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12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate https://gmatclub.com/forum/12daysofchristmasgmatcompetitionday5ifpqareeachgreate404133.html 
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Author:  Bunuel [ 18 Dec 2022, 07:00 ]  
Post subject:  12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate  
12 Days of Christmas GMAT Competition with Lots of Fun If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 II. pq > 1 III. q – p > 1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III

Author:  Suvankar8250 [ 18 Dec 2022, 07:19 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Answer is option A. Only I is true. 
Author:  samagra21 [ 18 Dec 2022, 07:22 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 II. pq > 1 III. q – p > 1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III I) take p=1/2, q=1/3. p/q=1.5>1 (True) II) pq >1 ? product of two proper fraction is always less than 1. (False) III) This will never happen because max val of q is <1, and min val of p is >0. (False) Hence A is the answer 
Author:  TBT [ 18 Dec 2022, 07:23 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Range of p,q is between 0 and 1. Q. asks "may be true" 1. If p=0.9 and =0.1 then yes so b out 2. pq > 1 the product of 2 no.s between this range will always be <1 . Try the same no's as 1 C,E out 3. q – p > 1 If all the no's are <1 then how can the difference be >1? You can try some no and check D out Ans: A 
Author:  wadhwakaran [ 18 Dec 2022, 07:27 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
0<p<1 0<q<1 product of any two numbers less than 1 can never be greater than 1. Therefore, statement II is definitely false. 0.99999........9 will be the greatest number which is less than 1 and when you subtract anything (greater than 0) from it. You can never get a number greater than or equal to 1. Therefore, statement III is definitely false.\ Statement I can be or cannot be true depending on the value of p & q p=1/2 and q=1/4;p/q=2 p=1/4 and q=1/2;p/q=1/2 Therefore, option A 
Author:  Kinshook [ 18 Dec 2022, 07:29 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Asked: If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 : If p=1/2 ; q = 1/3; p/q = 3/2 >1: MAY BE TRUE II. pq > 1 : 0<p<1 ; 0<q<1; 0<pq<1: NEVER TRUE III. q – p > 1 : 0<q<1: 1<p<0; 1<qp<1: NEVER TRUE A. I only B. II only C. I and II only D. I and III only E. I, II, and III IMO A 
Author:  Sarmadk5 [ 18 Dec 2022, 07:31 ]  
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate  
Bunuel wrote: 12 Days of Christmas GMAT Competition with Lots of Fun If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 II. pq > 1 III. q – p > 1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III
Only possible is I. II.. multiplication of below 1 will always result in less than 1. III... Subtraction of less than 1 amounts/ numbers will answer in less than . Answer is I as only Denominator lower than numerator will give results more than 1 if both numerator and denominator are between 0 and 1 . It satisfies the given . Posted from my mobile device 
Author:  Catman [ 18 Dec 2022, 07:33 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
I. p/q > 1 Possible for value of p=0.6 and q=0.2 II. pq > 1 Not possible p can have value as 0.9 and q as 0.8 product is 0.72 III. q – p > 1 Difference of number p,q in the range 0<p,q<1 will always be less than 1. IMO A. 
Author:  Archit3110 [ 18 Dec 2022, 07:36 ]  
Post subject:  12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate  
from given info we have following possibilities 0<p < q <1 or 0<q<p<1 1/2 , 1/3 can be used to test values which of following may be true I. p/q > 1 1/3 / 1/2 ; NO 1/2 / 1/3 ; yes II. pq > 1 1/3 * 1/2 ; 1/6 <1 not possible III. q – p > 1 1/31/2 ; (1/6) 1/21/3 ; ( 1/6) not possible I only OPTION A Bunuel wrote: 12 Days of Christmas GMAT Competition with Lots of Fun
If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 II. pq > 1 III. q – p > 1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III

Author:  Elite097 [ 18 Dec 2022, 07:50 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
I. p/q > 1 Yes if p=1/2 and q=1/4 II. pq > 1 No since fractions are proper fractions III. q – p > 1 No as the distance can never be > 1 as they are both b/w 0 and 1 Ans A 
Author:  sivatx2 [ 18 Dec 2022, 07:51 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
We know both p and q is a fraction whose value is between 0 and 1. We need to identify at least for some cases, if option I, II, and III are true. I. p/q > 1 Let p = 1/2 and q = 1/4. Then p/q = 2. For the above example p/q > 1. So keep options that include I. So, eliminate B. II. pq > 1 Multiplying 2 fractions both 0<p,q < 1, can only diminish the product result. Say both p=q= 9/10 = 0.9 Product = pxq = (9/10) *(9/10) = 81/100 = 0.81. 0.81< 0.9, proves that the product will diminishes the value further as both are less than 1 and greater than zero. Eliminate choices that have option II. So, B, C, E is gone, and only A and D remains. III. q – p > 1 Even if we assume q is larger than p, substraction will result in diminishing the number. Example, let's assume q = 9/10 and p = 1/10. qp = 8/10. So, never the result will be greater than 1. Eliminate options that include III. D is gone. So, the best answer choice is A. 
