GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 03:27 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  M32-15

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58430

Show Tags

1 00:00

Difficulty:   25% (medium)

Question Stats: 81% (01:36) correct 19% (00:52) wrong based on 42 sessions

HideShow timer Statistics

If $$x$$ is the tenths digit in the decimal $$9.x5$$, what is the value of $$x$$?

(1) When $$15 - 9.x5$$ is rounded to the nearest tenth, the result is $$5.4$$.

(2) When $$9.x5 – 5$$ is rounded to the nearest tenth, the result is $$4.7$$.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58430

Show Tags

2
1
Official Solution:

If $$x$$ is the tenths digit in the decimal $$9.x5$$, what is the value of $$x$$?

(1) When $$15 - 9.x5$$ is rounded to the nearest tenth, the result is $$5.4$$.

This implies that $$15 - 9.x5$$ must be between $$5.35$$ (inclusive) and $$5.45$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$5.4$$. So, we can write the following inequality:

$$5.35 \leq (15 - 9.x5) < 5.45$$;

Subtract 15 from all parts: $$-9.65 \leq -9.x5 < -9.55$$;

Multiply by -1 and flip the signs: $$9.65 \geq 9.x5 > 9.55$$, which is the same as $$9.55 < 9.x5 \leq 9.65$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

(2) When $$9.x5 – 5$$ is rounded to the nearest tenth, the result is $$4.7$$.

This implies that $$9.x5 – 5$$ must be between $$4.65$$ (inclusive) and $$4.75$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$4.7$$. So, we can write the following inequality:

$$4.65 \leq (9.x5 – 5) < 4.75$$;

Add 5 to all parts: $$9.65 \leq 9.x5 < 9.75$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

_________________
Intern  B
Joined: 01 Jul 2017
Posts: 6

Show Tags

Hi Bunuel,

Please can you tell me if my below approach is correct.

15−9.x5 -->
15.00
- 9.x5
______
5.y5
where y is (9-x).
Given-When 15−9.x515−9.x5 is rounded to the nearest tenth, the result is 5.4-->5.x5=5.35

Thanks,
CP
Manager  G
Joined: 14 Oct 2012
Posts: 160

Show Tags

Bunuel wrote:
Official Solution:

If $$x$$ is the tenths digit in the decimal $$9.x5$$, what is the value of $$x$$?

(1) When $$15 - 9.x5$$ is rounded to the nearest tenth, the result is $$5.4$$.

This implies that $$15 - 9.x5$$ must be between $$5.35$$ (inclusive) and $$5.45$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$5.4$$. So, we can write the following inequality:

$$5.35 \leq (15 - 9.x5) < 5.45$$;

Subtract 15 from all parts: $$-9.65 \leq -9.x5 < -9.55$$;

Multiply by -1 and flip the signs: $$9.65 \geq 9.x5 > 9.55$$, which is the same as $$9.55 < 9.x5 \leq 9.65$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

(2) When $$9.x5 – 5$$ is rounded to the nearest tenth, the result is $$4.7$$.

This implies that $$9.x5 – 5$$ must be between $$4.65$$ (inclusive) and $$4.75$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$4.7$$. So, we can write the following inequality:

$$4.65 \leq (9.x5 – 5) < 4.75$$;

Add 5 to all parts: $$9.65 \leq 9.x5 < 9.75$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

Hello Bunuel
Can you please explain/elaborate as to how you arrived at highlighted statements?
Thanks

This is what i did -
1)
15.00
- 9.x5
5.y5 = 5.4
y = [9 - (x+1)] ; (x+1) because we have 5.x5 ~ 5.4. So whatever value we get would be +1 because of 0.05 - i hope i am clarifying myself....

9 - x - 1 = 4
8 - x = 4
x = 4

2)
9.x5
- 5.00
4.y5 ~ 4.7
y = x+1 = 7
x = 6

Thus D
Please let me know how did you arrived at highlighted portion and what i did was wrong?
Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 58430

Show Tags

manishtank1988 wrote:
Bunuel wrote:
Official Solution:

If $$x$$ is the tenths digit in the decimal $$9.x5$$, what is the value of $$x$$?

(1) When $$15 - 9.x5$$ is rounded to the nearest tenth, the result is $$5.4$$.

