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# If y is a positive integer, what is the units digit of y?

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Senior Manager
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If y is a positive integer, what is the units digit of y?  [#permalink]

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30 Sep 2017, 20:03
4
6
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:16) correct 38% (01:26) wrong based on 154 sessions

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If y is a positive integer, what is the units digit of y?

(1) The units digit of y^2 = 6
(2) The units digit of (y+1)^2 = 5
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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30 Sep 2017, 20:08
1
B
St1 says it can be 4/6. Not sufficient
St2 says y is definitely 4. Hence option B

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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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07 Feb 2019, 23:19
1
csaluja wrote:
If y is a positive integer, what is the units digit of y?

(1) The units digit of y^2 = 6
(2) The units digit of (y+1)^2 = 5

Keyword: y is a positive integer

from 1, we can get 2 values 4 and 6

from 2, we get only one value i.e = 4
Sufficient
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If y is a positive integer, what is the units digit of y?  [#permalink]

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Updated on: 19 Jun 2019, 07:15
I have doubt for statement 2. The question stem says y=integer, and you have to find y's units digit, and the statement 2 says units digit of (y+1)^2 =5. Now what I found is y could be 4,14,24,34.....etc to get the units digit of 5. Also, nowhere in the question it is mentioned anything about the number of digits. So shouldn't this statement be insufficient? And overall the answer should be E? Bunuel pls help.
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Originally posted by EncounterGMAT on 19 Jun 2019, 07:06.
Last edited by EncounterGMAT on 19 Jun 2019, 07:15, edited 2 times in total.
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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19 Jun 2019, 07:11
1
2
EncounterGMAT wrote:
I have doubt for statement 2. The question stem says y=integer, and you have to find y's units digit, and the statement 2 says units digit of (y+1)^2 =5. Now what I found is y could be 4,14,24,34.....etc to get the units digit of 5. Also, nowhere in the question it is mentioned anything about the number of digits. So shouldn't this statement be insufficient? And overall the answer should be E? chetan2u Bunuel experts pls help.

Notice that the question does not ask to find the value of y: If y is a positive integer, what is the units digit of y? From (2) we can find that the units digit is 4.
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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19 Jun 2019, 07:17
Bunuel wrote:
EncounterGMAT wrote:
I have doubt for statement 2. The question stem says y=integer, and you have to find y's units digit, and the statement 2 says units digit of (y+1)^2 =5. Now what I found is y could be 4,14,24,34.....etc to get the units digit of 5. Also, nowhere in the question it is mentioned anything about the number of digits. So shouldn't this statement be insufficient? And overall the answer should be E? chetan2u Bunuel experts pls help.

Notice that the question does not ask to find the value of y: If y is a positive integer, what is the units digit of y? From (2) we can find that the units digit is 4.

Thank you Bunuel for pointing out my mistake!
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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19 Jun 2019, 08:03
B is correct
A. says it can be 4^ 2 = 16 & 6^2 = 36. Now 2 options are there 4 or 6 , so Not sufficient
B. says y is definitely 4. (4 + 1)^2 = 25 Hence option B
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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19 Jun 2019, 11:49
JS1290 wrote:
If y is a positive integer, what is the units digit of y?

(1) The units digit of y^2 = 6
(2) The units digit of (y+1)^2 = 5

#1
y=4 or 6 insufficieint
#2
y=4 only possible
IMO B
sufficient
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Re: If y is a positive integer, what is the units digit of y?  [#permalink]

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19 Jun 2019, 20:10
EncounterGMAT wrote:
I have doubt for statement 2. The question stem says y=integer, and you have to find y's units digit, and the statement 2 says units digit of (y+1)^2 =5. Now what I found is y could be 4,14,24,34.....etc to get the units digit of 5. Also, nowhere in the question it is mentioned anything about the number of digits. So shouldn't this statement be insufficient? And overall the answer should be E? Bunuel pls help.

Whenever we are looking at units digit, we should remember the cyclicity rules.
And these rules can be applied in various ways.
For example here, had it been something else other than 5 and 0, ans would be insufficient..
When positive numbers are squared..say z^2
1 can be the units digit when z is 1 or 9
2, 3, 7, 8 will never be a digit.. where does this help you.. if you are looking large numbers and you have to choose perfect square in the options. You can straightforward discard choices with these units digit.
4 can come from 2 and 8
0 and 5 can come only when the digits are 0 and 5 respectively
6 can come from 4 and 6
9 can come from 3 and 7
Thus, statement II would be sufficient only when the units digit shown was 0 and 5.

There are various ways in which the property of units digit can be tested on GMAT.
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Re: If y is a positive integer, what is the units digit of y?   [#permalink] 19 Jun 2019, 20:10
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