Jamboree and GMAT Club Contest: M and N are positive numbers. Is N > 0

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
Lets plug the values.
if M = 0.20
and N = 0.04
then M+N = 0.24. Now if we round 0.24 to tength digit we get 0.20.

if M = 0.20
and N = 0.07
then M+N = 0.27. Now if we round 0.27 to tength digit we get 0.30.

We observe when N > 0.04 then rounding M+N will not produce 'M'. Value of N has to be <=0.04.
Hence answer to the question "is N > 0.06" is "NO". (Definite Answer).
Hence, Sufficiet!

(2) N > 0.04

Here, 0.05, 0.06, 0.07 are all greater than 0.04 and N can take any of these values.

if N = 0.05, N is less than 0.06.
if N = 0.07, N is Greater than 0.06.
Answer is not definite.
Hence, In-sufficient.

Finally Answer to this question is "A".

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04
---------------
(1) The statement implies that M + N is rounded down. Thus, N < 0.05
(2) N could be more or less than 0.06
Answer: A

QUESTION #9:

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04


1:
If M is x.05 then N<0.10
With each additional unit added to the hundredths place of M, the N will come down. It will be the lowest when M=x.04, when N<0.01

Since 0.01<N<0.10, Statement 1 is not sufficient.

2:
N>0.04

Not Sufficient.

1 and 2:
0.04<N<0.10
So, N could take values between 0.04 and 0.06.

Not Sufficient

Answer: E

statement (1) says M + N = M (when rounded to tenth digit)
for example 9.5 + 0.06 = 9.56, when rounding to tenths digit -> 9.6 (which is greater than M)
So, for M+N to be M after rounding to tenth digit. N should be <= 0.04

Answer to the question Is N > 0.06 ... NO
Statement (1) is sufficient
Answer (A)

1. M= 1.1
N= 0.04
Sum= 1.14

If decimal part of N is equal to or greater than .05 , the tenths digit will be rounded to up . That is
1.1+.05 = 1.15 .
Since , the value of M+N rounded to tenths digit is the value of M .
N>0.06 --No
Sufficient.

2. N>.04
Not sufficient. As N can take values such as - .45 , .5 -- less than .06
or N can take values .65 -- greater than .06

Not sufficient

Answer A

A

1. Sufficient
As M+N rounded to tenth digit = M means N<0.05
Thus N>0.06 is No

2. Insufficient
As N>0.04, if it is 0.05 then No
if it is 0.07 then Yes
so 2nd statement not sufficient

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
This means N<.05..suff
(2) N > 0.04
N can be .045 or .055.. giving different answers YES?NO.. insuff
A

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04

(1) We know, when rounded, a digit should increase by 1 if the next (hundredths here) digit is more than 5. So, in case N>0.05, irrespective of the value of M the tenths digit of M+N would increase by 1 when rounded.
e.g. M= 1.00, N =0.06, so, M+N = 1.06 ~ 1.1 (rounded) = M.
So, N can't be >0.05 or N>0.06 is not possible. Sufficient.

(2) We know N > 0.04. N = 0.05 Ans: No. N = 0.07 Ans: Yes. Not Sufficient.

Answer: A.

The question asks whether N>.06?

Statement 1 says When M + N is rounded to tenths digit the value is M

Let try some values of M & N.

M = 5 and N = 0.04. M+N = 5.04 ; So after rounding 5.0 [equals to M and N<.06]
M = 5 and N = 0.05. M+N = 5.05 ; So after rounding 5.1 [NOT equals to M and N<.06]

It's observed that value of N will NOT be N>6 if the rounded to tenths digit of (M + N) is M. sufficient.

Statement 2 says N > 0.04, However no other information is given. So we can't specifically say whether n>.06. It could be N=.05; even N = .07. Dual answer. Insufficient.

So Option (A) wins.

N > 0.06?

