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# If x is a positive integer and 4^x – 3 = y, which of the following CAN

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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21 Jun 2018, 23:14
1
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00:00

Difficulty:

5% (low)

Question Stats:

96% (00:54) correct 4% (01:10) wrong based on 440 sessions

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If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

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Posts: 2568
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 02:31
3
2

Solution

Given:
• x is a positive integer
• $$4^x – 3 = y$$

To find:
• From the given options, which one cannot be the value of y

Approach and Working:

Apart from checking with the options, there is one more way of figuring out the correct answer
From the given expression $$4^x – 3 = y$$,
• $$4^x = y + 3$$

Now, for any value of x, $$4^x$$ will always end with either 4 of 6
• Hence, y must be ending with either 1 or 3

From the given options, only option B is not ending with either 1 or 3

Hence, the correct answer is option B.

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##### General Discussion
Intern
Joined: 08 Jul 2017
Posts: 17
Location: Greece
GPA: 3.31
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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21 Jun 2018, 23:26
If x=1: 4^1 - 3 = 1
If x=2: 4^2 - 3 = 13
If x=3: 4^3 - 3 = 61
If x=4: 4^4 - 3 = 253

The only value that y cannot take is 7.

Manager
Joined: 13 Feb 2018
Posts: 154
GMAT 1: 640 Q48 V28
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 00:29
OG 2019? very interesting
Intern
Joined: 03 Aug 2014
Posts: 18
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 01:15
1
1
4x-3 = y => 4x = y+3

This implies that y+3 should be a multiple of 4. Quickly scanning the options reveal that for option B, 7+3 = 10 is not a multiple of 4.

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Joined: 31 Oct 2013
Posts: 1116
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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22 Jun 2018, 01:16
Bunuel wrote:
If x is a positive integer and $$4^x – 3 = y$$, which of the following CANNOT be a value of y ?

A. 1

B. 7

C. 13

D. 61

E. 253

NEW question from GMAT® Official Guide 2019

(PS04797)

Note:

x = positive integer

Given,

$$4^x$$-3=y

we are asked to find out which can't be the value of y. No specific value of x is given.

Trail and error is the way to get the correct answer. Assume the value of x = 1 , 2 , 3 , 4. All the option matches except B.

$$4^1$$-3=1
$$4^2$$-3=13
$$4^3$$-3=61
$$4^4$$-3=253

Thus , B is the correct answer.
Intern
Joined: 20 Oct 2016
Posts: 36
Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN  [#permalink]

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12 Feb 2019, 03:42
https://youtu.be/egh47FplZQg
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Re: If x is a positive integer and 4^x – 3 = y, which of the following CAN   [#permalink] 12 Feb 2019, 03:42
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