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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
What is the square root of 239,121?  [#permalink]

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6 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:05) correct 26% (01:17) wrong based on 378 sessions

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What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

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Posts: 2
GMAT 1: 720 Q48 V41 GPA: 3.65
Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

According to divisibility rules, 239,121 is divisible by 9.

2+3+9+1+2+1=18

This means, that the answer choice must be divisible by 3

A) 4+7+6= 17 NO
B) 4+8+9= 21 YES
C) 4+9+7= 20 NO
D) 5+1+1= 7 NO
E) 5+2+4= 11 NO

B is the only answer that can work.
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Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

A, C and E out as the square of its last digit 6,7 and 4 is 6, 9 and 6 respectively.

$$500^2$$=250,000
So the square will be less than 500. So D is out as 511>500

B is the only possible answer.
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Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

I only looked at the last digit of 239121
only the last digits of B and D when squared will result in a 1 for the last digit.
500 squared is 250000 so D is out

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Re: What is the square root of 239,121?  [#permalink]

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1
1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.
2) B = 489^2 and D = 511^2
B = (500-11)^2 and D = (500 + 11)^2

Since we need the answer less than 250000 => D is out.
Thus we have B as the ans.
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What is the square root of 239,121?  [#permalink]

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Square root of$$\,\,\,\,239,121$$

Finding Last digit:
if unit's digit of Square is 1,
then possible unit's digit of Square Root is either 1 or 9

Finding First Digit:
Split the Square into groups of TWO digits from RIGHT TO LEFT
(if the extreme left group has only one number then it's also a group)
$$23\,\,91\,\,21$$
$$perfect\,square\,\leq\,first\,group$$
$$4^2\,\leq\,23$$

So answer should have $$4$$ as the first digit and $$1\,or\,9$$ as the last digit

Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: What is the square root of 239,121?  [#permalink]

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2
2
Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

The square root of 239,121 represents the number that, squared, will give you 239,121. With a calculator this problem is plug-and-play, and at most it will take 45 seconds to try all five combinations and see which answer is correct. Without a calculator to do all the heavy lifting, we have to get a little smarter.

The brute force approach will still work. Simply multiply 476 by 476 and find the product. If it is not 239,121, we rinse and repeat for all five numbers. This technique does work, but it will take a significant amount of time as it ignores the hints the exam is giving you to solve the question quickly.

A great concept to utilize here is the idea of the unit digit. If I multiply any two numbers, the unit digit will simply be the product of the unit digits of the two numbers. This is because there is no carry over from other positions possible. Hence, here we need a number that gives a unit digit of 1 when we multiply it by itself. Going through each option, we can eliminate A (6×6), C (7×7) and E (4×4). This should make a lot of intuitive sense because any even number multiplied by itself will give you another even number, so answers A and E were never in the running. Answer choice C could have worked, but 7×7 must yield a unit digit of 9, so it cannot possibly work.

Only two answer choices remain: 489 and 511. Unfortunately, they both give unit digits of 1, so we need a different strategy to determine which answer is correct. This is where the concept of order of magnitude can save us the trouble of actually having to calculate the numbers. It’s worth noting that at this point multiplying one of the numbers will either give the correct answer or the incorrect answer. Either option solves the question, and is a legitimate way of getting the correct answer. However, knowing that 5 x 5 gives 25 means that 500 x 500 must give 25 followed by four 0’s, or 250,000. Since our number is a little below that, we know the answer must be smaller than 500, but not by very much. Answer choice D is thus too big to be the correct answer, and answer choice B must be correct.

There are many questions like this one that can be solved without having to do any math whatsoever, simply by knowing how to apply mathematical properties. This is what makes the GMAT tricky. The questions will not ask for very difficult math to be executed, but figuring out the correct way to get the correct answer is never a question of blindly attacking the problem with a brute force approach. This is why there is a timing component on the GMAT: To avoid reliance on brute forcing the answer (also to allow multiple tests to be scheduled in the same day). Focusing your study approach on the how, rather than the what, will help you maximize your score.

An apropos comparison is to think of the GMAT as an industrial strength lock. If you try to force your way in, the resistance will be significant. However if you know the combination to the lock, it will open easily. The key (pun intended) is to ascertain how to approach each question and work on the skillful approach instead of the forceful approach. Best of all, inside the safe is a ticket to the business school of your choice. Your job is to find the best way inside the safe. The lock mechanism is designed to keep you out, but like a password that is just “password”, it only appears difficult until you crack the safe.
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What is the square root of 239,121?  [#permalink]

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guess I missed something! sorry don't follow this method! lol

Originally posted by GMATDemiGod on 05 Nov 2015, 22:54.
Last edited by GMATDemiGod on 05 Nov 2015, 23:58, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: What is the square root of 239,121?  [#permalink]

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GMATDemiGod wrote:
10 second approach i used,

look at last digit = 1, we know one of the answers is the square root, so, 9*9 will have a 1's digit. Select, move on and save time.

That's of enough. 511^2 also gives the units digit of 1.
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Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

All of the answers are around 500. Since this is an easy number to square, checking it first (500 x 500 = 250,000) reveals that the correct answer must be less than 500. Thus, we can eliminate D and E right off the bat. Next, since the units digit of the product is 1, we need to determine which numbers give us a units digit of 1 when squaring. Only 1 and 9 do - so, the correct answer must be B.
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Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:
What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

When calculating the square root of 239,121, we must remember that we are looking for a number such that when it’s multiplied by itself (or squared) it produces a units digit of 1 (since 239,121 has a units digit of 1).

Of our answer choices, the only two numbers that will produce a units digit of 1, when squared, are 489 and 511.

However, because 500^2 = 250,000, we see that 511^2 > 250,000, whereas 489^2 < 250,000. Thus, the square root of 239,121 must equal 489.

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Re: What is the square root of 239,121?  [#permalink]

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Square of 500 = 250000 which is more than 239121 , hence option D & E are incorrect.
out of options A,B and C - Only option B has 9 as units digits hence ensuring that a square of the same will end in 1 - leaves us with B as the only answer option !
Time taken : 15 seconds.
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Re: What is the square root of 239,121?  [#permalink]

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Bunuel wrote:

What is the square root of 239,121?

(A) 476
(B) 489
(C) 497
(D) 511
(E) 524

Kudos for a correct solution.

Since the unit digit is 1, therefore the square root of 239,121 must have either 9 or 1.

Now, we can eliminate options A, C and E. Of the remaining, B and D, options the nearest number is 500, whose square in 2500. Since our number in question stem is less than 2500. Therefore option B is the answer.

Please comment whether my reasoning is correct and whether my grammar is fine too .

Thanks Re: What is the square root of 239,121?   [#permalink] 02 Oct 2018, 23:52
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