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01 Jul 2023, 07:28
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Hi all,
I stumbled upon this question on a forum :
A retailer sells only radios and clocks. If there are currently exactly 42 total items in inventory, how many of them are radios?
(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
My solution was:
Statement 1 is insufficient. So I'm ruling out A and D. So it's either B, C or E.
Statement 2 : I translated it as 'the number of clocks is twice as many as radios' C = 2R
R+ C = 42,
Since C= 2R
R+2R = 42
R = 14, so C = 28.
So my answer choice was Statement 2 alone is sufficient, so choice B. However, the actual solution was different. I wasn't able to understand since right from translating statement number 2, I've made a mistake. It would be really helpful if someone can help me understand this, thank you so much!
Actual solution:
Translate the two equations:
c + r = 42
2c = r
Be careful with your translation! There are more radios than clocks, so multiply the lesser value (clocks) by 2 in order to get the greater value (radios). Next, substitute:
c + 2c = 42
3c = 42
c = 14
2c = r = 28
So there would be 28 radios and 14 clocks if there were exactly twice as many radios. But the second statement actually says that there are less than twice as many radios as clocks. It's possible that there are 27 radios (and therefore 15 clocks), but it's not possible that there are 28 (or more) radios. According to statement (2), the maximum number of radios is 27, but there could also be 26 radios (or 25, or ...). Since there are multiple possible values for the number of radios, this statement is not sufficient to answer the question.
(1) AND (2) SUFFICIENT: Put the two statements together. According to the statement (1), there are more than 26 radios—i.e., there are at least 27 radios. According to statement (2), the maximum number of radios is 27. Since there can't be more than 27 radios and there can't be fewer than 27 radios, there must be exactly 27 radios.
The correct answer is (C): Both statements together are sufficient to answer the question, but neither statement works by itself.
I stumbled upon this question on a forum :
A retailer sells only radios and clocks. If there are currently exactly 42 total items in inventory, how many of them are radios?
(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
My solution was:
Statement 1 is insufficient. So I'm ruling out A and D. So it's either B, C or E.
Statement 2 : I translated it as 'the number of clocks is twice as many as radios' C = 2R
R+ C = 42,
Since C= 2R
R+2R = 42
R = 14, so C = 28.
So my answer choice was Statement 2 alone is sufficient, so choice B. However, the actual solution was different. I wasn't able to understand since right from translating statement number 2, I've made a mistake. It would be really helpful if someone can help me understand this, thank you so much!
Actual solution:
Translate the two equations:
c + r = 42
2c = r
Be careful with your translation! There are more radios than clocks, so multiply the lesser value (clocks) by 2 in order to get the greater value (radios). Next, substitute:
c + 2c = 42
3c = 42
c = 14
2c = r = 28
So there would be 28 radios and 14 clocks if there were exactly twice as many radios. But the second statement actually says that there are less than twice as many radios as clocks. It's possible that there are 27 radios (and therefore 15 clocks), but it's not possible that there are 28 (or more) radios. According to statement (2), the maximum number of radios is 27, but there could also be 26 radios (or 25, or ...). Since there are multiple possible values for the number of radios, this statement is not sufficient to answer the question.
(1) AND (2) SUFFICIENT: Put the two statements together. According to the statement (1), there are more than 26 radios—i.e., there are at least 27 radios. According to statement (2), the maximum number of radios is 27. Since there can't be more than 27 radios and there can't be fewer than 27 radios, there must be exactly 27 radios.
The correct answer is (C): Both statements together are sufficient to answer the question, but neither statement works by itself.
01 Jul 2023, 16:58
Kudos
Bookmarks
Hi Kelsier1569.
Let's look at Statement 2.
(2) The retailer has less than twice as many radios as clocks in inventory.
Let's translate it.
Less than: < (This is the part of Statement 2 that you missed.)
Twice as many radios: 2
as clocks: c
So, the retailer has c clocks.
The retailer has < 2c radios.
So,
42 = c + <2c
42 < 3c
Let's look at Statement 2.
(2) The retailer has less than twice as many radios as clocks in inventory.
Let's translate it.
Less than: < (This is the part of Statement 2 that you missed.)
Twice as many radios: 2
as clocks: c
So, the retailer has c clocks.
The retailer has < 2c radios.
So,
42 = c + <2c
42 < 3c
01 Jul 2023, 17:21
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Super! Thank you so much for the crystal clear explanation, Marty!
-Kelsier.
-Kelsier.
