Must Solve Q51 level Question | GMAT 700 level Question | GMAT Number Properties

GMAT Maths Questions | GMAT Number Properties | GMAT 700 level Question | GMAT Data Sufficiency

This GMAT data sufficiency question is a must solve GMAT question. It tests concepts from the topics number properties.

Question:
Is the twelve-digit positive integer a perfect square ?
Statement 1: The number comprises only the digits 0, 1, and 2, each written four times.
Statement 2: The sum of the digits of the twelve-digit number is 12.

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[pranavsood]

you can simply find the digital root of the number i.e. the sum of all digits till you get a single digit number. If the digital root is not 1, 4, 7 or 9 then its not a perfect square. Here, the digital root is 3 in each of the statements, so the answer is D

[mudritsood]

Take any no. 0's 1's and 2's are always repeated 4 times hence every time the sum of digits will be 12. By the divisibility rule of 3 if sum of digits is divisible by 3 then number is divisible by 3. Plus if it is a sq number, all the primes would be in even powers on prime factorizing it. Hence n must be divisible by 3^2 i.e 9. By divisibility rule of 9 stating that the sum of digits must be divisible by 9 we see 12 is not divisible hence the number is not a perfect sq no.

I hope this makes things more clear for you 😊

[NeermalyaDas]

Just 1 doubt - Why did you leave 2 and consider only the prime number 3..??

What if I consider the number to be 120120120012 and Prime number 2 ..?
or maybe I consider the number to be 120120121200 and prime number 5 ..
The numbers are both divisible by (2 and 4) and (5 and 25) respetively..!! But its still not a perfect square...!! :(

Where am I going wrong..??

[mafimalone]

27 is divisible by 3, and 9, but 27 is perfect square ?

[panchakarlaranganadh]

But in an yes no data sufficiency questions we have to try alternatives to get both yes and no. But you simply took a number and did the data sufficiency. But there might be another number which might give an yes for the statements