When the positive number a is rounded to the nearest tenth GMAT data sufficiency

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

Statement (1) When a is rounded to the nearest integer, the result is less than a.
Statement (2) When b is rounded to the nearest integer, the result is greater than b.

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Solution and Explanation:

Approach Solution 1:
A number is rounded when it is reduced to a specific place value. Drop the excess decimal places, round up the last digit you maintain, and if the first dropped digit is 5 or higher. Round down (maintain the same) the final digit you keep if the initial dropped digit is 4 or less.
To illustrate, round 5.3485 to the closest tenth, which equals 5.3 because the dropped 4 is less than 5, to the nearest hundredth, which equals 5.35 because the dropped 8 is higher than 5, and to the nearest thousandth, which equals 5.349 because the dropped 5 is equal to 5.
Assume a = n.xyz.
Consequently, depending on what y is, b = n.x or n.(x+1).
(For example, 1.382 will round to 1.4 (x becomes x+1), whereas 1.342 will round to 1.3 (x stays the same).
We require knowledge about x's value.
(1) The result is smaller than a when an is rounded to the nearest integer.
Rounding n.xyz results in n.
Its rounding down indicates that x is one of 0/1/2/3/4.
(2) The outcome is bigger than b when b is rounded to the nearest integer.
B = n.(x+1) or n.(n.x)
The tenth digit (x or x+1), in order to round b up, must be one of the numbers 5/6/7/8/9.
There is only one value of x that is valid when using both statements.
That is how the tenths digit of b will result in rounding up since x must be 4, which means x+1 must be 5.
Hence, x = 4.
Correct option: C

Approach Solution 2:
Let's say a = ABC.PQR
The tenth digit of b, which is itself A rounded to tenths, is required for PQR.
Statement 1 effectively states that P must be 0, 1, 2, or 4
But we are unsure of what Q is.
For instance, if a=123.299 and b=123.300,
and b=123.500 if a=123.488 (insufficient)
Statement 2: Because we don't know the exact amount, we can't determine what the tenth digit of B should be.
Combining them results in a very interesting situation where a must have a tenths digit of 0, 1, 2, or 3, and b must have a tenths digit of 5, 6, 7, or 9. However, since b is just a number that has been rounded to the nearest tenth, the only situation where this is true is when a has 4 as its unit digit and b has 5 suffice.
Correct option: C

Approach Solution 3:
By convention, when rounding numbers to the closest integer, we presume that the value 0.5 must be converted to 1.
It's really a matter of tradition, in reality. So that we may handle this issue without creating uncertainty, we explicitly state our convention.)
(1) The tenth digit of A (our FOCUS), or (A rounded to nearest int) A, is less than 5…
Take A = 0.49 (rounded to the nearest integer is 0, which is less than A), and use that answer to calculate answer 4; take A = 0.39 (rounded to the nearest integer is 0, which is less than A), and use that result to calculate answer 3.
(2) (B rounded to closest integer) > B, meaning that B's tenth digit is at least 5.
Take B = 0.6 and round it to the next integer 1, which is greater than B, to get answer 5:: To get answer 6, use A = 0.66 (B = 0.7, rounded up to the nearest integer is 1, which is greater than B).
When we round A to the nearest tenth digit (=B), the tenth digit of this number (B) is not less than 5 (1+2) because we know the tenth digit of A (our Target) is less than 5.
This is sufficient to ensure that the tenth digit of A is 4 (our FOCUS).
Without losing generality, we shall continue to just take into account 0 A 1.
The general case is handled EXACTLY the same manner, where A>0 has any other integer part.
In actuality, A does not satisfy assertion (1) if 0.5 = A 1!
If 0 A 0.4, then B is 0.4 or less and does not satisfy condition (2), then A is not equal to B!
Correct option: C

“When the positive number a is rounded to the nearest tenth GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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