Find units digit of x^3? (1) x is odd (2) 10

Question

Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30 Source: https://www.GMATinsight.com

Archit3110 · Answer

#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

NeverEverGiveUp11 · Answer

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.

Adi2046 · Answer

IMO the answer is E

Given Question: 
Find the  units digit  of x3x^3.
 
 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. 
 
 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. 
 
 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. 
 
 Final Answer: (E) Statements (1) and (2) together are NOT sufficient.  ✅

Adi2046 · Answer

IMO the answer is E

Given Question: 
Find the  units digit  of x3x^3.
 
 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. 
 
 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. 
 
 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. 
 
 Final Answer: (E) Statements (1) and (2) together are NOT sufficient.  ✅

ManifestDreamMBA · Answer

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

Priya93harry · Answer

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 · Answer

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)

Find units digit of x^3? (1) x is odd (2) 10 < x^3 < 30

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