If n is an integer and 100 < n <200, what is the value of n?

"\(n\) is an integer and \(100<n<200\)" so \(n\) can not be zero.

Why not 90 in statement 2?

Cheers!
J

Because we are told that 100 < n <200, 90 is not in the range.

If n is an integer and 100 < n < 200, what is the value of n?

(1) n/36 is an odd integer.
(2) n/45 is an even integer.

Prompt analysis
n is an integer between 100 and 200.

Superset
The value of n will be an integer between 100 and 200

Translation
In order to find the value of n, we need:
1# exact value of n
2# an equation to find the value of n
3# any property to find the value of n

Statement analysis
St 1: 36*3 = 108, 36*5 = 180. so two possibilities. INSUFFICIENT
St 2: 45*4 = 180. one possibility. ANSWER

Option B

St.1: 36=2*2*3*3, so all multiples of 36 will be even. INSUFF

St.2: 45=5*3*3, multiple is even, only chance if the multiple ends 0 (divisible by 5). It can be 90,180 etc. SUFF

B

Statement (1) \(\frac{n}{36}\) is an odd integer.

36 = 2*2*3*3

The smallest Odd number it can be multiplied with, so that the product is greater than 100 but less than 200 is 3

i. 36 * 3 = 108

The next odd number is 5

ii. 36 * 5 = 180

Multiplying with any other odd number will make the product greater than 200. As we see there are two options, this statement is not sufficient.


Statement (2) \(\frac{n}{45}\) is an even integer

45 = 3*3*5

The smallest even number it can be multiplied with, so that the product is greater than 100 but less than 200 is 4

i. 45 * 4 = 180

The next even number is 6, but the product is greater than 200, hence this is not an option. So we see only one option is applicable here and that is 4.

This statement is sufficient.

Answer is B

It's a very simple question.
Given : 100<n<200
DS : value of n

Statement 1 : Let take odd multiple of 36. They are 36, 108, 180 .... So , 108, 180 lies between 100 and 200
NOT SUFFICIENT

Statement 2 : Let take even multiples of 45. They are 90, 180, ....... So only 180 lies between 100 and 200
SUFFICIENT

Answer B

OA: B

Given : \(n\) is an integer and \(100 < n <200\)

(1) \(\frac{n}{36}\) is an odd integer.

\(n\) can be \(108 \quad(36*3)\) or \(180 \quad(36*5)\)

As there is no unique value of \(n\),Statement 1 alone is insufficient.

(2)\(\frac{n}{45}\) is an even integer.

\(n\) is \(180\quad(45*4)\).

Statement 2 alone is sufficient.

St 2 is sufficient because we get a unique value of n, i.e. 180. Since 180/45 = 4. There isn't any other value of n which is between 100 and 200 and satisfies this condition in St 2 except for 180.

Correct ans is B.

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