This implies that $$15 - 9.x5$$ must be between $$5.35$$ (inclusive) and $$5.45$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$5.4$$. So, we can write the following inequality:

$$5.35 \leq (15 - 9.x5) < 5.45$$;

Subtract 15 from all parts: $$-9.65 \leq -9.x5 < -9.55$$;

Multiply by -1 and flip the signs: $$9.65 \geq 9.x5 > 9.55$$, which is the same as $$9.55 < 9.x5 \leq 9.65$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

(2) When $$9.x5 – 5$$ is rounded to the nearest tenth, the result is $$4.7$$.

This implies that $$9.x5 – 5$$ must be between $$4.65$$ (inclusive) and $$4.75$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$4.7$$. So, we can write the following inequality:

$$4.65 \leq (9.x5 – 5) < 4.75$$;

Add 5 to all parts: $$9.65 \leq 9.x5 < 9.75$$. From this we can deduce that $$x$$ can be only $$6$$. Sufficient.

Hello Bunuel
Can you please explain/elaborate as to how you arrived at highlighted statements?
Thanks

This is what i did -
1)
15.00
- 9.x5
5.y5 = 5.4
y = [9 - (x+1)] ; (x+1) because we have 5.x5 ~ 5.4. So whatever value we get would be +1 because of 0.05 - i hope i am clarifying myself....

9 - x - 1 = 4
8 - x = 4
x = 4

2)
9.x5
- 5.00
4.y5 ~ 4.7
y = x+1 = 7
x = 6

Thus D
Please let me know how did you arrived at highlighted portion and what i did was wrong?
Thanks

Take any number from that range, round it to the nearest tenth and you will be $$5.4$$.
_________________
Intern  B
Joined: 20 Apr 2018
Posts: 31
Location: United States (DC)
GPA: 3.84

Show Tags

Hi Bunuel

I am a bit confused by this explanation. Is there any easier way to deduce this?

I just assumed D because if we know that the hundredths digit ends in a five, then we know we must round the tenth digit up. Thus, we should be able to determine the tenths digit as a result. Is my logic flawed?

Math Expert V
Joined: 02 Sep 2009
Posts: 58430

Show Tags

1
norovers wrote:
Hi Bunuel

I am a bit confused by this explanation. Is there any easier way to deduce this?

I just assumed D because if we know that the hundredths digit ends in a five, then we know we must round the tenth digit up. Thus, we should be able to determine the tenths digit as a result. Is my logic flawed?

This is a tough question and does not have a silver bullet solution. You can check alternative solutions here: https://gmatclub.com/forum/if-x-represe ... 43252.html

Hope it helps.
_________________
Intern  B
Joined: 20 Apr 2018
Posts: 31
Location: United States (DC)
GPA: 3.84

Show Tags

Thanks Bunuel! I think the first response is a very helpful way to go about it.
Manager  S
Joined: 19 Feb 2018
Posts: 92

Show Tags

Bunuel wrote:
manishtank1988 wrote:
Bunuel wrote:
Official Solution:

This implies that $$15 - 9.x5$$ must be between $$5.35$$ (inclusive) and $$5.45$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$5.4$$. So, we can write the following inequality:

Hi Bunuel, can you please help me with the reason for inclusion and exclusion.
thanks.
Math Expert V
Joined: 02 Sep 2009
Posts: 58430

Show Tags

harsh8686 wrote:
Bunuel wrote:
Official Solution:

This implies that $$15 - 9.x5$$ must be between $$5.35$$ (inclusive) and $$5.45$$ (not inclusive). Any number from this range when rounded to the nearest tenth will be $$5.4$$. So, we can write the following inequality:

Hi Bunuel, can you please help me with the reason for inclusion and exclusion.
thanks.

5.35 rounded to the nearest tenth is 5.4 but 5.45 rounded to the nearest tenth is 5.5.

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, ROUND UP the last digit that you keep. If the first dropped digit is 4 or smaller, ROUND DOWN (keep the same) the last digit that you keep.

Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

So, according to the above 8.35y rounded to the nearest tenth will be 8.4 irrespective of the value of y.

For mote on this check the following posts:
Math: Number Theory
Rounding Rules on the GMAT: Slip to the Side and Look for a Five!

3. Fractions, Decimals, Ratios and Proportions

For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________ Re: M32-15   [#permalink] 11 Sep 2018, 05:41
Display posts from previous: Sort by

M32-15

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  