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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5

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KarunMendiratta
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   29 Aug 2021, 23:13
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5..png
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5.

Quantity A
Quantity B
Number of possible values for PT
10


A. Quantity A is greater
B. Quantity 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 Quant/Math Extreme Challenge Daily (2021) Edition
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D
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motion2020
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   30 Aug 2021, 17:31
Since possible values are within interval defined as 0<PT<14, answer is D
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Sirish123
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   30 Aug 2021, 18:37
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Can you explain the concept of how is the value of PT between 0 to 14 ?
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Re: In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   30 Aug 2021, 18:43
motion2020 wrote:
Since possible values are within interval defined as 0<PT<14, answer is D
KarunMendiratta wrote:
Attachment:
In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5..png

In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5.

Quantity A
Quantity B
Number of possible values for PT
10


A. Quantity A is greater
B. Quantity 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 Quant/Math Extreme Challenge Daily (2021) Edition


motion2020
Hi sir,

Thank you for your solution. Quick question here, if the possible values are between 0 to 14 and since the question doesn't ask for integral values, shouldn't the answer be A (infinitely many values)?

Thanks in advance!
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   30 Aug 2021, 19:16
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Sirish123 wrote:
Can you explain the concept of how is the value of PT between 0 to 14 ?


Hi Sirish123

You can construct 3 triangles PQT, QRT & RST

As we have two sides for triangle RST we start by finding 3rd side (RT) of this triangle

RS = 4, and ST = 5
Let RT be x
Thus, 5-4<x<4+5
1<x<9

Similarly, we can find the third side of QRT
QR=2, RT=Any value between 1-9
Thus, QT= 2-1<y<9+2
QT=1<y<11

Now for triangle PQT,
PQ= 3, QT= 1 to 11
PT= 3-1<PT<11+3=2<PT<14

Thus, PT has values between 2 and 14.

I am a bit confounded as to what the answer is as the question does not state whether the values are integers only, if yes, A=B and if it is any number including decimals A>B as godxyz stated.

KarunMendiratta could you please help here?

Hope this helps!

Regards
S!
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KarunMendiratta
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In pentagon PQRST, PQ= 3, QR = 2, RS = 4, and ST = 5 [#permalink] New post   31 Aug 2021, 00:18
1
Ks1859 wrote:
Sirish123 wrote:
Can you explain the concept of how is the value of PT between 0 to 14 ?


Hi Sirish123

You can construct 3 triangles PQT, QRT & RST

As we have two sides for triangle RST we start by finding 3rd side (RT) of this triangle

RS = 4, and ST = 5
Let RT be x
Thus, 5-4<x<4+5
1<x<9

Similarly, we can find the third side of QRT
QR=2, RT=Any value between 1-9
Thus, QT= 2-1<y<9+2
QT=1<y<11

Now for triangle PQT,
PQ= 3, QT= 1 to 11
PT= 3-1<PT<11+3=2<PT<14

Thus, PT has values between 2 and 14.

I am a bit confounded as to what the answer is as the question does not state whether the values are integers only, if yes, A=B and if it is any number including decimals A>B as godxyz stated.

KarunMendiratta could you please help here?

Hope this helps!

Regards
S!


The answer should be D only.
If we are picking the integers, Col. A < Col. B
If we are including all real numbers between 4 and 14, Col. A > Col. B
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