GMAT Questions Chat Group

Okay so in the last step when we get -1 - y, we’ve got to again substitute y as a negative number?

Whenever the root will open because x and y are negative the value will be -x and -y for roots of squares instead of x and y. Which will give y-1.

I too did it opposite way first and got C.

This what am saying if you can understand my handwriting.

has anyone taken gmatpoint free quant section test?

i found a little too difficult compared to official mocks

Can someone tell me

That how can we write (32)^k is equal to 3m+1 when k is even

(32)^k = 3m+2 when k is odd

If y is a negative number, -(y) is a positive number, which means that -(y)*|y| is a positive number, so I don’t get your point

Yes [-(y)*|y|] is a positive number. But when you open square root the concept is that the value can either be positive or negative. But question specifically says that the value is negative. So we taking root of above equation as negative.

Substitute k as 1 and 2.

m should always be divisible by 3.

Is someone able to explain this?

26

Sum of n consecutive integers is n/2(n+2a-1)=75 where a is the first number in the sum
=> n^2 + (2a-1)n - 150

Here product of roots is -150 means one is negative one is positive.
Possible values are (2,75),(3,50),(5,30),(6,25),(10,15) with either number of the two being negative.

Sum of roots is -(2a-1) = 1-2a
Since a>1 this sum is negative means of the two roots the bigger one is negative.

So sum of possible roots is 2+3+5+6+10=26

Because n>1

If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

A. 1
B. 6
C. 7
D. 30
E. 36

Can someone explain this

How to solve this question

by using Prime Factorization we get 6^6 is (2*3)^6 which is 2^6*3^6.
Now given the numbers x, 4^3 (could also be written as 2^6) and 6^5 we know that we need atleast one 3^6 in place of X so that LCM can be 6^6.
Thus X should be 3^6. It can also have a multiple of 2 upto power 6 and still the LCM would remain same.
Thus 1+6=7 values are possible

What do you mean by it can also have a multiple of 2 up to power 6?

Something like
1) 3^6*2
2) 3^6*2^2 and so on.. till 3^6*2^6 without affecting LCM .

Why would we do only till 2^6?

]after that if we consider 2^7 then that would change my LCM which is given as 2^6*3^6 which technically is not possible

Let's re-write each of the given numbers as their prime factors:
4^3 can be written as 2^6
6^5 can be written as 2^5*3^5
6^6 can be written as 2^6*3^6

LCM of any set of numbers is the multiplication of the highest power of all prime factors of all the numbers. So, if we were taking the LCM of only 4^3 and 6^5, the LCM would have been 2^6*3^5.
But, we know that the LCM of all three numbers, x, 4^3 and 6^5, is 6^6. So we can conclude that x must contain the highest power of 3 amongst the three numbers i.e., 3^6.
Now, x can either be just 3^6 or it can also be 3^6*2 or 3^6*2^2 and so on upto 3^6*2^6 without affecting the LCM.
Thus x can take 7 values.

Hope this helps!

Let's assume the length of the original wooden block is 6x (because the ratio of the lengths of the three pieces is 1:2:3, which sums up to 6).
Let's assume the price per unit length of the wooden log is p. So, the price of the original wooden block will be 6px.
We know that the three pieces have lengths x, 2x, and 3x. So, their prices will be px, 2px, and 3px respectively.
The total price of the three pieces will be px + 2px + 3px = 6px.
Given that the total price increased by Rs. 30 when the block was chopped, we get 6px + 30 = 6px
This equation is not valid, which means our assumption about the linear relationship must be missing some constant.

Let's assume the price of a wooden log of length L is given by pL + c, where c is a constant.
Thus, the price of the original log = 6px + c and the price of the smallest new log = px + c
According to the problem, 6px + c = px + c + 45. From this, we get 5px = 45 or px = 9.
Given that the total price increased by Rs. 30 when the block was chopped, we have 6px + 3c = 6px + c + 30 => c = 15.

The price of the largest new log is 3px + 15 = 3*9+15 = 42

This challenge in this question is to remember that a linear relationship doesn't always mean a directly proportional relationship of the form y=kx but could also have a constant added i.e., y=kx+c

Can someone solve this

Please

Find the remainder when 36^55^41 is divided by 55