Author:  szcz [ 18 Dec 2022, 07:58 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Qp<1 since qmax=1 and pmin=0 Let p=.75 and q=.25. p/q=3 Pq<1 Hence answer is A Posted from my mobile device 
Author:  akhtolkhyn [ 18 Dec 2022, 08:01 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Let's suppose p=0.8 q=0.5 I. 0.8/0.5>1 II. 0.8*0.5<1 III. 0.50.8<1 So A must be true. 
Author:  thisisit25 [ 18 Dec 2022, 08:09 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 Possible. p = 0.3, q = 0.2 p/q = 3/2 = 1.5 > 1 II. pq > 1 Never. 0 < p < 1 and 0 < q < 1. eg: p = 0.99999999, q = 0.99999999 would still not make pq > 1 III. q – p > 1 Not possible. Take close to largest value for q = 0.9999999999 and close to smallest for p = 0.0000000000001 If you subtract, the difference is still not greater than 1 because q itself is smaller than 1 and p is greater than 0. Answer: A. Only I 
Author:  Lizaza [ 18 Dec 2022, 08:15 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
This task is rather straightforward  we need to deal with the options one by one. I. Whenever \(p>q\), we will always get \(\frac{p}{q}>1\) For instance, \(\frac{0.8}{0.5} = 1.6\) Therefore, option I may be true. II. We have two decimals below 1. And when we multiply any number by a decimal less than 1, we always decrease this number, no exceptions: for instance, \(10*0.9=9\), where (obviously) \(9<10\). Therefore, by multiplying one number below 1 by another similar number will only further decrease the first multiple. That is to say, it is impossible to go beyond 1 by multiplying two number less than 1. Thus, option II may not be true. III. To see the solution to this option, let's compare the new data to the original task: We know that \(q<1\). Now we are told that \(qp>1\), or \(q>1+p\). Can this inequality be true? \(1+p < q < 1\) Of course not, unless P is negative (which is not the case). Therefore, option III may not be true. So, the answer is A. I only. 
Author:  nikhil553 [ 18 Dec 2022, 08:21 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
I. p/q > 1 when p=1/2 and q=1/4 p/q=2 so its true II. pq > 1 not true p=0.99 & q=0.99 pq<1 III. q – p > 1 since both q&P less than 1 & higher than 0 this case is also not true so And A. I only 
Author:  kavitaverma [ 18 Dec 2022, 08:26 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 II. pq > 1 III. q – p > 1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III  IMO A p/q >1 , eg  p=3/5, q=2/7, p/q = 21/10 pq cannot be greater than 1 as the numerator in both the cases are less than the denominator. so their product will also be less than 1 q  p cannot be greater than 1 as both the numbers are less than 1 and their difference can either be another fraction or a negative number. 
Author:  kratos0906 [ 18 Dec 2022, 08:41 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
I Let, p=0.5 , q=0.25 so, p/q=2>1. Hence, I may be true. II When two numbers between 0 and 1 are multiplied the result will always be a number between 0 and 1. III Difference between two numbers between 0 and 1 will always be a number between 0 and 1. Hence, IMO A. 
Author:  GauthamManoj [ 18 Dec 2022, 08:56 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
Given that 0<p<1 and 0<q<1 Option 1 p/q >1 If p = 0.5 and q = 0.1 p/q = 5, >1 This may be possible Option 2 pq > 1 Let us consider the largest value possible for both p and q to get the maximum value for the product p = q = 0.999 (cannot be negative) pq = 0.998.. <1 Will never be>1 Option 3 p  q >1 Even this is impossible Consider the maximum value for P and the minimum value for q (q cannot be negative) p = 0.999 and q = 0.001 even the pq not > 1 I only 
Author:  neetib [ 18 Dec 2022, 09:03 ] 
Post subject:  Re: 12 Days of Christmas GMAT Competition  Day 5: If p, q are each greate 
If p, q are each greater than 0 but less than 1, which of the following may be true? I. p/q > 1 valid when p=.2 and q=.1 II. pq > 1 cant possible since multiplication will bring a lower value III. q – p > 1 this is also not possible oa:A 
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