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# M32-15

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132607 [0], given: 12326

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18 Jul 2017, 04:32
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Difficulty:

25% (medium)

Question Stats:

86% (01:34) correct 14% (00:38) wrong based on 22 sessions

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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 $$4.7$$.
[Reveal] Spoiler: OA

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Kudos [?]: 132607 [0], given: 12326

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132607 [1], given: 12326

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18 Jul 2017, 04:32
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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.

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Kudos [?]: 132607 [1], given: 12326

Intern
Joined: 01 Jul 2017
Posts: 7

Kudos [?]: 0 [0], given: 167

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03 Aug 2017, 19:07
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

Kudos [?]: 0 [0], given: 167

Manager
Joined: 14 Oct 2012
Posts: 182

Kudos [?]: 54 [0], given: 961

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26 Oct 2017, 12:57
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

Kudos [?]: 54 [0], given: 961

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132607 [0], given: 12326

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26 Oct 2017, 21:43
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 $$5.4$$.
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Kudos [?]: 132607 [0], given: 12326

Re: M32-15   [#permalink] 26 Oct 2017, 21:43
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# M32-15

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