The 2-digit positive integer x has the property that it is divisible

Question

The 2-digit positive integer x has the property that it is divisible by its units digit. What is x?

(1) x^3 has a units digit of 7

(2) x + 1 is also divisible by its units digit.

doomedcat · Answer

Stat 1) Cyclic power of 3 and 7 will have 7 as a unit digit

Any two digit number of the form  A3^3  has unit digit 7 and  A7^1  will have unit digit 7

Now for the given condition that The 2-digit positive integer x has the property that it is divisible by its units digit we can multiple values of X satisfying statement 1
for eg 33 , 63, 93, 77 ; Multiple values of X hence  Not suff

Stat 2) X+1 is also divisible by its unit digit
here we can also have multiple values of X for eg 
X = 32 , 63
X+1 = 33, 64
hence  NOt Suff

Together

We can have only one value ie 63 that satisfies both condition hence Suff Ans C

anuj04 · Answer

From 1: Since X^3 has a unit digit 7, therefore, unit digit of x must be 3.
Now two digit numbers, which are divisible to its own unit digit are 33,63 & 93 - Since Multiple answer, therefore  not sufficient

From 2: if x=11 then x+1=12, all of these are divisible by it's unit digit. Similarly, (21,22), (31,32)......- Multiple answer-  Not Sufficient

Combining 1 & 2, we have only 63, which satisfy both.

Hence, C is the answer.

mrinalsharma1990 · Answer

Hi,

I have understand why and how a & b independently are not sufficient but can't seem to understand how both of them together are sufficient. i.e. how does 63 satisfy both the equations. 
63+1=64 which is not divisible by 3 the units digit of 63.
Please let me know.

Avinash_R1 · Answer

it is not about 64/3, instead it is 64/4

anuj04 · Answer

mrinalsharma1990 
It's not 63 rather 63+1=64 is divisible by 4.

Hope it helps!

TehminaIlyas · Answer

How we got number 33, 63, 93 and 77?

Sent from my RNE-L21 using  GMAT Club Forum mobile app

chetan2u · Answer

X is div by its units digit..

For some info on property
 a) All numbers finishing with 1 for example.. 11,21,..91
b) All numbers finishing with 2 for example.. 22,32..92
c) Numbers with units digit 3 and tens digit multiple of 3.. 33,63,93
d) Numbers with units digit 4 and even digit in tens... 24,44,64,84
e) All numbers ending with 5... 15,25,...95
f) Numbers with units digit 6 and multiple of 3 in tens digit..36,66,96
g) Numbers ending with 8 and even non multiple of 4 in tens digit... 24,64
h) Numbers ending with 9 and multiple of 9 in tens..99
 
 1) x^3 has a units digit of 7.. 
Only 3 fits in as per cyclicity..
So X has units digit 3, but all numbers 33,63,93 as shown above fit in..
Insufficient

2) X+1 is also div by its units digit. 
As can be seen all numbers ending with 1 will become even and div by 2, the new units digit.
Also 63to 64..
Insufficient

Combined ..
Statement I tells those ending with 3 and statement II says out of these only 63 fits in..
Sufficient

C

ruchik · Answer

The 2-digit positive integer x has the property that it is divisible by its units digit. What is x?

(1) x^3 has a units digit of 5

(2) x+1 is also divisible by its units digit.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
 Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
 EACH statement ALONE is sufficient to answer the question asked
 Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

ruchik · Answer

Statement 1 suggests that X^3 has unit digit of 5. Hence we know the unit digit of number is 5. as only 5^3 will have the number 5 as unit digit.
So the possible two digit number can be 15,25,35,45,55,65,75,85,95.
statement 1 is not sufficient.

Statement 2 says x+1 is divisible by its own unit digit.
We can have number pairs of X and X+1 as 11 and 12, 21 and 22, 31 and 32.
So clearly not sufficient.

Statement 1 and statement 2 combined will leave us with two numbers 35,65 both have x+1 divisible by it unit digit.
Hence not sufficient.

So answer is E.

Please give kudos if you like the explanation.

Bunuel · Answer

_______________
Merging topics.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The 2-digit positive integer x has the property that it is divisible

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The 2-digit positive integer x has the property that it is divisible

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards