The sum 7/8+1/9 is between

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

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

Answer: 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.

Answer: B.
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\(\frac{7}{8}+\frac{1}{9}<\frac{7}{8}+\frac{1}{8}=1\) and \(\frac{7}{8}+\frac{1}{9}>\frac{6}{8}=\frac{3}{4}\).

Hence, Answer C.
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7/8 + 1/9 ---> .864+ .11--->.97
Answer B

7/8 + 1/9 = 71/72, which is surely between 3/4 to 1.

So the answer choice B.

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

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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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.

71/72

approx== 0.9

c,d,e,- greater than 1 .
a- less than .75
hence B

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.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Topics merged. Please follow forum posting guidelines.

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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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.

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.

The answer is B.
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\(\frac{7}{8} = 0.875\)
\(\frac{1}{9}= 0.111\)
Sum = 0.986

Only ans choice B fits in

7/8 +1/9 ==> 71/72 ==> 0.98
hence, B

7/8 + 1/9 = 71/72

71/72 = 1-1/72

1/72 = 0.01

so, 1-1/72 = 0.99

3/4 < 0.99 < 1 (B)

7/8 = 0.86 , 1/9 = .11
summing up = 0.9 so , we have only one option B

7/8 = 0.86 , 1/9 = .11

summing up = 0.985

close to 1.

See that B is between 0.75 and 1- choose B

I wish all the questions on the gmat were this easy

\(\frac{7}{8} = 0.875 , \frac{1}{8} = 0.125\)

\(\frac{1}{9} = 0.111\)

Thus, \(\frac{7}{8}+\frac{1}{9}\) is \(0.236\), Answer must be (B)
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