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One of the GMAT Club's best came up with this question for fun. Originally it was at about 800 level but I think this version is close to 750 - would be curious to hear what you think. (I personally had not idea how to tackle it)

If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number (2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y.

(1) X = 0.TBCDBCD 10x = T. BCDBCD ………………………….1 1000(10x) = TBCD. BCDBCD………………2 Deduct 1 from 2: 9990x = TBCD – T x = (TBCD – T)/9990 x = 9115/9990 x = 1823/1998 x = 0.9124124124 Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3. Sufficient

T has 3 distinct factors. T can be 4 ( 4,2,1) OR 9 ( 9,3,1). W+Y+T=10W+Y for 9

SUFFICIENT.

For N=5 , T=0 and B,C,D are not different. 9115/N=0.4 Statement 1 NOT SUFFICIENT.

IMO B.

I also tried to use the value of T we got from (1) ; however it becomes complex. We have to use 2 values of X (0.913 and 0.931) in order to check the value of N.

Could you please explain how this one is D?
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when we divide any integer with the same digit number with all 9s we are sure to get a recurring decimal ex 1/9 = 0.11111111 10/99 = 0.101010101010.... 100/999 = 0.100100100.. 1000/9999 = 0.100010001000....

therefore for 9115/N to be recurring and also < 1, N =9999 and in that case X = 0.911591159115...... and in that case T =9, only problem this is of the form 0.TBCDTBCDTBCD and not 0.TBCDBCD and also B and C are not different since both = 1.....I give up here....somebody show the light please......

(1) X = 0.TBCDBCD 10x = T. BCDBCD ………………………….1 1000(10x) = TBCD. BCDBCD………………2 Deduct 1 from 2: 9990x = TBCD – T x = (TBCD – T)/9990 x = 9115/9990 x = 1823/1998 x = 0.9124124124 Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3. Sufficient
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How can we deduce the second statement from 1st statement.. whats is the approach..

I think the idea is that in Statement (1) that X = 9115/N where N is a whole number, but I am not sure that it works that way now that you are asking. Let me check.
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One of the GMAT Club's best came up with this question for fun. Originally it was at about 800 level but I think this version is close to 750 - would be curious to hear what you think. (I personally had not idea how to tackle it)

If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number (2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y.

(1) X = 0.TBCDBCD 10x = T. BCDBCD ………………………….1 1000(10x) = TBCD. BCDBCD………………2 Deduct 1 from 2: 9990x = TBCD – T x = (TBCD – T)/9990 x = 9115/9990 x = 1823/1998 x = 0.9124124124 Sufficient

(2) T should be 9, only odd with 3 distinct factors: 1, 3 and 9. Sum = 1+3+9 = 13 = 10(1)+3. Sufficient

bb wrote:

Neochronic wrote:

1. x = (TBCD – T)/9990

2. x = 9115/9990

How can we deduce the second statement from 1st statement.. whats is the approach..

I think the idea is that in Statement (1) that X = 9115/N where N is a whole number, but I am not sure that it works that way now that you are asking. Let me check.

IMO, 2 cannot be deduced from 1 above if x = 9115/N is not given.

Since X = 9115/N is given, x should be = 9115/9990. "9115 is/should be (TBCD -T) as given in statement 1 and N has to be 9990 if "TBCD -T = 9115".

Can you elaborate your problem that why 2 cannot be deduced from 1 if x = 9115/N is given in detail?
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How can we deduce the second statement from 1st statement.. whats is the approach..

10000x - 10x = 9990x. With a recurring decimal in the form of 0.TBCDBCD... only the numerator with 9990 as the denominator will consist of the recurring digits (that's not totally correct, there are other possible denominators, but they are irrelevant to a four digit numerator). Statement 1 gives x = 9115/N Therefore, TBCD - T = 9115 is the only possibility.

If X is a repeating decimal = 0.TBCDBCD, where T, B, C, and D are different integers, what is the value of T?

(1) X = 9115/N where N is a whole number (2) T has 3 distinct factors: W, Y and T and the sum of W, Y and T is 10W+Y

From 1: X = 0.TBCDBCD multiply both side by 10 (because ine digit from the decimal is not repeating. 10x = T. BCDBCD ………………………….1 Multiply 10 by 1000 (because 3 digits right to the decimal are repeating) 1000(10x) = TBCD. BCDBCD………………2 Deduct 1 from 2: 9990x = TBCD – T x = (TBCD – T)/9990 Since the neumarator of x is given, (TBCD-T) should be = 9115. With the given information (i.e 0.TBCD in which T is not a repeating but B, C, and D are), the neuramator of x can not be > 9115. So..

x = 9115/9990 x = 1823/1998 x = 0.9124124124 Sufficient

Can anyone show a proper Mathematical proof as to why (1) is sufficient?

TBCD - T is not based in any solid Mathematical framework... You can interpret TCBD as literally T*C*B*D or 10^3*T+10^2*C+10^1*B+10^0*D - 10^0*D...

But I still have no idea in hell how it magically morphs to 9115/X....... Sorry but nobody has provided any concrete Mathematics behind it.
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