St1: M + N = Rounded value of M to its tenth digit.
Let M = 1.45. Rounded value of M = 1.5.
N = 0.01 --> M + N = 1.5; N > 0.06? No
N = 0.09 --> M + N = 1.5; N > 0.06? Yes
Statement 1 alone is not sufficient.

St2: N > 0.04. Clearly not sufficient as we dont know the value of M.

Combining St1 and St2,
M = 1.45 and N = 0.05; M + N = 1.5; N > 0.06? No
M = 1.45 and N = 0.07; M + N = 1.5; N > 0.06? Yes
Not sufficient.

Answer: E

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04

Question is straightforward: Is N > 0.06

Statement 1: When M+N is rounded to tenths digit the value is M
Since rounding to the tenths digit results in M, M should have the tenths digit as the last significant number, e.g. 0.4, 2.5, etc. and rounding N to the tenths digit should result in 0.0
Now, because rounding numbers from 0.00 to 0.04999999... to the tenths digit = 0.0, we know that N < 0.05
Therefore, SUFFICIENT!

Statement 2: N > 0.04
N could be 0.045 or 0.07
Therefore, INSUFFICIENT!

Answer: A

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04

ANS:A
This is a DS question with direct answer YES or NO option. If from a statement you get only YES or only NO the statement is sufficient.
1. M+N is rounded to tenths digit the value is M-- Tenths digit= 0.VW--V is a tenth digit. Now whatever the value of M you take N is always less than .06.
Because rounding of .06 to tenths digit is .1 , but we are given M+N=M (rounding to tenths digit)
eg. 1.2+.02=1.22=1.2(M), 1.0+.04=1.04=1.0(M), 1.5+.04=1.54=1.5(M) So in every case we get NO as answer to the given question Is N>.06 statement is sufficient

2. N>.04 --- This statement gives YES and NO both as answer to the question Is N>.06
Taking values If N=.044 then NO but if N=.07 then YES.
Statement is not sufficient

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04


Stmt 1:
(1) When M + N is rounded to tenths digit the value is M
[M+N] = M -> This only means that N<0.1 and any thing added to the hundeths place of M did not result in rounding off to produce a number which has tenths place of the result greater than tenths place of M.
Hence N<0.05 -> sufficient

Stmt 2:
(2) N > 0.04

This does not provide any useful information on the value of N.
N can be 0.05 or 0.06 or 0.07. -> Hence Insufficient.

Ans: A

I believe it's E

Statement 1: N> .05 or M+N >.05
Statement 2: N> .04 could be .05 or .06

(1) When "M+N" is round to tenths digit, the value is M
=>:
- M has no hundredth digit, which means M is in the form of "a.b" (a and b is digits), and thus:
- "M+ N" must be in the form of "a.bc....", where c is 0,1,2,3, or 4 (so when being round to tenths digit, it becomes "a.b")

=> N is in the form of 0.0c..... (c=0,1,2,3,4) => N <0.06 => A is sufficient

(2)N>0.04: no other clues, so we don't know whether N is bigger than 0.06 or not => B is not sufficient

=> A is the correct answer

M and N are positive numbers. Is N > 0.06?

(1) When M + N is rounded to tenths digit the value is M
(2) N > 0.04

The answer is A.

(1) "When M + N is rounded to tenths digit the value is M" means that N is less than 0.05. Explanation in example:

M can be any number. Let's say 1.2. Then try N as numbers 0.05 and 0.04 to see the rounding effect.
When N=0.05 then M+N will be 1.2+0.05=1.25. Then round to tenth. The result is 1.3 not equal to M or 1.2.
When N=0.04 then M+N will be 1.2+0.04=1.24. Then round to tenth. The result is 1.2 Equal to M or 1.2. So N must be less than 0.04. It is definitely not more than 0.06. Sufficient.

(2) N > 0.04. In this case, N can be 0.07, 0.05, or 0.041. So N may or may not be more than 0.06. Insufficient.

Please refer to the attached file for the solution.







Saunak Dey