If a and b are single-digit positive numbers and a/b is NOT a recurrin

Question

If a and b are single-digit positive numbers and a/b is NOT a recurring decimal, what is the value of a?

(1) -1/3 > -a/b > -4/5
(2) b is equal to the sum of its positive divisors excluding b itself

Bunuel · Accepted Answer

OFFICIAL SOLUTION: If a and b are single-digit positive numbers and a/b is NOT a recurring decimal, what is the value of a? a and b are single-digit positive numbers means that a and b can be 1, 2, 3, 4, 5, 6, 7, 8, or 9. (1) -1/3 > -a/b > -4/5. Simplify by multiplying by -1: 1/3 < a/b < 4/5 Convert to decimals 0.(3) < a/b < 0.8. Since a/b is NOT a recurring decimal, then it can be 0.4 (a = 2, b = 5), 0.5 (a = 1, b = 2), ... Not sufficient. (2) b is equal to the sum of its positive divisors excluding b itself. From single digit numbers only 6 satisfies this condition: 6 = 1 + 2 + 3. Since a/b is NOT a recurring decimal, then a/6 can be 3/6 = 0.5, 6/6 = 1, or 9/6 = 1.5. Not sufficient. (1)+(2) From (2) a/b can be 3/6 = 0.5, 6/6 = 1, or 9/6 = 1.5. Only one of which is between 0.(3) and 0.8, namely 0.5. Sufficient. Answer: C.

NavenRk · Answer

1) Insufficient as there are many possibilities for a & b.

2) We know that b=6 as 6 = 1+2+3 (divisors other than the no itself)

From 1 & 2

b=6 & -0.33 > -a/b > - 0.8 . Hence the only value of 'a' for a terminating decimal can be 3. Ans C

Jackal · Answer

Hello all My attempt: This looks like a very tricky question to me but lets give it a try

Point to note is that the fraction \frac{a}{b} is a terminating decimal meaning that b is of the form 2^x * 5^y where x and y are whole numbers. Also a and b are single digit +ve numbers meaning that a,b={1,2,3...9} Statement 1: \frac{-1}{3} > \frac{-a}{b} > \frac{-4}{5} 0.33<\frac{a}{b}<0.8 Working with b in the form of 2^x * 5^y we have b in the set {2,4,5,8} but we must not forget that this condition of terminating decimal is dependent on the reduced fraction and therefore we will check at the end. So for b=2 we have \frac{a}{b} = \frac{1}{2} falls within 0.33 and 0.8 for b=4 we have \frac{a}{b} = \frac{2}{4} and \frac{3}{4} falls within 0.33 and 0.8 for b=5 we have \frac{a}{b} = \frac{2}{5} and \frac{3}{5} falls within 0.33 and 0.8 for b=8 we have \frac{a}{b} = \frac{3}{8} , \frac{4}{8} , \frac{5}{8} and \frac{6}{8} falls within 0.33 and 0.8 the odd case here is b=6 for b=6 we have \frac{a}{b} = \frac{3}{6} falls within 0.33 and 0.8 Alternatively we can just multiply integers to the fractions to find the reducible forms of the fraction. Thus a={1,2,3,4,5,6} . Hence we cannot solve this from this statement alone. Statement 2: Now the given statement basically means that b is a perfect number. Theory: A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Refer https://en.wikipedia.org/wiki/Perfect_number . First perfect number is 6 and the second is 28 . Now b=6 Thus the terminating fractions which can be formed are \frac{3}{3} , \frac{6}{3} , \frac{9}{3} So a={3,6,9} Hence we cannot find a from this statement alone. Combining the two statements: If we combine the two sets of a from statement 1 and 2 we have only one common solution which is a=3 . Hence solvable. I will go with option C

ak1802 · Answer

Phew, been a while since I looked at a problem and this one was a doozie.

I'm also going with answer C, however my approach involved using the number line and statement 2 before actually comparing "answers".

Statement (1) : plot a number line with -4/5 and -1/3 at each end. You know -a/b will fall somewhere in the range. Alternatively you can multiply by a negative, so you're dealing with positive fractions instead of negatives. Make sure you FLIP the signs if you choose to do this.

Tip - list out some fractions that fall within the range. This helps you get a "feel" for where the answer will lie.

This statement is clearly NS, as you will find multiple fractions that fall into this range.

Statement (2) : B is the sum of its positive factors excluding B itself. The only single digit, positive integer that B can be is 6. This still doesn't tell you A. NS.

St (1) St (2) : combined both statements provide a single, concrete answer for A = 3. With 6 as a denominator the only possible, non-repeating fraction is -3/6.

C. Both statements are sufficient.

sanguine2016 · Answer

My Approach: Given: If a and b are single-digit positive numbers and a/b is NOT a recurring decimal. 1.) -1/3 > -a/b > -4/5 ==> 1/3 < a/b < 4/5 ==>0.3333 < a/b < 0.8 ->Now there are many values of a and b satisfying this inequality, like a/b can be 1/2, 2/4, 3/6, 4/8,2/5, 3/5, 3/4, 2/8, 3/8, 5/8, 6/8. and a can be 1,2,3,4,5 or 6. So, Insufficient. 2.) b is equal to the sum of its positive divisors excluding b itself. so, for b=1,2,3,4,5,7,8,9 this is not possible. Only for b=6, we have divisors as 2,3,1 and 2+3+1=6. So, we have b=6. Again nothing is given about value of a. We can have a = 3 or a=6 or a = 9. So, (2) is also insufficient. Now using both 1 and 2 we get a = 3 answer. So, C.

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If a and b are single-digit positive numbers and a/b is NOT a recurrin

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