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GMATinsight
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 22 Feb 2020, 07:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

41% (01:13) correct 59% (01:05) wrong based on 178 sessions

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Find units digit of x^3?

(1) x is odd

(2) 10 < x^3 < 30

Source: https://www.GMATinsight.com
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C
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 22 Feb 2020, 08:44
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Find units digit of x^3?

(1) x is odd

(2) 10 < x^3 < 30

Source: https://www.GMATinsight.com

#1
x is odd we get ; 1,7,5,9 for ( 1,3,5,9 )
insufficient
#2
10 < x^3 < 30
x= 3 or 2√2 ; insufficient
from 1 &2 unit digit will be 7 ;
IMO C ; sufficient
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 25 Mar 2020, 03:44
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Find units digit of x^3?

(1) x is odd

(2) 10 < x^3 < 30

Source: https://www.GMATinsight.com

Asked to Find unit digit of x^3.

Given info: No constraints on X. That is X can be any real number

1) odd numbers are \(1,3,5,7\) which gives different unit digits as \(7,5,3,9\) upon cube. Hence insufficient.
2) \(x^3\) can be anything in between \(10 \)and \(30 \). That is \(x^3\) can be \(12, 13, 27\) etc. Note the given range is for \(x^3\) , do not mistake for value after cubing\( x \) Hence insufficient.
1) and 2) we clearly have 27 as the only answer.

Hence C.
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 09 Feb 2025, 05:13
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IMO the answer is E

[hr]
Given Question:
Find the units digit of x3x^3.
[hr]
Statement (1): xx is odd
  • This tells us that xx is an odd number, but it does not specify whether xx is an integer or a fraction.
  • If xx is an odd integer, then possible units digits of x3x^3 could be 1, 3, 5, 7, or 9, depending on the units digit of xx.
  • However, if xx is an odd non-integer (e.g., x=1.5x = 1.5), then x3x^3 is not necessarily an integer, meaning the concept of a "units digit" does not apply.
🔹 Since we cannot uniquely determine the units digit, Statement (1) alone is NOT sufficient.
[hr]
Statement (2): 10<x3<3010 < x^3 < 30
  • This gives a range for x3x^3 but does not specify whether xx is an integer.
  • If xx is an integer, the only possible value is x=3x = 3, since 33=273^3 = 27.
    • The units digit of 2727 is 7.
  • However, if xx is not an integer (e.g., x=2.5x = 2.5), then x3x^3 is not necessarily an integer, and the concept of a units digit may not be meaningful.
🔹 Since xx could be a non-integer, we cannot definitively determine the units digit. So, Statement (2) alone is NOT sufficient.
[hr]
Combining Both Statements
  • From (1): xx is odd (but not necessarily an integer).
  • From (2): 10<x3<3010 < x^3 < 30, meaning x3x^3 is constrained but not necessarily an integer.
  • Even if xx is odd, it could still be a non-integer (e.g., 1.5 or 2.1), in which case the units digit is undefined.
  • Since we still cannot guarantee xx is an integer, we cannot determine the units digit for sure.
🔹 Even together, the statements are NOT sufficient.
[hr]
Final Answer: (E) Statements (1) and (2) together are NOT sufficient. ✅
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 09 Feb 2025, 05:13
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IMO the answer is E

