.
If the inner square is 5-inches, it means it covers a total of 25 square inches.
From the original 7-inch square, we see that it is 49 inches. So, 49-25 = 24 inches left unshaded, out of the 49 possible, hence the fraction \frac{24}{49}.
B is your answer.
Manager
Joined: 07 Aug 2016
Posts: 59
Given Kudos: 0
GRE 1: Q166 V156
Re: In the 7-inch square above, another square is inscribed. Wha
[#permalink]
19 Nov 2018, 17:39
19 Nov 2018, 17:39
1
This can be solved in two ways.
First noticing that the small square will be part of pythagorean theorem where x^2 = 4^2 + 3^2 = 25 so the side of this square is 5 and the area would be 25.
The total area of the larger square is (4+3)^2 = 49
We subtract the smaller square from the larger 49-25 = 24
So it would be 24/49.
The other way is to notice that there are 4 triangles with base and height 4 and 3. So it would be 4*3 *1/2 = 6.
Since we have 4 triangles it then becomes 4 * 6 = 24/49
First noticing that the small square will be part of pythagorean theorem where x^2 = 4^2 + 3^2 = 25 so the side of this square is 5 and the area would be 25.
The total area of the larger square is (4+3)^2 = 49
We subtract the smaller square from the larger 49-25 = 24
So it would be 24/49.
The other way is to notice that there are 4 triangles with base and height 4 and 3. So it would be 4*3 *1/2 = 6.
Since we have 4 triangles it then becomes 4 * 6 = 24/49
