Given y = 1422960 * x . Which of the following is the value of x

Question

Given y = 1422960 * x . Which of the following is the value of x so that y is a perfect square?

A. 11
B. 13
C. 15
D. 17
E. 19

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

rosyln · Answer

C is the correct answer  (15).
1. 1,422,960 = 2^4 * 3^3 * 5 * 7^2 * 13
2.  For y to be a perfect square, all prime factors must have even powers.  In the factorization:
2^4 has an even power, so it's fine;
3^3 has an odd power;
5 has an odd power;
7^2 has an even power, so it's fine;
13 has an odd power.
3. To make all exponents even, x must include: 3 to balance 3^3; 5 to balance 5; and 13 to balance 13. Therefore: x = 3 * 5 * 13 = 195.
4. Substitute x = 195 back into y:
y = 1,422,960 * 195 = (2^4 * 3^3 * 5 * 7^2 * 13) * (3 * 5 * 13). Combine powers: y = 2^4 * 3^4 * 5^2 * 7^2 * 13^2. All powers are even, so y is a perfect square.

BHARGAVIMOGADALA · Answer

y=1422960 * x
Let’s first break the number 1422960 into the product of its prime factors.
1422960 =  2^{4} * 3^{1} * 5^{1} * 7^{2} * 11^{2}

To make any number a perfect square, all the powers of its prime factors must be even.
Here, the powers of 3 & 5 are odd. To make them even we need to multiply them by 3 and 5, respectively. 
Therefore x = 3*5 = 15 will make “y” a perfect square. The answer is  C (15) .

prantorboni · Answer

y=   1422960    * x

LMC of 1422960 is, 2*2*2*2*3*5*7*7*11*11

Clearly, value of x= 3*5=15, would make it a perfect square.

Answer: C.

Leo1507 · Answer

Hi 
What about :
60*11 = 660
60*13 = 780 
60*15 = 900
60*17 = 1020
60*19 = 1140

Only 900 is a perfect square (30*30) so C must be the right answer here?

Dbrunik · Answer

i simply cannot wrap my head around how to prime factorize these quickly, without a calculator.

ADisHere · Answer

Hi,
It is easy, but before that you need to practise a lot (it will come naturally)

just know the divisibility rules very well

if it ends in 0 ( you know it will have 5 and 2)

similarly keep on checking with 2,5 (which are easier to spot)

check with 3,11 ( you can add alternate number and check will save time)

try other primes as well like 7 ( which is rarely seen)

Hope this helps!

Dbrunik · Answer

i think where im getting stuck is with the 3s, and 11s,

i get that if you have 1422960 you can just do 2s and 5s right away

5s
 200,000 +80,000+4000+400+180+12 = 284,592

i have to break it out to see it, i cant do it any other way. how can i build up?

then i have 284,592 which sums to 30, so i know its divisible by 3.

heres where i dont know where to start. trial and error is way too time consuming. can you help break it down ?

AbhinayaGMAT30 · Answer

Lets start with n = 1422960

we start checking the divisibility of the number n with the prime numbers. We start with the smallest prime number 2 and then move to higher prime numbers sequentially i.e.3,5,7,11,13,17 etc.

Divisibility rule by 2  - If the number is even, it is divisible by 2.

After division by 2
n = 2 * 711480
Again after division by 2
n = 2*2*355740
Again after division by 2
n = 2*2*2*177870
Again after division by 2
n = 2*2*2*2*88935

Now, 88935 is not divisible by 2 as it is odd. Now, we need to check the divisibility by 3 i.e. the next prime number. But before checking that, we see that the number is clearly divisible by 5 because the last digit of 88935 is 5. Hence, we first divide 88935 by 5.

After division by 5 
n = 2*2*2*2*5*17787

Now, 17787 is not further divisible by 5. Now, we will check the divisibility by 3 as we left it earlier.

Divisibility Rule by 3 = Sum of the digits of the number is divisible by 3.

After division by 3,
n = 2*2*2*2*5*3*5929

Now, 5929 is not further divisible by 3 as the sum of digits of 5929 (5+9+2+9 = 25) is not divisible by 3. Hence, we check the divisibility by the next higher prime number i.e. 7

Divisibility Rule by 7  = Form an alternating combinations of 3 digits from right to left and the subtract the sum of even combinations from sum of odd combinations. If the result is divisible by 7, the original number is divisible by 7.

Ex- lets check the divisibility of  1369851 by 7. After forming an alternating combinations of 3 digits from right to left, we get 1,369,851. Now, subtracting the sum of even combinations from sum of odd combinations, we get 851 + 1 - 369 = 483. Since, 483 is divisible by 7, the original number is divisible by 7.

Now, take the number 5,929 
 To check its divisibility by 7, we take 929-5 = 924, which is divisible by 7.

After division by 7,
n = 2*2*2*2*5*3*7*847 
 Again after division by 7,
n = 2*2*2*2*5*3*7*7*121

Now, we check the divisibility of n by next higher prime number i.e. 11 (we have already checked divisibility by 2,3 and 7). Clearly 121 is divisible by 11.

n = 2*2*2*2*5*3*7*7*11*11

Further, you can learn the divisibility rule for division by 11 and 13. You do not need to go further than that in most cases.

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.

Given y = 1422960 * x . Which of the following is the value of x

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 Problem Solving (PS) Questions

Given y = 1422960 * x . Which of the following is the value of x

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