[hr]
Given Question:
Find the units digit of x3x^3.
[hr]
Statement (1): xx is odd
  • This tells us that xx is an odd number, but it does not specify whether xx is an integer or a fraction.
  • If xx is an odd integer, then possible units digits of x3x^3 could be 1, 3, 5, 7, or 9, depending on the units digit of xx.
  • However, if xx is an odd non-integer (e.g., x=1.5x = 1.5), then x3x^3 is not necessarily an integer, meaning the concept of a "units digit" does not apply.
🔹 Since we cannot uniquely determine the units digit, Statement (1) alone is NOT sufficient.
[hr]
Statement (2): 10<x3<3010 < x^3 < 30
  • This gives a range for x3x^3 but does not specify whether xx is an integer.
  • If xx is an integer, the only possible value is x=3x = 3, since 33=273^3 = 27.
    • The units digit of 2727 is 7.
  • However, if xx is not an integer (e.g., x=2.5x = 2.5), then x3x^3 is not necessarily an integer, and the concept of a units digit may not be meaningful.
🔹 Since xx could be a non-integer, we cannot definitively determine the units digit. So, Statement (2) alone is NOT sufficient.
[hr]
Combining Both Statements
  • From (1): xx is odd (but not necessarily an integer).
  • From (2): 10<x3<3010 < x^3 < 30, meaning x3x^3 is constrained but not necessarily an integer.
  • Even if xx is odd, it could still be a non-integer (e.g., 1.5 or 2.1), in which case the units digit is undefined.
  • Since we still cannot guarantee xx is an integer, we cannot determine the units digit for sure.
🔹 Even together, the statements are NOT sufficient.
[hr]
Final Answer: (E) Statements (1) and (2) together are NOT sufficient. ✅
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 09 Feb 2025, 10:51
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I think odd means the number is an integer. By def, odd number isn't divisible by 2. If we consider decimal numbers, then everything will be divisible by 2, for e.g. 10.1/2 = 5.05

So, the answer should be C
Adi2046
IMO the answer is E

[hr]
Given Question:
Find the units digit of x3x^3.
[hr]
Statement (1): xx is odd
  • This tells us that xx is an odd number, but it does not specify whether xx is an integer or a fraction.
  • If xx is an odd integer, then possible units digits of x3x^3 could be 1, 3, 5, 7, or 9, depending on the units digit of xx.
  • However, if xx is an odd non-integer (e.g., x=1.5x = 1.5), then x3x^3 is not necessarily an integer, meaning the concept of a "units digit" does not apply.
🔹 Since we cannot uniquely determine the units digit, Statement (1) alone is NOT sufficient.
[hr]
Statement (2): 10<x3<3010 < x^3 < 30
  • This gives a range for x3x^3 but does not specify whether xx is an integer.
  • If xx is an integer, the only possible value is x=3x = 3, since 33=273^3 = 27.
    • The units digit of 2727 is 7.
  • However, if xx is not an integer (e.g., x=2.5x = 2.5), then x3x^3 is not necessarily an integer, and the concept of a units digit may not be meaningful.
🔹 Since xx could be a non-integer, we cannot definitively determine the units digit. So, Statement (2) alone is NOT sufficient.
[hr]
Combining Both Statements
  • From (1): xx is odd (but not necessarily an integer).
  • From (2): 10<x3<3010 < x^3 < 30, meaning x3x^3 is constrained but not necessarily an integer.
  • Even if xx is odd, it could still be a non-integer (e.g., 1.5 or 2.1), in which case the units digit is undefined.
  • Since we still cannot guarantee xx is an integer, we cannot determine the units digit for sure.
🔹 Even together, the statements are NOT sufficient.
[hr]
Final Answer: (E) Statements (1) and (2) together are NOT sufficient. ✅
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 10 Feb 2025, 05:31
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if we consider that x is an integer by the virtue of definition of odd numbers, then shouldnt the correct option be B? because between 10 and 30 the only value of x^3 where x is an integer is 27.

