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13 Dec 2015, 05:31
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:17) correct
37%
(01:04)
wrong
based on 309
sessions
History
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If z is an integer, what is the units digit of z^3?
(1) z is a multiple of 5.
(2) \(\sqrt{z}\) is an integer.
(1) z is a multiple of 5.
(2) \(\sqrt{z}\) is an integer.
23 Jun 2017, 08:16
Kudos
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If z is an integer, what is the units' digit of \(z^3\)?
(1) z is a multiple of 5. The units digit of a multiple of 5 can be 0 or 5, so the units digit of z^3 could be 0 or 5 as well. Not sufficient.
(2) \(\sqrt{z}\) is an integer --> z = integer^2. Clearly insufficient.
(1)+(2) The units digit of z^3 could still be 0 or 5. For example, consider z = 25 and z = 0. Not sufficient.
Answer: E.
(1) z is a multiple of 5. The units digit of a multiple of 5 can be 0 or 5, so the units digit of z^3 could be 0 or 5 as well. Not sufficient.
(2) \(\sqrt{z}\) is an integer --> z = integer^2. Clearly insufficient.
(1)+(2) The units digit of z^3 could still be 0 or 5. For example, consider z = 25 and z = 0. Not sufficient.
Answer: E.
General Discussion
14 Dec 2015, 06:27
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Bunuel
Solution:
Statement 1) z is a multiple of 5.
if z=5 , then units digit of z^3 is 5.
if z=10 , then units digit of z^3 is 0.
Hence Insufficient.
Statement 2) \(\sqrt{z}\) is an integer.
z is an integer then z must be perfect square.
z=4,9,25,or 36... then units digit z^3 is different for different numbers.
Hence Insufficient.
Statement 1) and Statement 2) Together.
z can be 25 or 100 which are perfect squares and are multiples of 5.
units digit of 25^3 and 100^3 is different.
Hence Insufficient.
Ans E.
