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# The sum 7/8+1/9 is between

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 04:53
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Difficulty:

5% (low)

Question Stats:

90% (00:57) correct 10% (01:17) wrong based on 3098 sessions

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The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

Practice Questions
Question: 46
Page: 158
Difficulty: 550

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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 04:53
11
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SOLUTION:

The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2
________________________________

$$\frac{7}{8}+\frac{1}{9}=\frac{63}{72}+\frac{8}{72}=\frac{71}{72}$$.

Now, $$\frac{71}{72}$$ is less but very close to 1, so the answer is B.

Else, one can notice that since $$\frac{1}{9}$$ is less than $$\frac{1}{8}$$, thus $$\frac{7}{8}+\frac{1}{9}$$ is less than 1. Therefore we can eliminate answer choices C, D, and E. Next, since $$\frac{7}{8}>\frac{3}{4}=\frac{6}{8}$$, then answer choice A is also out. So, only answer choice B remains.

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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 05:24
3
7/8 + 1/9 ---> .864+ .11--->.97
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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 05:52
1
7/8 + 1/9 = 71/72, which is surely between 3/4 to 1.

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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 08:54
2
Bunuel wrote:

The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

taking LCM of denominator, the expression becomes
7/8 + 1/9 = (63+8)/72 = 71/72
This is slightly lesser than 1, which satisfies option B

Hence B
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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 10:45
2
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

Practice Questions
Question: 46
Page: 158
Difficulty: 600

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$$\frac{7}{8}+\frac{1}{9}<\frac{7}{8}+\frac{1}{8}=1$$ and $$\frac{7}{8}+\frac{1}{9}>\frac{6}{8}=\frac{3}{4}$$.

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Re: The sum 7/8+1/9 is between  [#permalink]

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24 Sep 2012, 11:44
2
LCM ----> 71/72 we can notice that 72/72 is 1 so 71/72 must be a bit less than 1 but is impossible to be under 3/4 (0.75). Must be between 3/4 and 1. So B
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Re: The sum 7/8+1/9 is between  [#permalink]

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28 Sep 2012, 04:25
2
SOLUTION:

The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2
________________________________

$$\frac{7}{8}+\frac{1}{9}=\frac{63}{72}+\frac{8}{72}=\frac{71}{72}$$.

Now, $$\frac{71}{72}$$ is less but very close to 1, so the answer is B.

Else, one can notice that since $$\frac{1}{9}$$ is less than $$\frac{1}{8}$$, thus $$\frac{7}{8}+\frac{1}{9}$$ is less than 1. Therefore we can eliminate answer choices C, D, and E. Next, since $$\frac{7}{8}>\frac{3}{4}=\frac{6}{8}$$, then answer choice A is also out. So, only answer choice B remains.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: The sum 7/8+1/9 is between  [#permalink]

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27 Dec 2013, 09:00
3
Bunuel wrote:
The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

Practice Questions
Question: 46
Page: 158
Difficulty: 550

If you know how to efficiently convert fractions to decimals, this question is pretty straightforward:

1/8 = 0.125 so 7/8 = 0.875... 1/9 = 0.111111...

So 0.875 + 0.111 = 0.986.. Only B works.
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Re: The sum 7/8+1/9 is between  [#permalink]

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10 Sep 2014, 09:10
Bunuel wrote:
The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

Practice Questions
Question: 46
Page: 158
Difficulty: 550

71/72

approx== 0.9

c,d,e,- greater than 1 .
a- less than .75
hence B
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Is there an easy way to solve this question?  [#permalink]

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30 Aug 2015, 12:45
Is there an easy way to solve this question? The question is # 49 from OG16 and for those who don't have the new OG16, the question is

The sum of 7/8 + 1/9 is between

a.) 1/2 and 3/4
b.) 3/4 and 1
c.) 1 and 5/4
d.) 5/4 and 3/2
e.) 3/2 and 2.

The answer at the back of the OG is given in terms of estimation. Is there any other way of estimating? Probably an easy way? I did find the answer but I took about 3 minutes to answer the question. I am just trying to find a quicker way to solve these type of questions. Also, if you guys could let me know if we have any similar type of questions on GMATCLUB that would be amazing. Thank you so much!!!!!
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Re: Is there an easy way to solve this question?  [#permalink]

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30 Aug 2015, 12:50
ozzykhan wrote:
Is there an easy way to solve this question? The question is # 49 from OG16 and for those who don't have the new OG16, the question is

The sum of 7/8 + 1/9 is between

a.) 1/2 and 3/4
b.) 3/4 and 1
c.) 1 and 5/4
d.) 5/4 and 3/2
e.) 3/2 and 2.