ManifestDreamMBA
I think odd means the number is an integer. By def, odd number isn't divisible by 2. If we consider decimal numbers, then everything will be divisible by 2, for e.g. 10.1/2 = 5.05

So, the answer should be C
Adi2046
IMO the answer is E

[hr]
Given Question:
Find the units digit of x3x^3.
[hr]
Statement (1): xx is odd
  • This tells us that xx is an odd number, but it does not specify whether xx is an integer or a fraction.
  • If xx is an odd integer, then possible units digits of x3x^3 could be 1, 3, 5, 7, or 9, depending on the units digit of xx.
  • However, if xx is an odd non-integer (e.g., x=1.5x = 1.5), then x3x^3 is not necessarily an integer, meaning the concept of a "units digit" does not apply.
🔹 Since we cannot uniquely determine the units digit, Statement (1) alone is NOT sufficient.
[hr]
Statement (2): 10<x3<3010 < x^3 < 30
  • This gives a range for x3x^3 but does not specify whether xx is an integer.
  • If xx is an integer, the only possible value is x=3x = 3, since 33=273^3 = 27.
    • The units digit of 2727 is 7.
  • However, if xx is not an integer (e.g., x=2.5x = 2.5), then x3x^3 is not necessarily an integer, and the concept of a units digit may not be meaningful.
🔹 Since xx could be a non-integer, we cannot definitively determine the units digit. So, Statement (2) alone is NOT sufficient.
[hr]
Combining Both Statements
  • From (1): xx is odd (but not necessarily an integer).
  • From (2): 10<x3<3010 < x^3 < 30, meaning x3x^3 is constrained but not necessarily an integer.
  • Even if xx is odd, it could still be a non-integer (e.g., 1.5 or 2.1), in which case the units digit is undefined.
  • Since we still cannot guarantee xx is an integer, we cannot determine the units digit for sure.
🔹 Even together, the statements are NOT sufficient.
[hr]
Final Answer: (E) Statements (1) and (2) together are NOT sufficient. ✅
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Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 10 Feb 2025, 05:52
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But B alone doesn't tell us that x is odd. We need to combine it with A to get x^3 = 27 (which is cube of an odd integer)
Priya93harry
if we consider that x is an integer by the virtue of definition of odd numbers, then shouldnt the correct option be B? because between 10 and 30 the only value of x^3 where x is an integer is 27.

ManifestDreamMBA
I think odd means the number is an integer. By def, odd number isn't divisible by 2. If we consider decimal numbers, then everything will be divisible by 2, for e.g. 10.1/2 = 5.05

So, the answer should be C
Adi2046
IMO the answer is E

[hr]
Given Question:
Find the units digit of x3x^3.
[hr]
Statement (1): xx is odd
  • This tells us that xx is an odd number, but it does not specify whether xx is an integer or a fraction.
  • If xx is an odd integer, then possible units digits of x3x^3 could be 1, 3, 5, 7, or 9, depending on the units digit of xx.
  • However, if xx is an odd non-integer (e.g., x=1.5x = 1.5), then x3x^3 is not necessarily an integer, meaning the concept of a "units digit" does not apply.
🔹 Since we cannot uniquely determine the units digit, Statement (1) alone is NOT sufficient.
[hr]
Statement (2): 10<x3<3010 < x^3 < 30
  • This gives a range for x3x^3 but does not specify whether xx is an integer.
  • If xx is an integer, the only possible value is x=3x = 3, since 33=273^3 = 27.
    • The units digit of 2727 is 7.
  • However, if xx is not an integer (e.g., x=2.5x = 2.5), then x3x^3 is not necessarily an integer, and the concept of a units digit may not be meaningful.
🔹 Since xx could be a non-integer, we cannot definitively determine the units digit. So, Statement (2) alone is NOT sufficient.
[hr]
Combining Both Statements
  • From (1): xx is odd (but not necessarily an integer).
  • From (2): 10<x3<3010 < x^3 < 30, meaning x3x^3 is constrained but not necessarily an integer.
  • Even if xx is odd, it could still be a non-integer (e.g., 1.5 or 2.1), in which case the units digit is undefined.
  • Since we still cannot guarantee xx is an integer, we cannot determine the units digit for sure.
🔹 Even together, the statements are NOT sufficient.
[hr]
Final Answer: (E) Statements (1) and (2) together are NOT sufficient. ✅
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