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EgmatQuantExpert
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If P = 177^x * 2487^y, where x and y are positive 28 Mar 2017, 11:07
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65% (hard)

Question Stats:

56% (02:09) correct 44% (02:24) wrong based on 172 sessions

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Q.
If \(P = 177^x * 2487^y\), where \(x\) and \(y\) are positive integers, what is the units digit of \(P\)?

    1. \(y = 7\)
    2. \(2x^2 + 4xy = 18 - 2y^2\)


A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.



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If P = 177^x * 2487^y, where x and y are positive Updated on: 31 Mar 2017, 03:22
Originally posted by EgmatQuantExpert on 28 Mar 2017, 11:07.
Last edited by EgmatQuantExpert on 31 Mar 2017, 03:22, edited 1 time in total.
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The official solution has been posted. Looking forward to a healthy discussion..:)
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If P = 177^x * 2487^y, where x and y are positive 29 Mar 2017, 04:20
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s1: y = 7, it gives the units digit of 2487^y as 3, but P's units digit will vary with 177^x units digit, hence not sufficient, since x is not given
s2: this can simplified as \((\sqrt{2}x+\sqrt{2}y)^2=18\), and since x and y are positive, then x+y = 3, so x can be 1 or 2, hence the units digit of P will be 3 (i.e., 177^2x2487^1 or 177^1x2487^2)
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If P = 177^x * 2487^y, where x and y are positive 31 Mar 2017, 03:22
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Solution



Steps 1 & 2: Understand Question and Draw Inferences

We are given that:
    • \(P = 177^x * 2487^y\)
    • And we are asked to find the units digit of \(P\)
    • To find the units digit of \(P\), we need to focus on the rightmost digit of \(P\), which is its units digit.
      o So \(P = 177^x * 2487^y\)
      o Units digit of \(P\) = Units digits of (\(7^x * 7^y\))
      o Units digit of \(P\) = Units digits of \(7^{(x+y)}\)
    • Thus, we can conclude that if we can find the \(x+y\) or the individual value of x and y, we can find the units digit of P.
    • Now let us analyse each of the statements.

Step 3: Analyze Statement 1 independently

    • Statement 1 states that \(y = 7\)
    • From the first statement we get the value of only \(y\) and NOT \(x\).
    • Hence statement 1 is not sufficicent to answer the question.


Step 4: Analyze Statement 2 independently

    • Statement 2 states that \(2x^2 + 4xy = 18 - 2y^2\)
    • After simplifying we get,
      o \(x^2 + 2xy +y^2 = 9\)
      o \((x+y)^2 = 9\)
      o Since \(x\) and \(y\) are both positive, \(x+y\) will also be positive.
      o Hence, \((x+y) = 3\).
    • Now that we have the value of \(x+y\), we can find the untis digit of \(P\).
    • Hence statement 2 is sufficient to answer the question.
    • And the correct answer is Option B.



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If P = 177^x * 2487^y, where x and y are positive 31 Mar 2017, 03:26
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krishna19
s1: y = 7, it gives the units digit of 2487^y as 3, but P's units digit will vary with 177^x units digit, hence not sufficient, since x is not given
s2: this can simplified as \((\sqrt{2}x+\sqrt{2}y)^2=18\), and since x and y are positive, then x+y = 3, so x can be 1 or 2, hence the units digit of P will be 3 (i.e., 177^2x2487^1 or 177^1x2487^2)
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Hey Krishna,

Finding the individual value of x and y was not necessary, so no need to take x =1 and y = 2 or vice versa. Just apply exponents and write it directly as \(7^{(x+y)}\) and since we have the value of x+y, we can get our answer from the second statement. :)


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If P = 177^x * 2487^y, where x and y are positive 18 May 2024, 12:11
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EgmatQuantExpert

Solution



Steps 1 & 2: Understand Question and Draw Inferences

We are given that:
    • \(P = 177^x * 2487^y\)
    • And we are asked to find the units digit of \(P\)
    • To find the units digit of \(P\), we need to focus on the rightmost digit of \(P\), which is its units digit.
      o So \(P = 177^x * 2487^y\)
      o Units digit of \(P\) = Units digits of (\(7^x * 7^y\))
      o Units digit of \(P\) = Units digits of \(7^{(x+y)}\)
    • Thus, we can conclude that if we can find the \(x+y\) or the individual value of x and y, we can find the units digit of P.
    • Now let us analyse each of the statements.

Step 3: Analyze Statement 1 independently

    • Statement 1 states that \(y = 7\)
    • From the first statement we get the value of only \(y\) and NOT \(x\).
    • Hence statement 1 is not sufficicent to answer the question.


Step 4: Analyze Statement 2 independently

    • Statement 2 states that \(2x^2 + 4xy = 18 - 2y^2\)
    • After simplifying we get,
      o \(x^2 + 2xy +y^2 = 9\)
      o \((x+y)^2 = 9\)
      o Since \(x\) and \(y\) are both positive, \(x+y\) will also be positive.
      o Hence, \((x+y) = 3\).
    • Now that we have the value of \(x+y\), we can find the untis digit of \(P\).
    • Hence statement 2 is sufficient to answer the question.
    • And the correct answer is Option B.



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In GMAT the DS statements should never contradict each other

According to statement 1 \(: y =7 \)
According to statement 2: \(x+y = 3\)

Using 1 and 2 :

\(x=-4 \)

This contradicts the question which says \(x\) and \(y\) are positive integers.

Perhaps if \(y\) were \(1\) or \(2\) question would not violate its own conditions! 

Hence I believe his question needs some introspection. Kindly let me know if I missed anything. Thank you.
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