The answer at the back of the OG is given in terms of estimation. Is there any other way of estimating? Probably an easy way? I did find the answer but I took about 3 minutes to answer the question. I am just trying to find a quicker way to solve these type of questions. Also, if you guys could let me know if we have any similar type of questions on GMATCLUB that would be amazing. Thank you so much!!!!!

This question is discussed here: the-sum-7-8-1-9-is-between-139470.html

Hope it helps.

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Re: The sum 7/8+1/9 is between  [#permalink]

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30 Aug 2015, 13:51
3
ozzykhan wrote:
Is there an easy way to solve this question? The question is # 49 from OG16 and for those who don't have the new OG16, the question is

The sum of 7/8 + 1/9 is between

a.) 1/2 and 3/4
b.) 3/4 and 1
c.) 1 and 5/4
d.) 5/4 and 3/2
e.) 3/2 and 2.

The answer at the back of the OG is given in terms of estimation. Is there any other way of estimating? Probably an easy way? I did find the answer but I took about 3 minutes to answer the question. I am just trying to find a quicker way to solve these type of questions. Also, if you guys could let me know if we have any similar type of questions on GMATCLUB that would be amazing. Thank you so much!!!!!

For this question (and most of GMAT Quant question) your first instinct should NEVER be to solve the question by brute force. GMAT questions are subtly disguised problems that will most often have easier answer routes.

In this question you are asked the value of 7/8 + 1/9 = a value very close to 1 + a small value = a value very close to 1 should be the final answer. Precise values: 0.875+0.11111... = 0.986

a.) 1/2 and 3/4. Eliminated as 1/2 = 0.5 and 3/4 = 0.75 . This range is not close to 1.
b.) 3/4 and 1. Keep
c.) 1 and 5/4. Eliminated as this range is >1
d.) 5/4 and 3/2. Eliminated as this range is >1
e.) 3/2 and 2. Eliminated as this range is >1

So you see 1 option is remaining and is thus the correct answer.

Additionally, you must remember the values of common fractions:

1/2 = 0.5
1/3 = 0.33..
1/4 = 0.25
1/5 = 0.20
1/9 = 0.11....
1/10 = 0.10
3/4 = 0.75
1/8 = 0.125 etc

Hope this helps.
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Re: The sum 7/8+1/9 is between  [#permalink]

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10 May 2016, 18:06
1
Attached is a visual that should help. This question is a good example of how you can compare numbers you do know (in this case, the sum of 7/8 and 1/8) to numbers you don't know (the sum of 7/8 and 1/9). I have also attached a geometric example with triangles. We know that a 6/6/6 triangle is 60/60/60 so a 6/6/7 triangle must have a smaller angle than 60 at its base.
Attachments

Screen Shot 2016-05-10 at 5.49.49 PM.png [ 59.54 KiB | Viewed 27852 times ]

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Re: The sum 7/8+1/9 is between  [#permalink]

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30 May 2016, 05:15
Bunuel wrote:
The sum $$\frac{7}{8}+\frac{1}{9}$$ is between

(A) $$\frac{1}{2}$$ and $$\frac{3}{4}$$

(B) $$\frac{3}{4}$$ and 1

(C) 1 and $$1\frac{1}{4}$$

(D) $$1\frac{1}{4}$$ and $$1\frac{1}{2}$$

(E) $$1\frac{1}{2}$$ and 2

Let’s first determine the sum of 7/8 and 1/9.

7/8 + 1/9

Getting a common denominator of 72 gives us:

63/72 + 8/72 =71/72

Notice that 71/72 is just a bit less than 1. This will be useful when analyzing our answer choices.

A) ½ and ¾

Since 3/4 = 54/72, we can see that 71/72 is greater than ¾. Answer choice A is not correct.

B) 3/4 and 1

We see that 71/72 is greater than ¾ and less than 1. Answer choice B is correct. To be certain, let’s check the other answer choices.

C) 1 and 1 1/4

Since 71/72 is less than 1, answer choice C is not correct.

D) 1 1/4 and 1 1/2

Since 71/72 is less than 1, answer choice D is not correct.

E) 1 1/2 and 2

Since 71/72 is less than 1, answer choice E is not correct.

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Re: The sum 7/8+1/9 is between  [#permalink]

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25 Oct 2016, 09:36
$$\frac{7}{8} = 0.875$$
$$\frac{1}{9}= 0.111$$
Sum = 0.986

Only ans choice B fits in
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Re: The sum 7/8+1/9 is between  [#permalink]

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27 Jan 2018, 07:20
1
7/8 +1/9 ==> 71/72 ==> 0.98
hence, B
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Re: The sum 7/8+1/9 is between  [#permalink]

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27 Jan 2019, 14:24
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Re: The sum 7/8+1/9 is between   [#permalink] 27 Jan 2019, 14:24
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