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What is the value of x? [#permalink]
 01 Jan 2011, 01:32
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24% (01:59) correct
75% (00:38) wrong based on 66 sessions
What is the value of x? (1) x^3 is a 2-digit positive odd integer. (2) x^4 is a 2-digit positive odd integer.
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shan123 wrote: What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.
I don't know whether the answer is correct. I got a different one. What is the value of x?Note that we are not told that x is an integer (1) x^3 is a 2-digit positive odd integer --> now, if x is an integer then x=3 as x^3=27 is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if x is not an integer then it can be cube root of any 2-digit positive odd integer, for example if x=\sqrt[3]{11} then x^3=11. Not sufficient. (2) x^4 is a 2-digit positive odd integer --> basically the same here: if x is an integer then x=3 or x=-3 as x^4=81 is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if x is an integer this statement is still insufficient as it gives two values for x: 3 and -3). x also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if x=\sqrt[4]{11} then x^4=11. Not sufficient. (1)+(2) x cannot be an irrational number (so that both x^3 and x^4 to be integers), so x must be 3. Sufficient. Answer: C.
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Bunuel wrote: shan123 wrote: What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.
I don't know whether the answer is correct. I got a different one. What is the value of x?Note that we are not told that x is an integer (1) x^3 is a 2-digit positive odd integer --> now, if x is an integer then x=3 as x^3=27 is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if x is not an integer then it can be cube root of any 2-digit positive odd integer, for example if x=\sqrt[3]{11} then x^3=11. Not sufficient. (2) x^4 is a 2-digit positive odd integer --> basically the same here: if x is an integer then x=3 or x=-3 as x^4=81 is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if x is an integer this statement is still insufficient as it gives two values for x: 3 and -3). x also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if x=\sqrt[4]{11} then x^4=11. Not sufficient. (1)+(2) x can not be an irrational number (so that both x^3 and x^4 to be integers), so x must be 3. Sufficient. Answer: C. Thanks for the answer and detailed explanation.
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Carelessly, I overlooked the possibility that x could be negative. Thanks Bunuel!
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Tricky one, I considered the integer constraint that didn't exist. Must take care with this. Bunuel wrote: shan123 wrote: What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.
I don't know whether the answer is correct. I got a different one. What is the value of x?Note that we are not told that x is an integer (1) x^3 is a 2-digit positive odd integer --> now, if x is an integer then x=3 as x^3=27 is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if x is not an integer then it can be cube root of any 2-digit positive odd integer, for example if x=\sqrt[3]{11} then x^3=11. Not sufficient. (2) x^4 is a 2-digit positive odd integer --> basically the same here: if x is an integer then x=3 or x=-3 as x^4=81 is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if x is an integer this statement is still insufficient as it gives two values for x: 3 and -3). x also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if x=\sqrt[4]{11} then x^4=11. Not sufficient. (1)+(2) x can not be an irrational number (so that both x^3 and x^4 to be integers), so x must be 3. Sufficient. Answer: C. |
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I always forget about radical roots. Thanks for the explanation Bunnel.
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Re: What is the value of x? [#permalink]
05 Jan 2013, 22:47
carcass wrote: What is the value ofx ?
(1) X^3 is a 2-digit positive odd integer.
(2)X^4 is a 2-digit positive odd integer. Hi carcass, Stat 1 : Only 2 digit positive integers for S1 are : x-------- 3 ------ 4 x^3 ----27-----64 Here odd integer is x=3 and x^3 = 27 SUFFICIENT Stat 2 : Only 2 digit positive integers for S2 are : x----------+/-2-------------+/-3 x^3----------16----------81 Here odd integer is x=+/-3 and x^3 = 81 INSUFFICIENT (two values for x) IMO A. But how come C? did i missed out anything?
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Re: What is the value of x? [#permalink]
05 Jan 2013, 22:55
Shanmugam, the problem doesnt explicitly state that x is an integer. It can be fraction. e.g. Choice (A), x can be fraction -> x^3 = 35 i.e. x = \sqrt[3]{35}Similarly Choice (B) alone is not sufficient. Hence (C) is the answer.
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Re: What is the value of x? [#permalink]
05 Jan 2013, 23:42
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Glad that helped. Always watch out for ZIP trap (assuming Zero, Integer, Positive) -> (Make sure to check for 0, factions and negatives) Especially for inequalities, algebraic, number/fraction problems.
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Re: What is the value of x? [#permalink]
06 Jan 2013, 05:47
Sorry Bunuel I do not "visualize" why in C x^3 and x^4cannot be rational numbers aka integers because an irrational can't be at the same time an 2 digits odd number ?' and of course only 3 meets both conditions ?' Can you explain me please ?' Thanks
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Re: What is the value of x? [#permalink]
07 Jan 2013, 04:12
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Re: What is the value of x? [#permalink]
07 Jan 2013, 05:29
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2) Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient But why we C is sufficient ?' why we can not consider the irrational numbers ?? Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly
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Re: What is the value of x? [#permalink]
07 Jan 2013, 06:11
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Re: What is the value of x? [#permalink]
16 Jun 2013, 03:59
Bunuel wrote: carcass wrote: basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)
Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient
But why we C is sufficient ?' why we can not consider the irrational numbers ??
Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3. Hi Bunnel, Still did not get this part: If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3Irrational no cannot be expressed as p/q, where p and q are integers. I made my understand it like this: Their is only 1 number possible whose cube is 27 and only one number has fourth power equal to 81. Which is integer 3. Please explain why have you mentioned it here.
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Re: What is the value of x? [#permalink]
16 Jun 2013, 04:15
cumulonimbus wrote: Bunuel wrote: carcass wrote: basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)
Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient
But why we C is sufficient ?' why we can not consider the irrational numbers ??
Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3. Hi Bunnel, Still did not get this part: If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3Irrational no cannot be expressed as p/q, where p and q are integers. I made my understand it like this: Their is only 1 number possible whose cube is 27 and only one number has fourth power equal to 81. Which is integer 3. Please explain why have you mentioned it here. I don't understand your question. Please elaborate.
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Re: What is the value of x?
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16 Jun 2013, 04:15
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