Data Sufficiency (DS) | If P = 177^x * 2487^y, where x and y are positive

Solution

•\( P = 177^x *2487^y\)
• 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 unitsdigit.

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 andy , we can find the units digit ofP .
• Now let us analyse each of thestatements.

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

• Statement 2 states that\( 2x^2 + 4xy = 18 -2y^2\)
• After simplifying weget,

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
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Statistics : Posted by stne • on 28 Mar 2017, 11:07 • Replies 5 • Views 1947

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