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A square has a side of length
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12 May 2021, 06:14
12 May 2021, 06:14
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Question Stats:
68% (01:48) correct
32% (02:04) wrong based on 25 sessions
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A square has a side of length š„ + 5 and a diagonal of length š„ + 10.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Quantity A |
Quantity B |
x |
5 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: A square has a side of length
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12 May 2021, 07:52
12 May 2021, 07:52
1
Solution:
We know that, if the side of the square is x then the diagonal will be x\(\sqrt{2}\)
Thus, if the side is x+5 the diagonal will be (x+5)\(\sqrt{2}\)
Therefore,
x+10= (x+5)\(\sqrt{2}\)
=x\(\sqrt{2}\)+5\(\sqrt{2}\)
10-5\(\sqrt{2}\)=x\(\sqrt{2}\)-x
\(\sqrt{2}\)=1.441
10-5(1.141)=x(\(\sqrt{2}\)-1)
10-7.07=x(1.414-1)
2.92=x(0.414)
\(\frac{2.92}{0.414}\)=x
x~7
Qty A> Qty B
IMO A
Hope this helps
We know that, if the side of the square is x then the diagonal will be x\(\sqrt{2}\)
Thus, if the side is x+5 the diagonal will be (x+5)\(\sqrt{2}\)
Therefore,
x+10= (x+5)\(\sqrt{2}\)
=x\(\sqrt{2}\)+5\(\sqrt{2}\)
10-5\(\sqrt{2}\)=x\(\sqrt{2}\)-x
\(\sqrt{2}\)=1.441
10-5(1.141)=x(\(\sqrt{2}\)-1)
10-7.07=x(1.414-1)
2.92=x(0.414)
\(\frac{2.92}{0.414}\)=x
x~7
Qty A> Qty B
IMO A
Hope this helps
Re: A square has a side of length
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12 May 2021, 23:55
12 May 2021, 23:55
since diagonal of this square is x+10
after applying pythagoras theorem
(x+10)^2= (x+5)^2 + (x+5)^2
answer cannot be C as X cannot be 5. ( put the values of X as 5, 15^2 cannot be equal to 2*10^2
Now put X=7 after simplification equation will be 289=288 ( approximately both RHS and LHS will be equal)
hence quantity A will be greater than quantity B
answer A
after applying pythagoras theorem
(x+10)^2= (x+5)^2 + (x+5)^2
answer cannot be C as X cannot be 5. ( put the values of X as 5, 15^2 cannot be equal to 2*10^2
Now put X=7 after simplification equation will be 289=288 ( approximately both RHS and LHS will be equal)
hence quantity A will be greater than quantity B
answer A
