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GRE question
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Updated on: 19 Jun 2019, 03:40
Updated on: 19 Jun 2019, 03:40
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Question Stats:
50% (02:40) correct
50% (00:44) wrong based on 6 sessions
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If p = \(10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?
A.28
B.29
C.30
D.31
E.32
A.28
B.29
C.30
D.31
E.32
Originally posted by rahulroy1676 on 19 Jun 2019, 01:58.
Last edited by Carcass on 19 Jun 2019, 03:40, edited 2 times in total.
Last edited by Carcass on 19 Jun 2019, 03:40, edited 2 times in total.
Edited by Carcass
Re: GRE question
[#permalink]
19 Jun 2019, 02:00
19 Jun 2019, 02:00
Since p = 10^x – 6, let’s find the possible values of p by substituting x=1,2, 3…. The idea is to see if there is a pattern in these possible values so that we can find p.
If x = 1, then p = 10 - 6 = 4
If x = 2, then p = 102 - 6 = 100 – 6 = 94
If x = 3, then p = 103 - 6 = 1000 – 6 = 994
See, we have a pattern. Without even solving, you can say that if x = 4, then p will be 9994.
Let’s check
If x = 4, then p = 104 - 6 = 10000 – 4 = 9994.
So, the number p will have 4 in the units digit and (x-1) 9s in the rest of the positions.
The question asks you to find p if the sum of its digits is 274.
For this to be true, the number of 9s in p must be 30 with a 4 in its units place i.e. 274 = 9 x 30 + 4.
Therefore, x = 31. The correct answer is D.
If x = 1, then p = 10 - 6 = 4
If x = 2, then p = 102 - 6 = 100 – 6 = 94
If x = 3, then p = 103 - 6 = 1000 – 6 = 994
See, we have a pattern. Without even solving, you can say that if x = 4, then p will be 9994.
Let’s check
If x = 4, then p = 104 - 6 = 10000 – 4 = 9994.
So, the number p will have 4 in the units digit and (x-1) 9s in the rest of the positions.
The question asks you to find p if the sum of its digits is 274.
For this to be true, the number of 9s in p must be 30 with a 4 in its units place i.e. 274 = 9 x 30 + 4.
Therefore, x = 31. The correct answer is D.
gmatclubot
Re: GRE question [#permalink]
19 Jun 2019, 02:00
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