whole biscuits

[wilson4mba]

At a particular moment, a restaurant has x biscuits and y patron(s), with x > 2 and y > 1. How many values of y are there, such that all the biscuits can be distributed among the patrons, with each patron receiving an equal number of whole biscuits and with no biscuits left over?

(1) x = a^2.b^3, where a and b are different prime numbers.

(2) b = a + 1

[Rahul@gurome]

At a particular moment, a restaurant has x biscuits and y patron(s), with x > 2 and y > 1. How many values of y are there, such that all the biscuits can be distributed among the patrons, with each patron receiving an equal number of whole biscuits and with no biscuits left over?

• (1) x = a^2.b^3, where a and b are different prime numbers.
  (2) b = a + 1

Given: x > 2 and y > 1 and x is completely divisible by y or in other words y is a factor of x.
Thus, we have to find the number of factors of x.

Statement 1: x = a²b³, a and b are different prime numbers.
There are infinite numbers of x of the given form.

Not sufficient.

Statement 2: b = (a + 1)
a and b has no relation with question.

Not sufficient.

1 & 2 Together: x = a²b³, a and b are different prime numbers and b = (a + 1)
Only possible values of a and b are 2 and 3 respectively.
Thus, x = 2²3³ = 4*27 = 108
Now we can easily find the number of factors of x!

Sufficient.

The correct answer is C.

[Curguar]

Statement 1: x = a²b³, a and b are different prime numbers.
There are infinite numbers of x of the given form.

But x = a²b³, does it not mean that x has 12 factors, and thus y can have 11 values (y has to be different than 1)?

In which case, OA would be A?

[diebeatsthegmat]

At a particular moment, a restaurant has x biscuits and y patron(s), with x > 2 and y > 1. How many values of y are there, such that all the biscuits can be distributed among the patrons, with each patron receiving an equal number of whole biscuits and with no biscuits left over?

• (1) x = a^2.b^3, where a and b are different prime numbers.
  (2) b = a + 1

Given: x > 2 and y > 1 and x is completely divisible by y or in other words y is a factor of x.
Thus, we have to find the number of factors of x.

Statement 1: x = a²b³, a and b are different prime numbers.
There are infinite numbers of x of the given form.

Not sufficient.

Statement 2: b = (a + 1)
a and b has no relation with question.

Not sufficient.

1 & 2 Together: x = a²b³, a and b are different prime numbers and b = (a + 1)
Only possible values of a and b are 2 and 3 respectively.
Thus, x = 2²3³ = 4*27 = 108
Now we can easily find the number of factors of x!

Sufficient.

The correct answer is C.

]
first of all i also think the same, and concluded that the answer is C
later, i think if x=108 y might be anu number such as 3,5,6
thus if y=5 , 108:5=21 with the remander 3
can you explain again, please?

[goyalsau]

Statement 1: x = a²b³, a and b are different prime numbers.
There are infinite numbers of x of the given form.

But x = a²b³, does it not mean that x has 12 factors, and thus y can have 11 values (y has to be different than 1)?

In which case, OA would be A?

Even i thought that answer should be A,
What is the OA, Wilson.

[beat_gmat_09]

x = a^2 * b^3
a and b are different prime numbers. Number of factors of x are - (2+1)*(3+1) = 12
This is regardless of prime numbers and what x turns out, number of factors will always be same.
Therefore y can have (12-1) =11 values.
A is sufficient.

[TOPGMAT]

Hi Rahul,
Do we need to know a & b ?
Waiting for your reply

[hitesht]

Can any expert please tell us what the answer might be...