問65
頻出度★★★
“商品値引き”表に示すとおり，値引き率が異なる商品群がある。30 個買ったときに最も合計価格が安いのは，どの ID の商品か。ここで，値引き数量以上の個数を購入した場合に，合計価格に対して値引率で示す値引きが適用されるものとする。 商品値引き
| 商品ID | 単価（円） | 値引き数量（個） | 値引率（%） |
|---|---|---|---|
| 0001 | 30 | 30 | 30 |
| 0002 | 25 | 40 | 40 |
| 0003 | 40 | 20 | 50 |
| 0004 | 35 | 35 | 60 |
平成24年度 秋期 ITパスポート試験 問65
ストラテジ系企業活動 › 業務分析・データ利活用
This question's explanation and your answers so far.
解説
問 65
Incorrectア
0001 has a unit price of 30 yen, and a purchase of 30 units exactly reaches its discount quantity of 30 units, so the discount does apply. However, its discount rate of 30% is the smallest of the four products, and its total price only comes to 30 yen × 30 units = 900 yen with the 30% discount taking effect, 900 × 0.7 = 630 yen. That is 30 yen more than the 600 yen of 0003, so it is not the cheapest. Since there are two products that meet the discount condition, 0001 and 0003, stopping there without calculating the discounted amounts of both leads you to mistake one for the other, and that is the pitfall of this choice.
Incorrectイ
0002 has the cheapest unit price of the four products at 25 yen, but its discount quantity is 40 units, and a purchase of 30 units does not reach it, so no discount applies at all. Its total price stays at 25 yen × 30 units = 750 yen, which is 150 yen more than the 600 yen of 0003. Looking only at the low unit price and forgetting to check the condition for the discount to apply (30 units < 40 units) is the typical wrong answer that results.
- ウ
正解 The correct answer is ウ, 0003. This question can be solved simply by first judging whether the discount applies and then actually calculating and comparing the total price of all four products. Start with the applicability check. The condition is “when the quantity purchased is at or above the discount quantity”, so for a purchase of 30 units only products whose discount quantity is 30 units or less become eligible for the discount. Looking at the table, 0001 (discount quantity 30 units) and 0003 (20 units) meet the condition at 30 units, while 0002 (40 units) and 0004 (35 units) do not reach it at 30 units and stay at list price no matter how large their discount rate is. Next, calculate the total prices. Since total price = unit price × quantity × (1 − discount rate), 0001 is 30 yen × 30 units = 900 yen with the 30% discount taking effect, 900 × 0.7 = 630 yen; 0002 is 25 yen × 30 units = 750 yen (no discount); 0003 is 40 yen × 30 units = 1200 yen with the 50% discount taking effect, 1200 × 0.5 = 600 yen; and 0004 is 35 yen × 30 units = 1050 yen (no discount). Lining them up gives 600 yen (0003) < 630 yen (0001) < 750 yen (0002) < 1050 yen (0004), so the cheapest is 0003 at 600 yen. Even though 0003 has the highest unit price of the four at 40 yen, its discount quantity of 20 units is the loosest, so a purchase of 30 units certainly meets the condition, and on top of that the large discount rate of 50% takes effect, so in actual amount after the discount it overtakes the others and becomes the cheapest. Neither a low unit price nor a high discount rate alone decides the ranking; only a calculation of actual amounts that includes the condition check determines the answer, and that is the heart of this question.
Incorrectエ
0004 has the highest discount rate of the four products at 60% and looks advantageous at first glance, but its discount quantity is 35 units, and a purchase of 30 units does not reach it, so the discount does not apply. Its total price is therefore the list price of 35 yen × 30 units = 1050 yen, the highest of the four products. Being captivated only by the size of the discount-rate figure without checking whether the discount is triggered in the first place is what leads to this choice.
ここがポイント
- Judge whether the discount applies first, and do the amount calculations afterwards — the condition is “quantity purchased ≧ discount quantity”, and a product that does not meet it is calculated at list price no matter how high its discount rate is. For a purchase of 30 units, 0002 (40 units) and 0004 (35 units) fall short of the condition, and only 0001 (30 units) and 0003 (20 units) become eligible. Because the wording is “at or above”, note also that 0001, which matches exactly, does qualify.
- Compare all candidates by actual amount with total price = unit price × quantity × (1 − discount rate) — a single item alone, such as a low unit price (25 yen for 0002) or a high discount rate (60% for 0004), does not decide the ranking. In fact 0003 (40 yen), which has the highest unit price, becomes the cheapest at 600 yen after its discount. Even between products that both meet the condition, you must always calculate the amounts and compare them.
用語