Data Sufficient - Manhattan

[akashkumar1987]

When the positive number a is rounded to the nearest tenth, the result is the number b. What is the tenths digit of a?

(1) When a is rounded to the nearest integer, the result is less than a.

(2) When b is rounded to the nearest integer, the result is greater than b.

Please explain

[Aman verma]

First thing: Please post this question in data sufficiency section.

Now, The question stem mentions that a is a positive number, and it is rounded to tenths so we have a decimal number with atleast two digits in the decimal portion. next the question mentions that the rounding gives us a number b.Now we cannot further assume at this stage. So lets take up the statements one by one:

Statement 1: When a is rounded to nearest integer, the result is less than a, which implies the 10ths digit of a could be any one of the 5 numbers-0,1,2,3,4. Not Sufficient

Statement 2: When b is rounded to nearest integer, the result is greater than b, which implies the 10ths digit of b could be any one of 5,6,7,8,9.Not Sufficient

Now combining the information given in both statements with the information given in the question stem we can deduce that a and b were different numbers so far as the 10ths digit is concerned. This implies that the tenths digit of the original number a was 4 which got rounded up to five to get the number b. So the tenths digit of a is 4. So the answer IMO c

[Aman verma]

Regret there was an error in my calculation, now corrected.

[vikram4689]

(1) When a is rounded to the nearest integer, the result is less than a.
implies that a retains integer part and that TENTHS digit of a can be any digit from 0-4

(2) When b is rounded to the nearest integer, the result is greater than b.
implies that integer part of b is incremented by 1 and that TENTHS digit of b can be any digit from 5-9

Note that, depending on hundredths digit of a, tenths digit of b can be same or different from tenths digit of a. e.g. [a=4.33,b=4.3] [a=4.37,b=4.4].

Above concept is useful for solving this question. since rounding a leads to same integer and rounding b leads to increment in integer by 1, it means that tenths digit of a is 4 and tenths digit of b is 5. Also we can deduce that hundredths digit of a is digit from 5-9

Tenths digit of a is 4. Hence C.

[Ankur87]

can please anyone help me regarding my understanding of this problem:
My approach:
Individually both statements are insufficient.
So,
Combining the statements:
When a is rounded to the nearest integer, the result is less than a.
a = 3.51, 3.52, 3.53, 3.54 is when rounded, the result is less than a i.e 3.5 which is equal to b.

When b is rounded to the nearest integer, the result is greater than b.
b = 3.5 which is when rounded becomes 4--> which is greater than 3.5

So answer is C.
i.e tenths place of a should be 5.
y everybody mentioned it as 4 ??

Help needed..

[GMATGuruNY]

When the positive number a is rounded to the nearest tenth, the result is the number b. What is the tenths digit of a?

(1) When a is rounded to the nearest integer, the result is less than a.

(2) When b is rounded to the nearest integer, the result is greater than b.

Statement 1: When a is rounded to the nearest integer, the result is less than a.
Thus, the tenths digit of a must be LESS THAN 5, so that a rounds DOWN to the nearest integer:
a = X.0, X.1, X.2, X.3, X.4.
Since the tenths digit of a can be different values, INSUFFICIENT.

Statement 2: When b is rounded to the nearest integer, the result is greater than b.
Thus, the tenths digit of b must be GREATER THAN OR EQUAL TO 5, so that b rounds UP to the nearest integer:
b = X.5, X.6, X.7, X.8, X.9.
It's possible that a = X.49, so that a rounded to the nearest tenth yields b = X.5.
It's possible that a = X.59, so that a rounded to the nearest tenth yields b = X.6.
Since the tenths digit of a can be different values, INSUFFICIENT.

Statements combined:
In statement 1, the greatest possible tenths digit for a = X.4.
In statement 2, the least possible tenths digit for b = X.5.
Thus, it must be true that a ≥ X.45, so that a rounded to the nearest tenth yields b = X.5, the least possible value for b.
Thus, the tenths digit of a must be 4.
SUFFICIENT.

The correct answer is C.